Modeling of Traffic on Fairways Optimizing the Allocation of Traffic

MODELING OF TRAFFIC ON FAIRWAYS OPTIMIZING THE ALLOCATION OF TRAFFIC

Quirine de Kloet

in partial fulﬁllment of the requirements for the degree of

Master of Science in Applied Mathematics

at the Delft University of Technology, to be defended publicly on 9th of December 2016.

Student number: 4148517 Specialisation: Computational Science and Engineering Faculty: EEMCS

An electronic version of this thesis is available at http://repository.tudelft.nl/.

PREFACE

As the last element of my masters in Applied Mathematics I have completed my graduation project at Rijk- swaterstaat. This is the executive agency of the Ministry of Infrastructure and the Environment; this agency works on keeping the Netherlands safe, habitable and accessible. In order to reach this goal Rijkswaterstaat manages and develops the main road network, the main fairway network and the main water system in the Netherlands.[1]

While there has been a lot of research into traffic on roads, traffic on fairways has been largely neglected. Within the Netherlands there are 3431 kilometers of inland fairways while there are only 3058 kilometers of highway. This is not even taking into account the 3523 kilometers of maritime routes on the North Sea, Wadden Sea and IJselmeer.[1] When one six barge convoy is used (a ship pushing six barges) this saves 660 trucks traveling on the road. Optimizing the use of fairways can diminish the traffic jams on roads. In order to give the fairways their much deserved research I have dedicated my graduation project to investigating the traffic on fairways. After a broad investigation of fairways and fairway traffic the subject of my thesis was specified to modeling fairway traffic. I am glad to have been able to do my graduation project investigating such an interesting topic.

I would like to thank my daily supervisor Krystyna Robaczewska for all the help and guidance she has given me during this project. I would also like to thank my academic supervisors Arnold Heemink and Jacob van der Woude for making it possible to complete my graduation project at Rijkswaterstaat. My gratitude goes to everyone at Rijkswaterstaat who helped me improve my knowledge about fairways, the trafﬁc on fairways and who were always open to discus my project. Without these people it would not have been possible to determine a model that comes this close to the situation observed in reality.

Quirine de Kloet, December 2, 2016

Academic Supervisors: Prof.dr.ir. A.W. Heemink Dr. J.W. van der Woude Company Supervisor: Drs. K. Robaczewska

Thesis committee: Prof.dr.ir. A.W. Heemink TU Delft, EEMCS (DIAM) Dr. J.W. van der Woude TU Delft, EEMCS (DIAM) Dr. M. Snelder TU Delft, CEG (Transport & Planning) Drs. K. Robaczewska Ministerie I&M, Rijkswaterstaat (CIV) Ir. L. Kuiters Ministerie I&M, Rijkswaterstaat (WVL)

iii

ABSTRACT

There has been a lot of research done into traffic on roads and multiple traffic models have been set up for this type of traffic. A subject that has been largely neglected is the traffic on fairways. The research goal set for my graduation project is to define a model that can simulate the traffic on fairways and use this model to optimize the allocation of this traffic. To achieve this the existing traffic models have been investigated. This way a model was found that could be extended to fairway traffic, the mesoscopic model. Within the mesoscopic model there is a possibility to incorporate a more detailed microscopic model for the objects (locks and bridges). Several microscopic models were defined for the locks and bridges. Optimization models were set up based on previous work done into lock modeling. However, optimization models cannot include all rules used in reality; this makes heuristic models more efficient. For bridges the optimization model can be defined starting from the lock optimization. This optimization model can determine what the best time to open a bridge is. In the case of bridges the situation decides which model is best to use. When no information is available, the best result comes from an optimization model. Some bridges have fixed opening times; simply using this schedule gives the same result in less time.

The mesoscopic model was implemented on a practical case in Zeeland. Using this model it is possible to gain insight into several elements:

• Give a value to the efﬁcient use of objects when trafﬁc is spread over the day and night equally.

• Effect of different situations that can occur when maintenance reduces the capacity of the network.

• Effect of stimulating skippers to travel at a time when there is less trafﬁc, optimizing the allocation of trafﬁc.

CONTENTS

Preface iii Abstract v List of Figures xi List of Tables xiii

I Introduction 1 1 Introduction 3 1.1 Motivation of the project...... 3 1.2 Research objective...... 4 1.3 Structure...... 4 2 Previous work 5 2.1 Traffic models...... 5 2.1.1 Microscopic models...... 5 2.1.2 Macroscopic models...... 5 2.1.3 Mesoscopic model for road traffic...... 5 2.1.4 Railway traffic...... 6 2.2 Lock scheduling process...... 6 2.2.1 Double optimization...... 6 2.3 SIVAK...... 7 2.4 IVS90...... 7 2.5 VCM Traffic-planner...... 7 2.5.1 Lock scheduling method...... 7 2.5.2 Estimating traffic...... 7 2.5.3 Travel times...... 8 2.6 Usability in this project...... 8 2.6.1 Traffic models...... 8 2.6.2 Lock scheduling process...... 8 2.6.3 VCM traffic-planner...... 8 2.6.4 Research objective...... 9

II Model design 11 3 Modeling aspects 13 3.1 Fairway modeling...... 13 3.2 Ship information...... 14 3.3 Mesoscopic model...... 14 3.3.1 Extending the mesoscopic model to fairway trafﬁc...... 15 4 Object modeling 17 4.1 Different kinds of objects...... 17 4.1.1 Locks...... 17 4.1.2 Bridges...... 18 4.2 Lock model...... 18 4.2.1 Optimization model...... 19 4.2.2 Double optimization model...... 20 4.2.3 Heuristic model - Rules...... 20 4.2.4 Placement heuristic...... 22

vii viii CONTENTS

4.2.5 Dangerous cargo...... 24 4.2.6 Comparison of the models...... 25 4.2.7 Checks added for additional elements...... 26 4.3 Bridge model...... 27 4.3.1 Optimization model...... 27 4.3.2 Schedule model...... 27 4.3.3 Comparison of the models...... 28 5 Routing 29 5.1 Costs at nodes...... 29 5.2 Time dependent routing...... 30 5.3 Rerouting...... 30 5.4 Routing based on reliability...... 31 6 Simulation 33 6.1 Step 1: Pre-processing...... 33 6.2 Step 2: Simulation...... 34 6.2.1 Short edges...... 36 6.3 Step 3: Analysis...... 38 6.4 Step 4: Changing routes or departure time...... 38 6.5 What information to use and to save...... 39

III Practical case 41 7 Practical case - Zeeland 43 7.1 Locks...... 44 7.1.1 Sub-chambers in locks...... 45 7.2 Bridges...... 45 7.3 Expected arrival time...... 46

IV Results 49 8 Basis simulation 51 8.1 Sub-chambers...... 51 8.2 Bridges at locks...... 52 8.3 Dangerous cargo...... 53 8.4 Increasing the amount of ships...... 53 8.4.1 Capacity usage...... 55 9 Maintenance at Kreekrak 57 9.1 Chamber closed completely...... 57 9.2 Short maintenance...... 59 9.3 Different maintenance options...... 63 10 Optimizing the allocation of ships 65 10.1 Basis situation...... 65 10.2 Increased amount of ships...... 66 10.3 Maintenance at Kreekrak...... 67 10.4 Increasing delays...... 67 11 Conclusion 69 11.1 Capacity usage of locks...... 69 11.2 Kreekrak...... 70 11.2.1 Chamber closed the whole day...... 70 11.2.2 Short maintenance...... 70 11.2.3 Different options for maintenance...... 71 11.3 Sub-chambers...... 72 11.4 Optimizing the allocation of ships...... 72 11.5 Contribution...... 73 CONTENTS ix

V Discussion 75

12 Reliability of results 77 12.1 Object models...... 77 12.1.1 Lock model...... 77 12.1.2 Bridge model...... 78 12.2 Dangerous cargo...... 78 12.2.1 Sub-chambers...... 79 12.2.2 Effect of quantity of ships carrying dangerous cargo...... 79 12.3 Bridges at locks...... 79 12.4 Terneuzen...... 79 12.5 Canal through Walcheren...... 80 12.6 Human behaviour...... 80

13 Parameters chosen 81 13.1 Simulation parameters...... 81 13.2 Fairways...... 81 13.3 Locks...... 82 13.4 Bridges...... 82 13.5 Ships...... 82

14 Further research 83 14.1 Reliability...... 83 14.2 Sub-chambers...... 83 14.3 First Come First Serve...... 84 14.4 Tides, currents and water-level...... 84 14.5 Human behaviour...... 84 14.6 Waiting berth...... 85 14.7 Recreational trafﬁc...... 85 14.8 Extending the model...... 86

VI Appendices 87

A Terms 89 A.1 Speciﬁc terms...... 89 A.2 Abbreviations...... 91

B Parameters for the practical case 93 B.1 Simulation parameters...... 93 B.2 Fairways...... 94 B.3 Lock sizes...... 95 B.4 Bridge dimensions...... 97 B.4.1 Scheduled opening times of the bridges...... 97 B.4.2 Bridges located at locks...... 98 B.5 Ships...... 99 B.5.1 Ships on routes...... 99 B.5.2 Dangerous cargo...... 99 B.6 Ships allowed on routes...... 100

C Object models details 101 C.1 Locks...... 101 C.1.1 Optimization model...... 101 C.1.2 Double optimization model...... 105 C.2 Bridges...... 105 C.2.1 Optimization model...... 105 x CONTENTS

D Using R 109 D.1 Packages...... 109 D.1.1 Graph algorithms...... 109 D.1.2 Solving MILP...... 109 D.1.3 Importing data...... 109 D.1.4 RNeo4j...... 109 D.1.5 Exporting data...... 110 D.2 Data types...... 110 D.3 Programs written...... 110 D.3.1 Mesoscopic model...... 110 D.3.2 Changing departure time...... 110 D.3.3 Comparing situations...... 110 E CEMT classes 111 F Dangerous cargo 113 Bibliography 115 LISTOF FIGURES

1.1 The fairways in the Netherlands...... 3

3.1 Different types of crossings possible in the mesoscopic model...... 16

4.1 Time needed between two lockages...... 19 4.2 The heuristic method using rules...... 21 4.3 The placement method...... 23 4.4 The skyline in blue...... 23 4.5 Updating the skyline in option 2...... 25

6.1 Explanation of the horizon...... 34 6.2 Steps taken within each time-step...... 35 6.3 Steps taken within each time-step, including short edges...... 37 6.4 Passage time and delay for a lock...... 38

7.1 Picture of the practical case[2]...... 43 7.2 The graph of the practical case including end-points...... 44 7.3 The locks including the number of chambers...... 45

8.1 The delays at Volkerak and Kreekrak with additional ships...... 54 8.2 The delays at Krammer and Hansweert with additional ships...... 55

9.1 Passage time and queues at Kreekrak when divided over day and night...... 58 9.2 Passage time and queues at Kreekrak when more ships are traveling during the day...... 59 9.3 Passage time at Kreekrak without any maintenance...... 59 9.4 Difference in passage time at Kreekrak when ships are divided equally over day and night.... 60 9.5 Difference in passage time at Kreekrak when there are more ships during the day...... 61 9.6 Passage time at Kreekrak without any maintenance...... 61 9.7 Difference in passage time at Kreekrak when ships are divided equally over day and night.... 62 9.8 Difference in passage time at Kreekrak when there are more ships during the day...... 62 9.9 Passage time at Kreekrak without any maintenance...... 63 9.10 Difference in passage time at Kreekrak when ships are divided equally over day and night.... 64 9.11 Difference in passage time at Kreekrak when there are more ships during the day...... 64

11.1 The locks in the mesoscopic model...... 69

A.1 Schematic top view of a lock...... 90

B.1 The network for the practical case including the locks and endpoints...... 100

LISTOF TABLES

7.1 Time needed for passing each lock...... 47 7.2 Time needed for passing each bridge...... 47

9.1 The different maintenance options...... 63

11.1 Increase of ships possible when accepting a 30 minute delay...... 69 11.2 Delays seen at Kreekrak...... 70 11.3 Delays at Kreekrak when chamber closed for 1, 2 and 3 hours...... 70 11.4 Delays at Kreekrak when chamber closed for 2, 4 and 6 hours...... 71 11.5 The different maintenance options...... 71 11.6 Amount of sub-chambers in the Netherlands...... 72

B.1 Simulation parameters used...... 93 B.2 The values for a and b used in the heuristic model of section 4.2.3...... 93 B.3 The values needed for the microscopic bridge models explained in section 4.3...... 94 B.4 Fairways in the practical case...... 95 B.5 Locks in the practical case...... 96 B.6 Time used in the mesoscopic model...... 96 B.7 Merged bridges in the practical case...... 97 B.8 Bridges in the practical case...... 97 B.9 Opening times of the bridges...... 97 B.10 Time needed for passing each bridge...... 98 B.11 Bridges located at the locks...... 98 B.12 Number of ships traveling on each route...... 99 B.13 Percentage of ships in the different categories...... 99

E.1 The already-deﬁned ships including their names and characteristics[3]...... 111 E.2 The classiﬁcation of fairways [4]...... 112

xiii

I INTRODUCTION

1 INTRODUCTION

Over the years there has been a lot of research into transportation networks. However this research mainly focused on railway and highway trafﬁc. A subject that has been largely neglected is transportation over fairways.

1.1.M OTIVATIONOFTHEPROJECT Traffic over fairways doesn’t have the same characteristics as railway or highway traffic, therefore the methods already developed cannot easily be extended to fairway traffic. To model railway traffic, an often-used fact is that there can always be only one train on each segment of a track. The opposite is true in the case of a fairway, most of them are wide enough that multiple ships can Figure 1.1: The fairways in the Netherlands travel beside one another. This makes models developed for railway traffic not immediately applicable for fairway traffic. Unfortunately models developed to simulate vehicle traffic over highways also cannot easily be extended toward modeling traffic on fairways. These models are mostly based on the relation between the density of the cars on the highway and the speed that the cars drive. To get this relation measurements are needed to determine the maximum speed reached on a section of the highway and the maximum density of cars that can be handled on this section. In the case of a fairway it’s not easy to find these parameters. Mainly because this behaviour might only be true for certain objects (bridges and locks); on the fairway itself the amount of traffic almost never comes close to the capacity. Another assumption made in these models is that the cars travel at (approximately) the same speed. However this is not true in the case of traffic over fairways, where fully loaded ships will not be able to reach the same speed as the empty ships. At locks and bridges the passage times will vary between ships as well; the differences between the ships in size and cargo will result in a variety in passage times.

3 4 1.I NTRODUCTION

1.2.R ESEARCHOBJECTIVE The main research objective of this project is: Defining a model that can simulate the traffic on the fairway network. Using this model to determine the optimal allocation of traffic over the fairway network. In order to meet this objective some sub-questions need to be answered. 1. What details does the model need to take into account in order to give relevant information? 2. How do the fairways need to be modeled in order to model the traffic accurately? 3. How detailed do the object models need to be? 4. Which differences in ships need to be taken into account? When a traffic model has been defined there are some results that are interesting to investigate. 5. What route changes can be taken into account? 6. What is the effect of an increase in the amount of traffic? 7. What is the effect of decreasing the capacity of the network?

1.3.S TRUCTURE I Introduction Chapter 1 Introduction of the report. Explanation of the research that has already been done in this ﬁeld, Chapter 2 concluding with the usability of this research in this project. This makes it possible to further detail the research questions. II Model design Introduction of modeling aspects, incorporates the answers of ques- Chapter 3 tions 1, 2 and 4. Explanation of the microscopic models used to simulate the objects Chapter 4 (bridges and locks); answers question 3. Chapter 5 Explains different types of routing Chapter 6 Explanation of the simulation done with the model. III Practical case Chapter 7 Introduces the practical case on which the model has been applied. IV Results Results of the basis simulation, modeling the current situation. This Chapter 8 makes it possible to simulate the effect of increasing the amount of trafﬁc, answering question 6. The results of investigation done into maintenance at the Kreekrak Chapter 9 locks, this answers question 7. Chapter 10 Results of optimizing the allocation of ships, answering question 5. Summation of the simulation conclusions, concludes with an expla- Chapter 11 nation of the contribution reached with this project. V Discussion Chapter 12 Discussion into the reliability of the results. Chapter 13 Discussion of the parameters chosen for the practical case. Chapter 14 Summary of possible further research. VI Appendices Appendix A List of nautical terms and abbreviations used in this project. Appendix B Parameters used in the practical case. Appendix C Details of the object models. The model was programmed in R, some information about the ele- Appendix D ments of R that are used in programming the models. Information about the CEMT classes, it’s not possible to use these Appendix E CEMT-classes when dividing the ships and fairways into group. Appendix F The details of the regulations set for ships carrying dangerous cargo. 2 PREVIOUSWORK

Fairway trafﬁc has not been a heavily investigated topic yet. That doesn’t mean that there has been no investigation of the topic at all, or that there where no publications that could be adapted for fairway trafﬁc. A literature study was done and in this chapter the publications and projects done at Rijkswaterstaat will be described. This information will then be used in specifying research questions formulated in chapter1.

2.1.T RAFFIC MODELS Trafﬁc models are already widely used, most are determined for highway trafﬁc. These models can be divided into two main categories, microscopic and macroscopic models.

2.1.1.M ICROSCOPICMODELS Microscopic models are often based on concepts as the car-following model or on the lane changing model.[5] The traffic on a fairway is not restricted to lanes and other ships can easily be passed in most cases, therefore these concepts are not valid for traffic on fairways. Because of this the microscopic models cannot be extended to model traffic on fairways.

2.1.2.M ACROSCOPICMODELS The macroscopic models are often used for traffic over highways. Instead of modeling all cars separately, they are modelled as a density. If that density is close to or higher than the capacity of the highway, the speed of the cars will decrease (simulating a traffic jam). These models rely heavily on the fact that there is a lot of traffic on the roads, and that these roads have a maximum capacity.[6] In the case of modeling the traffic on the fairways neither of these characteristics is true; thereby these models are unsuitable for modeling traffic on fairways.

2.1.3.M ESOSCOPIC MODEL FOR ROAD TRAFFIC It is possible to use a model that fits between these two extremes, this is a mesoscopic model. This model can describe the traffic on a network of roads, instead of only one road[7,8]. Along the edges of the network used in the model, the behaviour of the cars is assumed to be the same as with the macroscopic model. As more cars use the edge, their speed will decrease. However, when a car reaches the end of the edge it will not immediately exit this edge. In the network, the nodes will be positioned at crossings between the roads. At these crossings a more detailed microscopic model will describe how cars are let through to their next edge. This way a traffic light can be modelled, either using a fixed schedule or a schedule that depends on the amount of traffic. Another part of the model is that when there are delays on a route, a driver might decide to change the route in order to arrive at the destination earlier. By rerouting cars based on the delays that occur in the model, an iterative process is defined. A method is included here to ensure a converging solution.

5 6 2.P REVIOUSWORK

2.1.4.R AILWAY TRAFFIC There are several models for railway traffic. A totally different approach is used in describing railway traffic[9], because only one train can be on a stretch of railway (an edge in the network). This results in blocking times; whenever a train enters a section of the railway no other train is allowed to use this section of the rail until the train has left this section. This approach is useful in the case of railway traffic, but it’s not valid to be used for traffic on fairways. Having one ship enter a section of the fairway will not stop another ship from traveling on the same section of the fairway. Something that is included in these models is a robustness check on the generated timetable. Robustness says something about the effect of small delays on the complete timetable. When small delays do not effect the complete timetable much, then this timetable is called robust. Using random delays a check is made to see if with small changes to the timetable it is possible to make this timetable feasible again. Something similar could be useful to add to any traffic model, this can highlight which schedules (for instance at a lock) are the most reliable, even when taking into account the possibility of delays.

2.2.L OCKSCHEDULINGPROCESS Even though there is not much investigation done into navigating on fairways, the lock scheduling process has been investigated thoroughly. This process determines which ships can be transferred in the same lockage[10,11]. Lock scheduling is a complex process, whenever a ship cannot be locked immediately, it will get a delay passing the lock and therefore a delay in its arrival time at its destination. As all ships have a different shape that is often unknown to lock operators, this exact shape is not taken into account in the scheduling. Instead all ships are scheduled as if their shape would be rectangular, with their given length and width. This means that in basis the lock scheduling problem resembles the 2D bin fitting problem, where the packages with known width and length (the ships) need to be fitted into bins of a known size (the lock). The lock scheduling problem also resembles the job scheduling problem, where jobs with a known arrival time (the ships) need to be processed by a machine (the lock) as efficiently as possible. In the case of multiple chambers (for instance a large and a smaller one, or two of the same size) this would result in a problem similar to the multi-processor scheduling problem. Since the multi-processor scheduling problem and the 2D bin fitting problem are known to be NP-hard, it’s easy to conclude that the ship placement problem is NP-hard as well.1 Even though it might take a long time to calculate the solution, it’spossible to define an exact optimization model (MILP) for both the scheduling part and the placement part of the lock scheduling problem. Similar to the lock scheduling problem the MILP is a NP-hard optimization problem.

The exact optimization method for the placement problem doesn’t necessarily give a good placing for the ships within the lock. The solution that is obtained for the ships might be optimal (meaning that this way the number of ships that fit in each lockage is the highest), but it’s not easy for the lock operator to check if this solution is truly feasible. The unconventional positions obtained from the solution will not automatically be accepted by the skippers. Both a feasibility check by the lock operator and acceptation of the placing by the skippers is needed before executing a lockage. Therefore instead of using the exact optimization technique, the multi-order best fit heuristic can be used to find the ship placement[13]. This heuristic will result in a solution that is almost optimal, but has several advantages over the optimal solution. It results in positions for the ships that are more common, and the total placement is easier to check on feasibility for the lock operator (the lock operator decides which placement will be used). Another advantage of this method is that the calculation time is much lower and doesn’t change over different iterations as the exact (MILP) method does.

2.2.1.D OUBLEOPTIMIZATION For the locks on the Upper Mississippi River a different strategy has been introduced.[14] Instead of allowing ships to pass a lock strictly based on their arrival time a reordering of the ships is allowed. This reordering is structured using a double optimization strategy. The ﬁrst optimization run is used to determine at which time a ship is locked when no reordering is allowed (also called a First Come First Serve rule). In the second

1Different complexity classes for optimization problems: [12] P – A problem for which there exists a polynomial time algorithm NP – A problem for which there exists a polynomial time algorithm that can determine feasibility NP-complete – A problem that is NP and at least as hard as any known NP problem NP-hard – A problem that is not necessarily NP and at least as hard as any NP problem 2.3. SIVAK 7 optimization this order is not required any more. Instead a restriction is set on how much later a ship is allowed to be locked compared to the situation without reordering. This way a more optimal schedule can be found by altering the ordering of the ships, while limiting the additional delays that ships can obtain from changing the order.

2.3. SIVAK A simulation model has been built (SIVAK: SImulatie VAarwegen en Kunstwerken); this model is still used in Rijkswaterstaat. SIVAK uses an event based simulation where different processes are set for the different actors involved. For instance the lock operator decides when a ship will be locked, whereas the ships themselves have a set speed for traveling between the different objects. The language used for building SIVAK is PROSIM.[15, 16] This model is mainly used in policy research, or for instance when investigating maintenance at speciﬁc locks[17].

2.4. IVS90 Information about ships is recorded within IVS90 (Informatie- en Volgsysteem voor de Scheepvaart), this system reduces the need for repeatedly reporting the same information. The system records information about the ship and the the cargo a ship carries. When this information is needed (for instance at objects) instead of having to report it again, the information is available via IVS90. Some basic trafﬁc modeling is contained in IVS90, average travel times are used to estimate the time a ship will arrive at points further along their journey. That can for instance given an estimation of the trafﬁc that will arrive at a lock. Lock scheduling is recorded within IVS90 as well. However, the lock operator needs to determined the schedule by hand.

2.5.VCMT RAFFIC-PLANNER Within Rijkswaterstaat a project has been done investigating the possibilities to realise a more optimal use of the fairways and to get more effective and efficient services (the project is called VerkeersmanagementCen- trale van Morgen). As a part of this project a traffic planner has been made (denoted as VCM traffic planner) for traffic over the fairways. The planning of routes is combined with the scheduling at objects (for now only locks are taken into account in the planner). For scheduling the lockages an estimated time of arrival (ETA) is set for the objects a ship has to pass; with these ETA’s a schedule can be made at the objects. The source for the ETA’s is in principle the skipper. Way-points including arrival times are used as an input for the model (this input is given by the skipper). Some of the capacity at the locks is saved for those ships that are unknown to the traffic planner (for instance recreational ships). From the documentation of this journey planner the following information can be obtained. [18]

2.5.1.L OCKSCHEDULINGMETHOD The most significant delays are obtained at locks, therefore a lock scheduling method was introduced in the traffic-planner. This method uses a set of rules to decide which ships will use a lockage.[18] To see if these ships can fit into the chamber together the multi-order best fit heuristic explained in section 2.2 is used.

2.5.2.E STIMATING TRAFFIC When the planning horizon of the traffic planner is large it becomes difficult to determine the departure and arrival times of all ships at objects. Some ships might not have been registered yet in the system or have not decided their exact departure time at their starting point at the time the model started. Part of the capacity of the locks is reserved for ships that are not registered in the system. Another solution is used in the traffic planner is used when planning far ahead. Instead of using the interaction between ships to define the travel-time historic data is used. A value is set as a boundary and if the time crosses this boundary, the planning will from there on be done using the historic data instead of the interdependence between ships. This means that the traffic planner uses two separate models to simulate the way the ships move over the network. The simulation used for the first part of the modeling is time-based, while the model in the later time-instances uses event-based simulation. 8 2.P REVIOUSWORK

2.5.3.T RAVEL TIMES A choice needs to be made in how the travel times over the several parts of the network are deﬁned. In the trafﬁc planner the choice is made to use an average over historic data to calculate these times. These travel times are only used in order to decide which route a ship will take. When that route has been determined it’s possible to use a more detailed model to calculate the exact time a ship will arrive at each object. When these arrival times are calculated for all ships, it’s possible to determine the schedules at the objects and thereby the delays that will occur.

2.6.U SABILITYINTHISPROJECT It’s important to determine how this previous research can be used in achieving the research objective. And if the research questions can or need to be reformulated based on the research already done.

2.6.1.T RAFFIC MODELS The amount of traffic on a fairway is much less than the amount of traffic on the highways. Because of the width of the fairways different kinds of traffic with different speeds will not be bothered by each other as much compared to the road traffic. As a result the concepts used in modeling highway traffic are not valid for traffic on fairways. The main concept behind the modeling of railway traffic is that only one train can be on a segment of the track. This is not something that is true in the case of traffic on fairways, as most fairways are wide enough to let multiple ships travel beside one another. In the rare situation that a fairway is too small for ships in different directions to pass each other it would be useful to implement (a part of) this model. However, the mesoscopic model does come close to describing the behaviour of traffic on the fairway. The mesoscopic model depends heavily on the delays that are obtained at crossings, whereas the traffic on a fairway depends heavily on the amount of delays that are obtained at the different objects. Therefore this model will be used as a basis for the model that will be implemented. This model is described in section 3.3.

2.6.2.L OCKSCHEDULINGPROCESS The investigation done into lock scheduling will be used not only for defining a model for locks, but also for bridges. By removing the placement-part of the lock-model, it becomes suitable for modeling traffic at bridges. Next to the single optimization, the double optimization strategy will be used in defining a model for the locks.

2.6.3.VCM TRAFFIC-PLANNER In the traffic planner information given by the skippers (about the route of a ship) is used to find a schedule at the different locks. As a result the delays that will be obtained can be calculated. However, not all skippers give that information. This can result in a ship ’appearing’ within the model when the ship arrives at a lock, for instance in the case of recreational traffic. Part of the capacity of a lock is reserved for these ships. When ships have AIS (Automatic Identification System) their current position is known. Using this position it is possible to estimate the route the ship will take to the next crossing or lock. Once a ship has reached a lock, it will be added within IVS90 (Informatie- en Volgsysteem voor de Scheepvaart). Using the data in IVS90 and the AIS position the traffic-planner determines the most likely route a ship will take. When several routes between start and endpoint are available, taking a longer route with less delays might result in a ship arriving at its endpoint earlier. Even when this is not the case a skipper might be able to adjust its departure time, based on the expected delays at the locks. This way the ship can avoid the ’rush hour’ at the locks, resulting in less travel time needed. It is interesting to investigate which route is the most reliable, for instance when departing slightly later you don’t want to increase the travel time much. In order to find this route it’s possible to use a robustness- check as was done for the railway schedules.[9]

The traffic planner has been defined for real-time use, it models the traffic 8 hours ahead. This modeling is used for the scheduling at locks and makes it possible to monitor the amount of traffic on a route. A modeling tool has not been defined to simulate the traffic on the fairways without real-time information. When determining this simulation model it is possible to use the knowledge gained from building the traffic planner. 2.6.U SABILITYINTHISPROJECT 9

2.6.4.R ESEARCHOBJECTIVE Now that it’s known what investigation has already been done, it’s possible to further detail the research questions stated in chapter1. The main research objective of this project is:

Defining a model that can simulate the traffic on the fairway network. Using this model to determine the optimal allocation of traffic over the fairway network.

In order to meet this objective some-sub-questions need to be answered.

1. What details does the model need to take into account in order to give relevant information? Besides simulation it’s desirable that the output of the model can be used to gain information about some factors on the network. Interesting factors are the safety values associated with the traffic, the speed of the ships (lack of delays) and the environmental consequences of the traffic.[19] Within this project the focus lays on investigating the delays obtained and the methods that can be used to limit these delays. When the amount of delays decreases fewer ships will be on a part of the fairway; this will lead to fewer dangerous circumstances thereby influencing the safety values as well. More information about the model can be found in chapter3.

2. How do the fairways need to be modeled in order to model the traffic accurately? In order to model the traffic on the fairway, first the fairways themselves need to be modelled. They will be modelled as a directed graph, where both the edges and the nodes can contain costs and constraints. The answer to this question will be further explained in chapter3.

3. How detailed do the object models need to be? Besides the fairways, the different objects (bridges and locks) need to be modelled as well. They can be modelled as a node where trafﬁc is let through according to a schedule, but more accurately would be if this schedule is depending on the amount of trafﬁc that wants to pass the object. This can be done with an optimization based on the research explained in section 2.2, but alternatively you could use a heuristic approach. In chapter4 more details about these object models can be found.

4. Which differences in ships need to be taken into account? Among ships there are a lot of differences in size, cargo and thereby speed. The size of a ship determines which routes a ship can take, therefore several groups will be deﬁned, containing ships that can use the same fairways. Of course each ship has its own origin and destination, possibly the route has been given or it can be determined from the routes the ship is allowed to use. How this is incorporated in the model will be explained in chapter3.

When a trafﬁc model has been deﬁned there are some results that are interesting to investigate.

5. What route changes can be taken into account? Besides simulating trafﬁc with a known route and departure time, it is relevant to look at the effects of giving the resulting information back to a skipper. When a skipper knows when and where there are delays expected, it might be possible to adjust the departure time or even the route in order to avoid arriving at these points at these times. The implementation in the model and the effect of this can be found in chapter 10.

6. What is the effect of an increase in the amount of trafﬁc? It’s important to know how much additional capacity can be found within the network. Therefore it’s important to determine how much the amount of trafﬁc can increase, while keeping the delays within an acceptable level. The results corresponding to this can be found in section 8.4.

7. What is the effect of decreasing the capacity of the network? When maintenance needs to be done on the locks, or when an accident has happened, it might be necessary to close (one of) the chamber(s) of a lock. As a result the capacity of the network will decrease. It’s important to know what the effect is of having fewer chambers available at a lock. It’s interesting is to investigate if there are now more ships (per lockage) locked in the remaining chambers. With this information it is possible to decide what strategy is best to use in case of scheduled maintenance; closing a lock several times for a short period, or closing it once for a longer period. More information about this can be found in chapter9.

II MODELDESIGN

3 MODELINGASPECTS

In chapter2 it is explained that the mesoscopic model comes closest to the situation on the fairways. The original mesoscopic model depends heavily on the delays that are obtained at crossings of roads, whereas the traffic on a fairway depends heavily on the amount of delays that are obtained by passing bridges and locks. Therefore this model will be used as a basis for defining a traffic model on the fairways in section 3.3. In order to apply this model you need to model the fairways themselves first. How this is done can be found in section 3.1. It is important to investigate what information needs to be known about the ships within the model, this can be found in section 3.2. Once these elements have been determined, it is possible to define the mesoscopic model. First the original mesoscopic model is explained, followed by the method used for extending the model to fairway traffic. Within the mesoscopic model it’s possible to use microscopic models to find the best schedule for the locks and bridges. These microscopic models will be further explained in chapter4. Most research done into navigation on fairways is related to the lock scheduling process[13]. Based on this research a microscopic model will be built both for the locks situated in the fairway, and a simplification of this model will be used to simulate the behaviour of ships at moveable bridges situated over the fairways. Besides the optimization models that can find the best schedule to be used at a lock or bridge, it is possible to use a heuristic method. Heuristic methods can find an almost optimal solution using a faster method.

3.1.F AIRWAY MODELING In order to model the traffic on the fairways, first the fairways themselves need to be modelled, this will be done using a directed graph. At the different objects it’s necessary to separate the traffic between the two directions, therefore the ships traveling on the edges should be divided in two directions as well. This makes it possible to give different characteristics to the two directions. This can for instance be useful in the case of strong currents slowing down ships traveling upstream. As a basis edges are defined where there are fairways and nodes are defined where these fairways begin or end and where more than two fairways come together. Such a network of fairways is already available at Rijkswaterstaat and will be modified for the purpose of this project. The network available can display all possible routes a ship can take. However, it doesn’t take into account the objects that a ship encounters along the edges. These objects are added to the graph by defining nodes at their locations. On these nodes some restrictions (for instance on ship size) will be available stating which ships are allowed to pass an object. For each object (a bridge or a lock) a schedule will be needed, stating when and how many ships are allowed to pass the bridge or join a lockage. This schedule can be fixed (e.g. a bridge that opens every 30 minutes), or it can depend on the ships that want to pass an object. It is possible that ships having certain dimensions can pass freely (in the case of a bridge). More information about the object modeling can be found in chapter4. For the fairways (edges in the graphs) some information is needed. Firstly the restrictions on ship size need to be known, such that one can determine which ships are allowed to travel the fairway. Secondly needed is the maximum speed allowed on this part of the fairway and the length of the fairway. In the case that the speed allowed is not uniform over the edge one of the following options needs to be chosen. Either an (weighted) average speed can be used or the edge can be split in multiple pieces such that there is a uniform

13 14 3.M ODELINGASPECTS maximum speed on each edge. Remember that for any fairway, two edges were added to the directed graph (one in either direction). These two edges can have the same characteristics, but it’s possible that there are differences between upstream and downstream navigation.

3.2.S HIPINFORMATION Besides information about the fairways, one needs to know some information about the ships themselves. There are different ships; the size of a ship might restrict the number of fairways it’s allowed to travel on. When using graph algorithms such as the shortest path (to decide the best route to take), any edges that cannot be used need to be removed from the graph. This means that a separate graph needs to be generated for each ship size in order to compute the shortest path for each ship. To simplify this process (i.e. have fewer graphs) it might be possible to separate the different ships into groups, that do not have the exact same size, but do have the same allowed network. Besides this it is possible to include ships in one group that have almost the same network and define one network for these ships. This will result in less groups needed, but the network will be inaccurate for some of the ships. Some balance needs to be found when deciding the number of groups to define. For efficiency purposes the amount of groups should not be too high, but having groups containing lots of different ships will make results inaccurate (because the group a ship is in doesn’t match the exact same network as the ship). Groups defined for ships are already used, these groups have been defined on similar sized ships. These groups, known as CEMT classes, can be found in AppendixE. An advantage of these predefined groups is that all fairways have a known CEMT-class. On a fairway with CEMT-class "X" only vessels with a CEMT-class "X"or a lower CEMT-class are allowed to navigate. Even within a CEMT-class there are still differences between fairways. For instance one fairway might allow slightly larger ships than the other, or a height restriction is set (while on other fairways there might be no limit at all). As a result the exact dimensions allowed on each fairway can even differ within a CEMT-class. Instead of using CEMT-classes groups are defined based on the network investigated (and the different restrictions in dimensions seen within this network). An example of how this is done can be found in appendix B.6. Not all ships travel with the same speed, the speed of a ship depends on the ship itself (for instance it’s construction and the motor(s) it has) and by the amount of cargo the ship is currently carrying. As a result not all ships in one group (CEMT-class or another group) have the same speed. These differences change the travel time of a ship, which is defined as the costs at the different edges, but the structure of the graph can stay the same. As a result only one graph is needed, but with several cost functions. Other differences among the ships should be evaluated to see if they can be dealt with in a similar matter (changing values on the graph, instead of changing the graph itself).

3.3.M ESOSCOPICMODEL Mesoscopic models are those that take some elements from macroscopic models and some elements from microscopic models. An interesting variant is a model based on queuing, because it’s really comparable to the situation on the fairways. First a short description of this model will be given (used for vehicle trafﬁc on a network of roads), before explaining how this model can be extended to fairway trafﬁc.

As a basis for the mesoscopic model, a graph is used displaying the network of roads. For all nodes in the graph a model of how traffic at this node is handled needs to be defined. On any edge traffic speed is determined by the density of cars on the link. However, if the node where the edge ends is not able to handle all traffic, part of the edge will be ’reserved’ for the queue that forms. [7,8] In this model the assumption is made that the nodes are the places where most delays will occur. This is precisely the case when looking at the fairways, as most delays will occur at locks and bridges (these where added as nodes in the graph, see section 3.1). Because the individual vehicles (or ships when extending to fairway traffic) are modelled it’s possible to combine this model with a more detailed microscopic model without having to do additional steps to get the right information (this would be the case when modelling a flow of vehicles/ships). 3.3.M ESOSCOPICMODEL 15

3.3.1.E XTENDING THE MESOSCOPIC MODEL TO FAIRWAY TRAFFIC The original mesoscopic model has been deﬁned for modeling highway trafﬁc. The two main characteristics of this model are:

1. The speed on the highway is depending on the number of vehicles that are on the highway.

2. On the cross sections the trafﬁc might be delayed, for instance in the case of having trafﬁc lights. Re- membering the cross-sections were the nodes of the network; delays are obtained at the nodes.

The first characteristic is not necessarily true on the fairways. The amount of traffic is almost never so high that it’s no longer possible to travel at the highest possible and allowed speed. Therefore the speed is defined based on the ship and the fairway it’s currently on. This is done by taking the minimum of the maximum speed allowed on this part of the fairway and the maximum speed this ship can reach. This makes it possible to include the fact that not all ships can travel with the same speed. The second characteristic is partly true on the fairways. The places where two or more fairways cross each other are large enough that the ships can pass (almost) unhindered by each other. However, in front of objects it is possible a queue can form. In the case of locks it’s almost impossible to have no queues at all, as a ship might arrive at a time when the chamber is available on the other side (the gate on the side of the ship is closed and the gate on the other side is open). When the amount of ships is larger than the amount of ships that can pass within a time period the length of these queues will grow. As ships cannot all fit within the next lockage after they arrive, the ships will suffer an additional delay. By defining nodes at the objects as explained in section 3.1 it’s possible to include the second characteristic. This way delays are obtained at places where nodes are defined, as was the case in the original mesoscopic model. By adding nodes at the locks and bridges it becomes possible to use the mesoscopic model for simulating the navigation of vessels on the fairways.

COMBININGWITHAMICROSCOPICMODEL For some bridges the schedule might already be set; for instance in the case of a railway bridge. There the time instances that the object can be passed by ships are fixed. This schedule can be used as a parameter in the model that decides when traffic can pass the object. Less likely, but possible, is that a lock is operated using such a schedule. This would mean that the time a lockage will be executed is known (for instance every half an hour). When such a schedule is not available, a microscopic model (for instance containing an optimization) is used to decide when lockages take place or ships are allowed to pass the bridge. Based on the ships that want to pass an object (the queue) and a predefined strategy (for instance an optimization), a schedule is determined for the ships. The strategy used will depend on the object and the different strategies will be further explained in chapter4.

EXPECTEDARRIVALTIME In order to use a microscopic model, the ships that want to pass the object need to be known. When an exact arrival time at the lock (or bridge) is not yet known, an expected arrival time is calculated for this ship. These expected arrival times are based on the average time needed to pass each object and the average travel times along the fairways. Whenever the ship has traveled further, the arrival time needs to be updated. For instance because the ship needs less time for passing an object (compared to the average); updating the expected arrival time makes sure that it stays as exact as possible. This expected arrival time will get closer to the true arrival time when the ship is closer to the object. Therefore a horizon is set; only ships expected to arrive within this horizon are taken into account in the microscopic model. For instance only the ships that are expected to arrive within the next hour are taken into account. More information about the horizon and the way it’s used can be found in chapter6. When calculating the expected arrival time at the object there is an average used for those edges and objects that still have to be passed by the ship. This results in costs both on the nodes and the edges of the graph. How to handle the situation with costs at both edges and nodes, is explained in chapter5. More information about how these expected arrival times are calculated for the practical case examined can be found in section 7.3. 16 3.M ODELINGASPECTS

CROSSINGS Crossings (meaning any point where three or more fairways come together) might result in some delays. Compared to the crossings on the roads, the crossings on fairways are wide and the amount of traffic on them is low. Therefore it is possible to model crossings by introducing a fixed delay, instead of modeling exactly how traffic will pass the crossing. In the mesoscopic model there can be nodes at places where only two edges meet, as displayed in figure 3.1. This can indicate that another fairway joins the fairway at this point; a fairway that is not taken into account in the mesoscopic model. This can for instance be done because this fairway is used less than the other two. There is another possibility; remember there are points introduced whenever the specifications of the fairway change. In both cases these points, where two fairways meet, will be modelled similar to the crossings, by setting a fixed delay for ships (that delay is allowed be equal to 0). Setting a fixed delay at these points means that the amount of microscopic models needed within the mesoscopic model decreases, thereby creating more simplicity, and a more rapid calculation. In order to use this simplification it’s assumed that there is a low amount of traffic that passes these points (or that the traffic doesn’t hinder each other). Therefore it should be investigated that the amount of traffic doesn’t grow to the point that modeling is necessary at these points (nodes of the graph).

True crossing Crossing with two incoming edges

Figure 3.1: Different types of crossings possible in the mesoscopic model 4 OBJECTMODELING

The central focus of the project are the delays that are obtained by a ship during it’s journey. For a large part these delays are determined by the objects (locks and bridges) that a ship has to pass. In order to calculate what delays are obtained at an object some planning information needs to be taken into account. This information can be a basic pattern (for instance every 30 minutes the bridge opens and a maximum of 10 ships can pass it), but in reality this schedule will of course be dependent on the ships that are already waiting at the bridge or lock. Once it’s known when a ship will pass a bridge or start a lockage it’s possible to calculate the delay it obtains. The delay of a ship is deﬁned as the time between the arrival of a ship at the object and the time it passes the bridge or starts a lockage. In this chapter the different methods for simulating the processes that occur at both bridges and locks will be described. The different models will be introduced here and a basic explanation of them will be given. There are several methods that can be used for simulating locks and bridges, a comparison will be made in order to determine the best model to use in the simulation. A detailed description of the models used in the simulation is included here. For the models that were not included in the model a more detailed explanation can be found in appendixC.

4.1.D IFFERENT KINDS OF OBJECTS Even though nodes are all the same in a graph, within the network they represent different objects. As a result the traffic will not have the same behaviour at all nodes, therefore different models will be defined. All objects can give a restriction to the size of ships that can pass this object. This restriction is related to the size of the object; the largest ship that can fit within the lock chamber or the largest ship that can fit underneath a bridge. The size of objects and the size of the ships allowed on the fairway are dependent on each other. If there are large ships allowed on a fairway, the objects will allow these large ships as well, and the other way around.

4.1.1.L OCKS The objects that are the most difﬁcult to model, are the locks. A decision needs to be made whether to wait on the next ship, resulting in a delay for the ship(s) already at the lock, or to start the lockage, resulting in a delay for the ship that still needs to arrive. Not only the time element needs to be taken into account, the ships also need to ﬁt in the chamber together. There are several methods that can be used to model the processes that occur at locks, three methods have been implemented. Their explanation and a comparison between these methods can be found in section 4.2. The model used here simulates a complete lock, in which several lockages are simulated. In the case of multiple parallel chambers, lockages in all chambers will be included in the same model.

FIRST COME FIRST SERVE In most situations the First Come First Serve (FCFS) rule is used when scheduling ships to pass a bridge or lock; in the Netherlands this is mandatory. This means that ships will be scheduled in the order they arrive in (for ships traveling in the same direction). For a lock an exception is made when a ship cannot ﬁt into the

17 18 4.O BJECTMODELING remaining space, if that’s the case the ship arriving after it can join the lockage instead (assuming this ship does ﬁt within the lockage). When adding the FCFS constraint to an optimization model it needs to be linear. It’s not possible to add the exception just mentioned to a linear constraint, therefore the exception cannot be included in a linear optimization strategy. This means that the FCFS in the optimization means that a ship in the same direction arriving later, can never be locked earlier. When implementing the FCFS to a heuristic method it is possible to add the exception at the locks.

RULESFORSHIPSCARRYINGDANGEROUSCARGO There are speciﬁc rules set for locking ships carrying dangerous cargo. These ships are not allowed to be in the same lockage as a passenger vessel, and depending on their cargo they might even have to be locked alone. Even when ships carrying dangerous cargo are allowed to be in the same lockage as other ships, additional safety distances need to be kept. [20] These rules and their implementation in the different methods at locks are explained in section 4.2.5.

4.1.2.B RIDGES Bridges are not as complex as locks, as they only contain the time element. A bridge can be fixed or moveable, or a combination of the two (having two parts; one fixed and one moveable). A bridge has a width and height stating which ships can pass. Any ships that fit these two restrictions can pass the bridge (almost) without delay.

MOVEABLEBRIDGES A moveable bridge has two heights, one when it’s closed and one when it’s open. This last height can be infinite, but can be finite (if the bridge limits the height of ships even when it’s open). Depending on the bridge there might be periods when the bridge is not allowed to open. For instance during rush hour on the road, or, in the case of a railway bridge whenever there is a train scheduled. The exact time at which the bridge opens can be set using a fixed schedule, which is explained in section 4.3.2. Another possibility is to find the exact time at which the bridge should open using an optimization (similar to the one used to find the best lock schedule); this method is explained further in section 4.3.1.

FIXEDBRIDGES Fixed bridges, when not combined with a moveable part, deﬁne a maximum height that a ship can have on this part of the fairway. As trafﬁc might have to slow down, and maybe wait on one another, this will result in a slight delay, compared to the situation without bridge. In the mesoscopic model, it is possible to leave this bridge out, and simply add some delay at the edge containing this bridge, or to slightly lower the speed that a ship is allowed to have on the edge. This has as an advantage that the number of edges in the graph will decrease and this results in less calculation time needed for the model.

4.2.L OCKMODEL There are several methods that can be used to model locks, in all models there is a need to include both a time-element (deciding which ships will be in the same lockage and at what time) and a method that can find the placing of the ships within the lock. More important it needs to be determined if there is a placing possible for the ships(within this chamber); do these ships fit in the chamber together? How to use optimization to find the best schedule for traffic passing the lock has already been investigated [10,11, 13]. Based on this documentation a method was defined that will be explained in section 4.2.1. A second method using a double optimization technique has been defined and will be explained in section 4.2.2.[14] A third method was added that doesn’t use an optimization. Instead a number of rules states whether to execute a lockage or to wait until the next ship has arrived; this third method will be explained in section 4.2.3. The differences between these methods are only in the time-element of the schedule. All three use the same method to find the placing of the ships within the chamber; this method will be explained in section 4.2.4. Both within the planning of lockages and in the placement algorithm, there are rules set for ships carrying dangerous cargo. These rules will be further explained in section 4.2.5 along with their implementation in the different models. After the different methods have been explained a comparison will be made in section 4.2.6, detailing the advantages and disadvantages of each method. 4.2.L OCKMODEL 19

4.2.1.O PTIMIZATIONMODEL Most locks will not be operated using a fixed schedule because their operations will depend on the amount of traffic that wants to pass the lock. Therefore an optimization can be used to decide what is the best schedule to use for these locks based on the amount of traffic. In order to use such an optimization scheme, one needs to know what the goal of the optimization is. For instance one could try to minimize the amount of lockages that are needed, or minimize the average waiting time. Most likely a combination of those two will be used. The optimization will be done using a MILP,this means that both the optimization goal and the constraints that have to be satisfied need to be linear functions of the variables used. In this section an overview will be given of the method, whereas details (including the equations used) can be found in appendix C.1.1. The optimization model will only determine which ships will use a lockage, and the time at which this lockage takes place. When there are multiple chambers at a lock the decision of which chamber to use is made within the optimization. For all lockages the placement method that will be explained in section 4.2.4 is called to find a placing for the ships within the lock. This method determines if it is possible to place this combination of ships within the chamber. When this is not possible, constraints are added to make sure these ships will not be placed together in this chamber again and the optimization will be done again.

CONDITIONS First the conditions need to be defined. Only when these conditions are satisfied the resulting solution is deemed feasible. • When a lockage is executed only traffic in one direction is allowed. • The ships have to arrive on time to be allowed to use a lockage (the ships have to arrive before the gate closes). • Of each chamber the direction of the first lockage is known, this direction is not necessarily equal for all chambers. • The next time the chamber executes a lockage it will be in the other direction (with respect to the previous lockage). If there are no ships traveling in this direction an empty lockage (or no lockage) will be executed. • There is a fixed minimum amount of time between two lockages in the same chamber. This time is set based on the time needed for the lockage and the time for ships to enter and leave the lock. See figure 4.1 for an explanation of the time needed between two lockages.

Time between two lockages

Ships leaving Ships entering Locking the lock the lock

Start lockage Start lockage

Figure 4.1: Time needed between two lockages

• There is a maximum percentage of the area inside the chamber that the ships can use. When there are more ships placed in a lockages (thereby increasing this percentage), more time will be needed for ships entering and leaving the lock. This constraint makes sure that there are not too many ships placed within one lockage(now the percentage is set at 80%). • For each ship it’s known which chambers it’s allowed to use. This can be limited for instance due to the dimensions of the ship and the dimensions of the chambers. • A First Come First Serve rule (FCFS) is applied: Ships traveling in the same direction are locked in the order they arrive in (a later arriving ship in the same direction, will never be locked earlier). When not all ships can be ﬁtted in the number of lockages that are scheduled in the optimization; the ships arriving ﬁrst will be scheduled. 20 4.O BJECTMODELING

OPTIMIZATIONGOAL A functions needs to be set deﬁning what should be minimized in the optimization. This will be a weighted average of the following;

• The number of lockages that are used.

• The average time at which the ships are allowed to pass the lock.

• The maximum delay obtained by the ships.

• The number of ships that pass the lock (additional costs are added whenever a ship doesn’t pass the lock).

Depending on the situation the weights used can be set, that will influence the amount of delays that are obtained by the ships. When the most weight is given to the delays, then the delays resulting from the optimization are lower than when most weight is given to the amount of lockages used (for instance because of water saving). There is some overlap between the last three elements in the optimization goal, but they are not exactly equal. Including the average time at which the ships pass the lock is equivalent to including the average delay obtained by ships (the difference between the two is a constant, this only influences the value of the optimization goal, but not the place of the minimum). Equivalent to using this value (the average time the ships are locked) is including the total delays obtained (multiplying the average gives the total delays, again this only influences the value of the optimization goal). When minimizing the average, it can result in one ship having a huge delay. For instance because a lockage starts just before the ship arrives, the ship is left behind to wait for the next lockage. To limit this effect, a maximum delay is added in the optimization goal. This means that a balance is found between minimizing the average delays, without this resulting in huge delays for one (or more) ship(s). In order to limit the delays (both the average and the maximum) the model could choose to not lock some ships. When a ship is not locked, it doesn’t contribute to the delays. In reality this means that the ships are only locked after the lockages (scheduled by the optimization) have taken place. By adding the additional costs for ships that are not locked, ships are only left behind when there is no other choice (as all ships simply do not fit within the lockages that are scheduled in the optimization).

4.2.2.D OUBLEOPTIMIZATIONMODEL Instead of using a single optimization it is possible to use a method with two optimizations.[14] The ﬁrst optimization run is equal to the optimization from section 4.2.1 and is used to determine the time at which a ship is allowed to pass the lock in the situation including all constraints set in the optimization. In the second optimization run the First Come First Serve (FCFS) constraint is removed from the optimization constraints. Instead a new constraint is set for each ship using the times obtained from the ﬁrst optimization. A ship is allowed to be locked earlier than previously calculated (assuming that the ship has arrived of course), but a limit is set to how much later it’s allowed to be locked. This way an optimal schedule can be found by altering the ordering of the ships, while limiting the additional delays that ships can obtain from removing the FCFS rule. More details about this method and the equations used can be found in appendix C.1.2.

4.2.3.H EURISTICMODEL -RULES It’s possible to determine the schedule for a lock based on a set of rules. This schedule might not be optimal, but with this method it’s possible to add the ﬁrst come ﬁrst serve rule as it’s currently used in practice. Some- thing that is impossible to include in both the optimization methods. The rules used in the heuristic model are the following;

• Place a ship in the ﬁrst lockage the ship ﬁts in.

– All rules set for ships carrying dangerous cargo need to be satisﬁed. – This ship and the ships that are already placed in this lockage need to ﬁt in the chamber together. There needs to be a feasible placement found with the model explained in section 4.2.4.

When one of these two constraints is not satisﬁed, the ship is not allowed to join this lockage. 4.2.L OCKMODEL 21

• When a ship is not allowed to join a lockage, the next ship is allowed to join if that ship does satisfy all constraints.

• Once the ﬁrst ship has joined a lockage, only ships that are arriving in the next a minutes are allowed to join.

• Empty lockages are allowed when no ships on current side, and none arriving in the next b minutes.

When no other ships will be joining the lockage; either because of time or placement constraints. Then the lockage will be started immediately.

The values used for a and b are deﬁned for each lock separately, such that the amount of delays is minimized. When locking is not allowed to be done too often (for instance because of the water levels), then these values should be increased to simulate this.

Start Calculate time Any lockages left? and direction for Done no the next lockage yes

Determine Execute an Find ﬁrst lockage partial queue empty lockage

yes Ships arriving in the Ships on other side? next a minutes? no

yes no Skip chamber

A lockage yes Any ships on current no with ships side?

Ships left in partial no Execute the queue? lockage

yes yes

Try to add the ﬁrst ship Any ships exceeding in the partial queue waiting time (b)?

no Ships satisfy rules for dangerous cargo? Remove ship from yes partial queue Feasible placement no possible? Add ship to the lockage yes

Figure 4.2: The heuristic method using rules 22 4.O BJECTMODELING

Before being able to execute the model several values need to be set. A decision needs to be made into how many lockages should be scheduled. In the mesoscopic model two lockages are scheduled in all chambers (if multiple chambers are available at the lock); this makes it possible to take ships in both directions into account. For all chambers the earliest time that the first lockage can be executed needs to be given along with the direction of this lockage. The direction a lockage is in will decide the partial queue; this queue contains all ships that can use this chamber and are traveling in the same direction as the direction of the next lockage in the chamber. Once the exact time of the first lockage is found, adding the needed lockage time gives the minimum time for the next lockage. This lockage will of course be done in the other direction as the first one. An explanation of the algorithm defined with these rules is given in figure 4.2.

4.2.4.P LACEMENTHEURISTIC Besides the time-element of this scheduling problem, it is important to know if the ships can be placed within the chamber together. Instead of finding the exact (optimal) solution, the multi-order best fit heuristic is used. To find a placing several orderings of the ships (arrival time, decreasing width, decreasing length, decreasing area) are used; the ships are placed within the lock in this order. When the resulting placement fits within the lock (both in width and length) this placing is used; otherwise the next ordering will be tried. This heuristic method fails to find a feasible solution when there is one in less than 1% of the cases (note that the method is always used to find a placement using less than 60 ships [13]). When using an optimization model instead of this heuristic method, it is possible to find a feasible solution in this last 1% of the cases. However, the placing found as the result of such an optimization can be more difficult to check on feasibility by the lock operator. The reason for this is that the optimization can return unconventional placings that do satisfy all constraints. This check is needed because the lock operator will ultimately decide the placement used, and can therefore reject the placing given by the model. Another disadvantage is that the calculation time needed is not stable and can be high in some cases. The method, detailed in figure 4.3 tries to place a ship as far in the chamber as possible. To do this a skyline is kept stating the farthest point a new ship can be placed at. An example of how this skyline has been set is given in figure 4.4a. The ships are traveling from top to bottom, and the skyline denotes the place the front of the next ship can be placed (taking into account the safely distances needed between ships). Whenever there is no ship that can be placed in the lowest point of the skyline this point will be increased toward the lowest neighbor as has been done in figure 4.4b.

ORDERING Once the placement is known, now it is possible to find the order in which the ships need to travel into the lock. It would of course be best if the ships can travel into the lock in the order they arrived in. Therefore this is the order that we start with. For every ship (starting with the first) a check is made. If all ships that are placed before it are already in the lock, then it can indeed travel into the lock. If not, this ship is skipped and the next ship is checked, continue checking the ships till one is found that can be placed. Once a ship has been found start from the first ship to arrive again, and continue doing this till all ships have been placed. 4.2.L OCKMODEL 23

Done, return this No feasible placing Start placing found

yes

Is the length used Any orderings left? OK? no no

yes

Order ships by the next ordering

Any ships left that no are not placed?

yes

Find lowest point in the skyline

List the ships Increase to ﬁtting width lowest neighbor

Ships left in the list? Update the skyline no

yes

Try to add the ﬁrst Can the ship dock to yes ship in the list the left side? place the no ship here Remove ship Can the ship dock to from the list no the right side? yes

Figure 4.3: The placement method

lowest point in the skyline

(a) (b)

Figure 4.4: The skyline in blue 24 4.O BJECTMODELING

4.2.5.D ANGEROUSCARGO For ships carrying dangerous cargo on the Dutch fairways rules are given in the ’Binnenvaartpolitiereglement’[21]. These rules are valid for most locks therefore they will be implemented in the mesoscopic model. However, there are some locks where a different set of regulations is valid; more information about these regulations, the similarities and their differences are given in appendixF. There are different kinds of dangerous cargo. Speciﬁc calculations decide in which group a ship falls. As a basis the ships can be separated into the following three groups;1

1. Ships carrying ﬂammable cargo

2. Ships carrying cargo that is can be detrimental to health, these are further separated into two groups

(a) The ship is carrying dry cargo, solely containers, ICB’s, bulk containers, multiple element gas containers (MEGCs), portable tanks or tank containers (b) Any other type of cargo

3. Ships carrying explosive cargo

4. Ships that have a certiﬁcate but are not carrying cargo as explained above.

The ships within the first group are required to carry one cone, the second group is required to carry two, and the third group is required to carry three cones. This is done so that any other ship know that they carry dangerous cargo. When navigating over the fairway, ships have to keep a set distance (50 meter[21]) from ships carrying dangerous cargo. Ships in the fourth group are not required to carry any cones, but can chose to carry one cone anyway. The advantage for this group is that without carrying a cone they can lock as a normal ship and as a ship belonging to group 1. This means that these ships have a higher chance to being allowed in a lockage soon after arriving. Now that the different groups have been defined, the rules that need to be satisfied for all lockages are:[20, 21]

• All ships that fall in groups 3 and 2b have to be locked alone.

• Ships that fall in group 2a can be placed in the same lockage as ships from that same group, group 1 or group 4 (as long as this ship than carries one cone). There needs to be a distance between the ships of at least 10 meter, both in the length and width direction.

• Ships from group 1 cannot be placed in the same lockage as a passenger vessel.2

• All ships have to keep at least a 10 meter distance from ships belonging to group 1, this distance is not needed for other ships belonging to group 1 or ships belonging to group 4.

Note that for all remaining ships (the ’normal’ ones) this means that they are allowed to be locked with all ships not in category 2 or 3.

IMPLEMENTATION Implementing these rules can be done for all models; the optimization model, double optimization model and heuristic model. Before implementing of these rules, they ﬁrst need to be separated into two groups. The ﬁrst group contains rules that decide if ships are allowed to be within the same lockage. The second group contains rules that give additional constraints for the placing of the ships within the chamber. There are three rules that decide if ships are allowed within the same lockage;

• If the lockage contains a ship that is in groups 3 or 2b, then the maximum number of ships allowed in the lockage is one.

1The calculations and the speciﬁc rules that decide in which group a ships falls exactly can be found in BPR[21] and ADN[22]. 2Passenger-vessels are deﬁned as any ship that is allowed to carry twelve passengers.[21] Recreational ships will, depending on their size, be either a passenger-ship (when there are allowed to be twelve passengers or more on the ship), or it will be handled as a ’normal’ ship. This means that in the case of small recreational ships, there is no rule saying they are not allowed to be in the same lockage as ships carrying one cone. This of course doesn’t mean that this is actually done in practice, most likely no recreational ships will be allowed to be in the same lockage as a ship carrying any kind of dangerous cargo. 4.2.L OCKMODEL 25

• It’s not allowed to have both passenger vessels and ships carrying dangerous cargo in one lockage.

• It’s not allowed to have both ships from group 2a and ’normal’ ships in the same lockage.

These rules need to be included in the part of the model that decides which ships will be placed in which lockage. In the optimization models (optimization model from section 4.2.1 and double optimization model from section 4.2.2) there are two methods that can be used to include these rules. It’s possible to add the constraints to the MILP from the start (this method was used when implementing the rules). Another possibility is to do a check after finding an optimal solution and to add constraints only when necessary. When using the heuristic model, these rules are added to check if a ship is allowed to join a lockage or not. Similar to the situation where a ships doesn’t fit within a lockage, when a ship is not allowed to join a lockages because one of these three rules, the next ship is allowed to join the lockage. The rules for ships carrying dangerous cargo result in three possibilities for which a placement strategy needs to be defined. As there are slight differences in the safety distances that need to be satisfied, the placement heuristic is modeled separately for these three options.

1. A lockage which contains at least one ship of group 2a. This means that the only other ship groups allowed are ships of group 1 or 4. In this case there needs to be a distance of 10 meter between all ships, this indicating that ships are not allowed to moor to one another (only to the sides of the the lock).

2. A lockage that contains at least one ship of group 1 and at least one ’normal’ ship. This lockage may contain ships from group 4, for those ships a decision needs to be made if they want to be locked as a ’normal’ ship or as group 1. This separates the ships into two categories (after the ships of group 4 have been placed in one of them), between ships of different groups there needs to be a distance of 10 meter, between ships in the same group the ’standard’ safety distances apply.

3. Any remaining lockages only need to satisfy the ’standard’ safety distances, 1 meter in length direction and 10cm in width direction.

These rules are implemented into the placement heuristic. The options 1 and 3 are implemented in by setting the safety-distances according to the values needed; New skyline in option 1 the possibility of mooring to another ship is removed. For option 2 this changes some elements to the Old skyline placement heuristic:

10 meter • When checking if the ship can be docked(to the left 10 meter or right); include a check to see if the correct dis- < tances are kept.

• Instead of increasing to the lowest neighbor: Find all ships already placed and do not satisfy the 10 meter constraint to the sky. These could make it impossible for some ships to be placed. See how far the sky should be increased for one of the ships to satisfy the 10 meter constraint, call this value Figure 4.5: Updating the skyline in option 2 new_sk y. Find the height of both neighbors (if there are neighbors): increase the skyline to the lowest value of the three.

4.2.6.C OMPARISON OF THE MODELS One of the main disadvantages of the optimization models is that they are unable to include the First Come First Serve (FCFS) constraint as it’s currently used in practice. In these optimization models one can include the FCFS rule by stating that a ship arriving later is not allowed to be locked earlier. This means that if a large ship doesn’t fit in the remaining space of a lockage, none of the ships arriving later are allowed to join this lockage. An option to resolve this would be to remove the FCFS constraint altogether. That makes it possible 26 4.O BJECTMODELING for two smaller ships to take the place of one larger ship that arrived earlier (as this can lead to a more optimal result, taking into account the average delay). As this effect is not desired, removing the FCFS constraint is not an option, as a result the optimization model is not a good method to use when modeling locks. Within the heuristic method, it’s possible to use the FCFS as the rule is used in practice. Whenever a ship doesn’t fit in the remaining space of the lockage, the ship arriving after it’s allowed to join the lockage (assuming this ship can fit in the remaining space). Because of this the heuristic lock model will be used in the mesoscopic model, including the FCFS as it’s currently used (in nonlinear form). The same decision as was made for the VCM trajectory-planner. Instead of using an optimization technique, a heuristic approach was used making it possible to include the FCFS (as it’s currently used).[18]

4.2.7.C HECKSADDEDFORADDITIONALELEMENTS There are still some additional elements that need to be taken into account when modelling locks. These elements are not taken into account when scheduling the ships. For some a check was included in the model. Using this check it can be seen how often a situation occurs that demands further implementation. Next to the sub-chambers and bridges explained here there are more elements that could have been included in the lock model. For instance the water levels (tides) have an inﬂuence on the lockage time. More information about these elements can be found in chapter14.

SUB-CHAMBERS Some locks have the possibility of locking in sub-chambers. In this case one (or more) of the chamber(s) has an extra set of gates placed in the middle of the chamber. This makes it possible to use only one part of the chamber when locking; the two (or more) parts might not be equal in size. As there is less water that needs to be removed or added to the chamber, the time needed for the lockage will be shorter. Moving less water is also better in the case of water saving. The sub-chambers can not only used in order to save time when locking, another use of them is to cheat the rules set for dangerous cargo. Using the sub-chambers it is possible to do two lockages in sub-chambers, instead of doing one lockage in the complete chamber. Because there are now two lockages, the rules set for dangerous cargo can now be satisfied easier. It’s important to keep in mind that the first lockage in a sub-chamber (after locking with a complete chamber), always needs to be in the front part of the lock (looking from the side it’s at). The reason for this is the current water level in the lock. When using these sub-chamber, they need to be used in pairs. Either both sub-chambers need to be used after another in the same direction. Otherwise one of the sub-chambers can be used twice, once in one direction and once in the other direction. Within the model a check is made to see which of the planned lockages would fit within a sub-chamber. If there are situations where two lockages after another fit within the same sub-chamber, this sub-chamber could be used instead of the complete chamber now used in the model. This check only takes into account the situation of using one sub-chamber twice, once in either direction. The situation where the two sub- chambers are used in the same direction after one another is not looked into. This situation is more compli- cated, as this separation can result in fewer ships fitting within the lockage(s), or for more ships to being able to join. Therefore it’s unknown how many ships need to be taken into account when checking if it’s possible to use the sub-chambers.

BRIDGESLOCATEDATLOCKS At some locks there are bridges located over or close to the gates of a chamber. As these bridges can influence whether or not ships can use a certain chamber these bridges will be added to the lock model. Whenever these bridges are fixed, they simply add a restriction for the height of ships that are allowed to use this chamber. When the bridges are moveable, for every lockage it needs to be determined whether or not the bridge needs to be opened. Within the mesoscopic model it’s assumed that the bridge will always open if this is needed for one of the ships placed in the lockage. Another possibility is that it’s not allowed to open the bridge during a certain time-period (for instance during rush hour on the road). In this time-period the high ships will be excluded from the lockages, so they cannot be locked when the bridge is not allowed to open; a list of these ships will be kept. When this list contains many ships, it would indicate that these time-periods should be taken into account when modeling the lock. When the time-periods in which the bridge is forced to stay closed are known, it’s reasonable to assume that (almost) no high ships will arrive during this time-period. Ships will adjust their schedule, or if that is impossible find a berth before reaching the lock. 4.3.B RIDGEMODEL 27

4.3.B RIDGEMODEL When looking at bridges, scheduling become a lot less complex. The only constraint to be looked at now is the time-element. How late do the ships arrive and at what time can these ships pass the bridge? The difﬁculty of the bridge model comes from the interaction with the trafﬁc on the road. Similar to the lock model, it’s possible to use an optimization technique that is further explained in section 4.3.1. Another possibility is to use a model based on the schedule known for the bridge, that is explained in section 4.3.2, these two methods will be compared in section 4.3.3. It’s important to realise that not all ships need to be scheduled. Some ships might be able to pass the bridge without the bridge opening, and will therefore pass this bridge immediately after arriving.

4.3.1.O PTIMIZATIONMODEL The bridge model shares some of the constraints of the lock model. However, some constraints are different from the locks or are not even part of the lock optimization. The framework used is still an MILP.

CONDITIONS • Each time the bridge opens vessels in both directions are allowed to pass, the ships have to arrive on time to be allowed to pass.

• One of the directions is allowed to pass the bridge first, then the ships coming from the opposite direction are allowed to pass the bridge. The direction that is allowed first is known before starting the optimisation (a good choice would be the direction of the first ships that arrives). When the clearance of a bridge is wide enough, it might be possible for vessels in either direction to pass at the same time.

• There is a set maximum time the bridge is allowed to stay open.

• There is a set minimum time for the bridge to stay closed after it has been opened. This is done to give the trafﬁc on the road the opportunity to pass the bridge.

• The ships are allowed to pass by a First Come First Serve rule, meaning that a ship that arrives later, will not be allowed through earlier. This rule is enforced only between ships that arrive in the same direction. As a result if not all the ships can pass the bridge, then the last ship that arrives will be the one that has to wait till the next time the bridge opens.

• For each ship it’s known how much time it needs to pass through the bridge.

• There is a known time to open the bridge, and to close it again.

• Most bridges have blocked times, in which the bridge is not allowed to open. This can for instance be during rush hour, or because there is a train traveling over the bridge at that time. During these blocked times the bridge needs to be closed.

4.3.2.S CHEDULEMODEL For some bridges there is a schedule, stating at which time these bridges will open for traffic on the fairway. If this schedule is available, it’s possible to use this to decide when ships will pass the bridge. Ships will pas the bridge at the first time the bridge will open (according to the schedule) after they arrive at the bridge. This method is accurate as long as the amount of ships is low enough to allow this. If there are a lot of ships arriving at the bridge at the same time it might not be possible for all these ships to pass the bridge at the next time the bridge opens. Whenever the amount of ships grows high enough to give problems (not all shops are able to pass the bridge when it opens) an investigation should be done to see how this situation is handled in reality. For instance the bridges seen in the practical case (within the canal through Zuid-Beveland and canal through Walcheren) are allowed to introduce an additional time-period in which the bridge opens, if the amount of traffic on the fairway demands this. This situation was not encountered in the mesoscopic model and was outside the scope of this project. 28 4.O BJECTMODELING

4.3.3.C OMPARISON OF THE MODELS The best method to use for bridges depends on the information we have about the bridge. If the bridge has ﬁxed time at which it opens, it would be best to use the schedule model. It’s still possible to use the optimization model, but this would give the same result. On the other hand if there are no such time-slots known, it’s not possible to use this schedule model. If that is the case the only possibility is to use the optimization model. 5 ROUTING

For each vessel it is necessary to determine the route from origin to destination using the fairway network. This can be done using a shortest path algorithm. In the case of the initial setup, the delays along the fairways are not yet known. Two possibilities exist to ﬁnd the best route in this case. The ﬁrst possibility is to choose the shortest path without taking any delays into account (assuming the delays are zero everywhere). However, this might direct all ships over a route that has a lot of delays. Another possibility is to use historic data to estimate the delays. This will make the resulting path and travel time more accurate (this method is implemented).

When looking at travel times as costs used in the shortest path, there are two unconventional elements that need to be included. First, because objects (locks and bridges) are located at the nodes, it’s possible that there are costs to include at the nodes, this will be further detailed in section 5.1. Another unconventional element is that the costs will be time-dependent, instead of being constant over time, this will be explained in section 5.2.

5.1.C OSTSATNODES Any normal shortest path algorithm is meant to only take into account the costs that occur when traveling along edges. In the case of the network of fairways, there are also costs that occur at nodes. This is because the objects (locks and bridges) are located at the nodes and the passage-time for the objects needs to be taken into account in the costs. These costs can be calculated from simulations already done with the mesoscopic model, or estimations used for initial setup (before the model has been run, using historic data). There are several methods that can be used to take these additional costs (at nodes) into account as well. • Deﬁne a shortest path algorithm that can handle these costs as well as costs on the edges. A disadvantage of this method is that the ’normal’ shortest path algorithms have already been implemented, including all possibilities for speeding up the algorithm. A shortest path algorithm which can handle both costs on edges and nodes, has not yet been deﬁned in an optimized form.

• Another possibility is to change the graph such that a ’normal’ shortest path algorithm can take the costs on the nodes into account as well. This can be done is several ways:

– Separate all nodes that have costs into an incoming node and an outgoing node, connected by an edge having the same costs as the node has. This method needs to be used on a directed graph, where all edges going toward the node connect to the incoming node and all edges going away from the node are connected to the outgoing node. The disadvantage of this method is that this way the number of nodes will be twice as big, resulting in the algorithm needing more computation time. – It’s possible to simply add the costs of the nodes to the edges that connect to these nodes. Again in a directed graph add the costs of the node to all edges that go out of the node. It’s possible to add half of the costs to the edges going out and half to the edges going in. This last method can be used in case of an undirected graph, by adding half of the costs to all edges connected to the node.

29 30 5.R OUTING

In the mesoscopic model a directed graph is used, and the costs are added to the outgoing edges only. The reason for adding all costs to the outgoing edges is that this way the arrival time at the different nodes is equal to the actual arrival time at the object. The importance of this will become clear in the next section. This method is implemented in the mesoscopic model. If the node represents a bridge or lock there are only four edges connecting it (two incoming and two outgoing). That makes it possible to include different passage times for the different directions. The passage time for the ﬁrst direction will be added to the corresponding outgoing edge, while the passage time for the other direction is added to the other outgoing edge.

5.2.T IMEDEPENDENTROUTING When taking into account delays (after the mesoscopic model has been run at least once), the costs of passing an object will most likely become time dependent. Similar to the traffic on the highway, the amount of traffic (on the fairways) will change over time. In order to find the shortest path in this case, a time-dependent shortest path should be used.[23] Instead of finding the shortest path once, it needs to be found for different departure times. If the departure time of a ship has already been set, it is only needed to find the shortest path for this departure time. This time dependent shortest path is again defined using costs on the edges only. However the nodes are the places where the delays will occur. These delays define a function that states the delay given an arrival time at the object. Now the reason for adding the costs of nodes to the outgoing edges becomes clear. The time a ship arrives at an object will determine the delays the ship will get, and this arrival time is now equal to the time the ship arrives at the node. It’s important to realize that for different starting times, there can always be different routes that are the fastest. After finding the best route for each starting time, it is interesting to see how these routes perform at other times. This because it might be better to use a slightly slower route, if the risks of getting delays on that route are lower. When defining the function for the delays from the data it is important to see if the First Come First Serve (FCFS) rule applies. Meaning that any ship that arrives at an object later, cannot be let through earlier (it is allowed to be let through at the same time). Even though FCFS is used in operations, this doesn’t mean that ships are always let through in the order they arrived in. Whenever a ship cannot fit into a lockage, the ship after it’s allowed to join the lockage instead (if this ship does fit the lockage). At bridges it’s even easier to change the order of ships as lower ships can just pass a bridge, whereas the higher ships will have to wait for it to open. As a result the function for the delays will not always satisfy the FCFS rule.

5.3.R EROUTING When the routes have been chosen and the mesoscopic model has been run, the exact delays are now known. Knowing these delays it might be better for some ships to take a different route to their destination. These ships can be rerouted, but the model needs to be run again to calculate the delays after rerouting. Then it is possible that some (other) ships need to be rerouted as well. A problem that might occur is that ships might start switching between two routes. In order to reduce the chance of this happening, a simple approach has been proposed.[7] Instead of each time using the ’new’ costs including the most recently calculated delays, a weighted average between the current and previous costs is used. That means that not only the current delays are taken into account when deﬁning the costs; the knowledge of the previous delays is used as well. This should make sure that the route will not start switching between two possibilities. It’s important to realise that there are not as may fairways as there are roads. Not all fairways allow all ships to travel; some might only be suitable for the smaller ships. This means that even when there are two fairways between two points, they might not be available for all ships. And for the ships that can travel both routes, in most of the cases the difference in travel time can be huge. This means that in a ’normal’ situation it’s unlikely that rerouting takes place, interesting is to investigate if changing the departure times of ships can result in lower travel times. 5.4.R OUTINGBASEDONRELIABILITY 31

5.4.R OUTINGBASEDONRELIABILITY Instead of only looking at a ﬁxed travel time, another possibility is to deﬁne which route (or departure time) is the most reliable. One would like to take the route on which there is the least change of huge delays occurring. Therefore instead of only using the time-dependent travel times, additional delays are added at several points. Using random delays it’s possible to determine which route (and/or departure time) has the lowest chance of getting high delays. The random delays should be based on the delays that can be obtained at these places.

6 SIMULATION

When performing a simulation using the mesoscopic model this simulation can be divided into three parts. First a pre-processing step will be taken. Second the simulation itself will be executed. Third the simulation will be analysed; in this step for instance the delays that occurs at different objects can be calculated. After these three steps it is possible to add a fourth step; looking at the possibility of changing the route or departure time of some ships. This could either be rerouting, if a different route is faster when including the delays on top of the original travel time. Another possibility is that leaving at a different time can reduce the travel time signiﬁcantly. In order to determine if no additional delays will occur from these changes in route and departure time, steps two and three need to be taken again after some or all of the ships have changed their route and/or departure time. This makes creates an iterative process, to prevent the solution from keep ’switching’ between two solutions an average between the old and new costs is used.[7]

6.1.S TEP 1: PRE-PROCESSING Before being able to do the actual simulation, some information needs to be known. This information either needs to be filtered from input or when it’s not available it needs to be calculated from the available information. The first thing needed in the simulation is the fairway network used. This network should be given as (or transformed to) a directed graph, containing nodes at the start/end of fairways, at places where fairways cross and at locks and bridges. Whenever a fairway can be used in both directions, it needs to be separated into two directed edges, one for each direction. For each part of the network (the fairways and the objects) the maximum dimensions for ships allowed are needed. Information about the ships that are modelled is needed, for instance their dimensions (needed to decide if a ship can travel along a fairway, use a lock or pass a bridge) and the maximum speed a ship can reach. The route a ship will take can be given, or only the start and end points of the journey. Using the dimensions of the ship the best route can be found from the start and end node using a shortest path algorithm. Besides knowing the dimensions of the ships and their route, the departure time at their start node is needed. If this is not known, a random variable (parameters of this random variable need to be given in that case) can be used to set this departure time. Now that the paths and departure time of the different ships are known; it’s possible to calculate an expected arrival time for the objects that a ship will pass. Until an exact arrival time has been calculated, this expected arrival time will be used when executing the object models. In order to calculate this expected arrival time an additional graph is defined. In this graph the costs (travel time) for the edges are defined using an average speed. Because not all ships can reach this speed, 5 15 minutes are added (depending on the length of the edge) to make sure this average travel time is not − too low. For the different objects an average delay is added along with the minimum time needed for passing the object. The value of this averaged passage time is set such that for most ships this is an overestimation of the time actually needed (higher than the true average). The reason for overestimating is that the effect of getting an expected arrival time later than the actual arrival time is less than when the expected arrival time is earlier than the actual arrival time. These passage times for objects are costs that are defined at nodes, as explained in chapter5 they are added to the costs of the outgoing edges connected to these nodes.

33 34 6.S IMULATION

6.2.S TEP 2: SIMULATION For the simulation some parameters need to be chosen: • The time step size that should be used must be lower than the time needed for a ship to complete any fairway. (For all fairways (edges of the graph) the minimum time needed to travel this fairway is higher than the time step size.)

• The total time period needs to be chosen. Setting this period high doesn’t affect the calculation time (when all ships have completed their route the simulation is stopped). Deﬁning this time period shorter, could mean not all ships have completed their route at the end of the simulation. At the start and end of the simulation the delays seen might not be accurate because there are fewer ships on the network than in the reality.

• When using a microscopic model to find the best schedule, an additional parameter needs to be included stating when to use this model. This can for instance be every 5 time steps. This model is not executed in every time-step (between two time-steps not much has changed, the same ships still want to pass the lock or bridge). Doing a run with the microscopic model will give the same result. At any time-step the most recently calculated schedule is used for the lock or bridge. A horizon needs to be defined; this horizon states how far to look ahead for ships to include in the model. A horizon of 60 minutes would mean that all ships arriving in the next hour are ’seen’ and added to the model. An explanation how this horizon is used can be found in figure 6.1.

Horizon

Current time End of horizon

Ships already Ships arriving within the horizon Ships arriving after the horizon at the lock

Ships are taken into account in the model Ships are not taken into account in the model

Figure 6.1: Explanation of the horizon

After these parameters have been defined, it’s possible for the simulation to start. During the simulation it’s important to keep track whether or not ships have reached the end of their journey. If this is the case for all ships, the remaining time-steps can be skipped. If not the following elements need to be executed in each time-step. The steps taken are visualized in figure 6.2. 1. Let the ships whose departure time falls in the interval (the interval belonging to time-step i would be c[i 1,i] when the time step size equals c) start on their first edge. It’s done by setting their starting time − on that edge equal to their departure time.

• An exception needs to be made for ships that start at a lock. These ships can only start on their ﬁrst edge when they have been locked. Therefore these ships will be started at their ﬁrst edges when they have been scheduled to pass the lock, and will be skipped in this step.

2. For all crossings (any point where more than two fairways meet); find the fixed delay for this crossing. Let the ships whose expected exit time falls within the time interval pass toward their next edge. Set their exit time equal to their expected exit time adding the delay. This delay models the fact that ships might have to lower their speed in order to pass each other at that crossing. This delay is fixed for each crossing, but these fixed delays do not need to be equal to one another. The start time at the next edge is equal to the exit time at the current edge.

• Points where only two fairways meet, but where no objects are placed, will be handled in this step. Depending on the characteristics of this point there might be no delays (if it’s a point added because the characteristics of the fairway change here) or a ﬁxed delay (if it denotes a crossing with a fairway that is not added in this network). 6.2.S TEP 2: SIMULATION 35

3. All objects use one of the following options:

(a) If it’s an object with a fixed schedule: • Check if the scheduled ships should be allowed to pass the object in this time-interval. If so determine which of the ships will be allowed to pass and set their exit time corresponding to the schedule. Set their starting time at their next link; this starting time is equal to their exit time after adding the time needed to pass the object (lock or bridge). (b) Objects that uses an optimization or heuristic method to decide the schedule: • If an optimization or heuristic needs to be done this time interval: – Find the ships that are expected to arrive before the horizon ends. An explanation of how the horizon is used can be found in figure 6.1. – For those ships find the optimal or heuristic schedule (based on some predefined optimization scheme and objective function or heuristic scheme). To find this schedule the arrival times of the ships are used (or the expected arrival time when the exact arrival time is not yet known). – Note that it’s not necessarily true that these ships arrive at their expected arrival time; some might arrive earlier others later. • For all time-periods: Find the ships that according to the latest schedule should be allowed to pass the object in this time period. Check to see if the ships arrived at the object before the time they are scheduled to pass the object. If not, remove this ship, it will be scheduled the next time an optimization or heuristic needs to be executed, this results in an additional delay. For the ships that do arrive on time; set their exit time at this link and set their starting time at the next link according to the results of the optimisation or heuristic.

4. Let the ships travel along the fairways: To do this, ﬁrst ﬁnd all ships that start the edge (a fairway cor- responds to an edge within the graph) in the time interval. For these ships calculate their expected exit time for that edge, using the speed the ship can reach and the length of the fairway. The speed a ship can reach is determined using the speed allowed on this fairway and the maximum speed this ship can reach (the minimum of those two). Remember that the time-step size was chosen lower than the time needed for an edge (fairway). This means that the expected exit time calculated will never fall in the same iteration. Therefore ships travel over the fairways as the last step within each time-period.

These steps are continued until all ships have reached their destination or the end of the time-period that you are interested in is reached.

Start next Find ships starting 1 Start ﬁrst time-step journey in this time-step time-step

Ship starting at an yes Wait for ob- object? ject schedule

no 2 and 3 Start ship on Let ships no ﬁrst edge pass nodes

4 Reached end of no All ships reached Let ships travel simulation time? their end-points? along edges

yes yes Simulation is done

Figure 6.2: Steps taken within each time-step 36 6.S IMULATION

There are several points in the optimization when the expected arrival time of ships can (and should) be updated.

• In step 3: After calculating when a ship will be allowed to pass an object; it’s possible to recalculate the expected arrival times at objects further along the path of the ship based on this scheduled time.

• In step 4: After the expected exit time of the edge has been calculated; this expected exit time (equalling the arrival time at the next node) can be used to recalculate the expected arrival times at the objects the ship still has to visit.

Even though the expected arrival time is updated in the model it’s only equal to the arrival time once this arrival time in known in the model (that could be only a few minutes before this arrival time). This makes it possible that the arrival time used in the optimization is not correct. When the true arrival time is earlier than the expected one, this could mean that it might have been possible to lock the ship earlier (or let the ship pass the bridge earlier). Another possibility is that the arrival time is later than expected, meaning a ship could have missed it’s turn. If that is the case it will be scheduled the next time an optimization or heuristic is done. This will result in quite a lot of additional delays compared to the situation where the ship arrives earlier than expected.

6.2.1.S HORTEDGES In a practical case it might be possible that there are several edges with very low traveling times. This can for instance be caused by two objects located close to another. Remember that the time-step size needs to be lower than the time needed for any edge. As a result those short edges, if not taken into account separately, will give an upper bound for the time-step size. To remove this upper bound it’s possible to update these edges between all of the steps explained before. This makes it possible to increase the size of the time steps. A set is created containing the edges that have a ’length’ that is lower than the size of the time-steps. Here the ’length’ of each edge is the minimum time needed to travel the edge, calculated by dividing the length of the edge in km by the maximum speed allowed. The order in which the different steps are taken can be found in figure 6.3, including additional steps for the short edges. The explanation of the different elements described can be found in section 6.2. When there are no short edges (edges with lower minimal travel time than the time-step-size) in the model the green elements could be removed from the model displayed in figure 6.3. When there are short edges the green elements make sure that these edges are updated often enough. The points where this needs to be added depend on the fairway network the model will be used on, in figure 6.3 the steps needed for the network described in chapter7 are given. When removing the updates of the short edges this can result in a ship being stuck halfway in it’s journey. In this case a ship might start an edge within a time-period, but finish it in the same time-period. Without taking into account the short edges this would result in the node following the edge (can be a crossing, lock or bridge) already having been updated in the time-period, therefore the ship will not pass this node and get stuck. The two additional points in the simulation where not all edges, but only the short edges are updated, make sure that all ships complete their journey. 6.2.S TEP 2: SIMULATION 37

Find ships Start next Start ﬁrst starting journey time-step time-step in this time-step

Start ship on no Ship starting at a yes Wait for lock ﬁrst edge lock? schedule

Ships started on yes Let ships travel short edges? along short edges no

Let ships pass crossings

Let ships Ships started on no Let ships pass bridges short edges? pass locks no yes

Let ships travel along short edges

Reached end of no All ships reached Let ships travel simulation time? their end-points? along edges

yes yes Simulation is done

Note: These steps are determined speciﬁcally for the simulations done using the network in chapter7. Within this network ships only start at an edge or at a lock. The two updates of short edges and the order of updating nodes (crossings, bridges and locks) are speciﬁc to this network.

Figure 6.3: Steps taken within each time-step, including short edges 38 6.S IMULATION

6.3.S TEP 3: ANALYSIS Now that all ships have been simulated it’s possible to analyze the results, for instance the delays that occur can be calculated. Other elements to investigate are the number of ships that arrive at each object and how close to each other they arrive. Delays: The delays are defined as the time between the expected exit time of a ship and the true exit time for the incoming edge. Using this information it’s possible to define a function for the delay with respect to the time. The simplest method that can be used for this is to calculate the average delay on each time interval (it is useful to use a larger interval than the time-steps in the simulation). If there are no ships in the interval, then set the delay equal to zero. Passage-time: Instead of only calculating the delays, another possibility is to look at the complete passage time for the objects. The passage-time is the difference between the expected exit time of the incoming edge and the start time at the next edge. For the locks this value gives more information because it also includes the time needed for ships to travel into and out of the lock. The difference between the delays and the passage time is explained in figure 6.4.

Passage time

Delay of the ship Time ship spends within the lock

Ship arrives Ship enters Ship has at the lock the lock left the lock

Figure 6.4: Passage time and delay for a lock

Travel time: When the passage time for the different objects is known, it’s possible to calculate the total travel time needed for a certain route. This is done using the time-dependent shortest path technique, to calculate the travel time over a route for different departure times. There are values that can be saved during the simulation. For instance the number of ships in each lockage and the length of the queues at the different objects over time. Interesting is to see how many ships will take each route (it’s known at the start of the simulation) and how many ships will pass the different objects.

6.4.S TEP 4: CHANGINGROUTESORDEPARTURETIME When the travel times are known it’s possible to determine if rerouting will result in an advantage. Instead choosing a different route another possibility is to calculate the time it takes to travel the current route for different departure times. This way it’s possible to see if changing the departure time can result in lower travel times. Because in true life one will always want a true advantage, some reluctance to change your route (or departure time) will be added before deviating from the original plan. This reluctance is added by saying that the new route (or departure time) needs to save at least 30 minutes. If this is not the case a ship will not take this new route (departure time). This makes sure that additional delays (from the fact that more ships now take this route) will not immediately make this new route preform worse than the original one. Some ships might not have the ﬂexibility to reroute (or change their departure time), therefore within the mesoscopic model only 25% of the ships have the possibility to reroute. After changing the route or departure time of ships, the steps 2 and 3 have to be done again using these new routes (or departure times), this way one can check if this change is truly better. Once these steps are taken it’s possible to redo step 4, to check if there are (other) ships that should be rerouted from their current route or should change their departure time. 6.5.W HAT INFORMATION TO USE AND TO SAVE 39

6.5.W HATINFORMATIONTOUSEANDTOSAVE During the simulation information is saved for the fairways, locks and bridges (all edges and some of the nodes of the graph). For each ship that travels along a fairway three values are saved: The time a ship starts the fairway, the time the ship will reach the end of the fairway (expected exit time) and the time the ship will leave the fairway (it’s processed by the end node of the edge). For the objects an expected arrival time is calculated and this is updated during the simulation. For the bridges along with this expected arrival time, a value is set stating if the ship can or cannot pass underneath the bridge without the bridge opening. With these values the position of ships during the simulation can be found. During the simulation there is some information saved for the locks and bridges; this information is not needed for the simulation itself. For the locks several values are saved for the ships that pass this lock: The time at which they arrive, the time they start entering the lock and the time they start exiting the lock (after the lockage) are saved. The chamber that the ship has been locked in is saved as well. At the bridges values are only saved for the ships that need the bridge to open, for those ships the arrival time, the time the ship is allowed to start passing the bridge and the time the ship has passed the bridge are saved. These values make it possible to calculate the delays and passage-time for the locks and bridges after the simulation is ﬁnished.

III PRACTICALCASE

7 PRACTICALCASE -ZEELAND

As a practical case, the mesoscopic model is implemented for part of the fairway network in Zeeland; this part is displayed in ﬁgure 7.1. The main route for ships in this network is between Antwerpen and Volkerak, from where ships can travel toward Rotterdam or toward Germany. De- pending on the size of the ship it can either travel over the Kreekrak lock (using the Schelde-Rijn connection) or it can travel over the Krammer and Hansweert locks (canal through Zuid-Beveland). The difference in travel time between these two routes is high, this means that it is not likely that true rerouting will take place for ships on this route under ’normal’ circumstances. However, it’s interesting to see if changing the departure times of ships can result in lowering the total travel times. Investigation should be done to see if there are situations in which true rerouting Figure 7.1: Picture of the practical case[2] would be interesting. For instance when one (or both) of the chambers of the Kreekrak locks is (are) not available, the delays might become so high that rerouting would become interesting. The Kreekrak locks are located on the fastest route between Antwerpen and Volkerak. Important to realize is that the two routes arrive at a different point in Antwerpen. Any time needed for traveling within Antwerpen (a lock; Zandvliet or Berendrecht, needs to be passed for this) can increase the time difference between the two routes further. The locks that need to be passed within Antwerpen are dedicated to maritime navigation, for inland navigation this can result in huge delays. This because the inland vessels are only locked when maritime navigation allows this (for instance when some space is left within the chamber). Besides the routes between Volkerak and Antwerpen, there are some other destinations the ships can have; traveling toward Terneuzen (from where they might continue toward Gent) and toward Vlissingen (this is the endpoint for ships headed for the ocean). Ships going to Terneuzen from Volkerak will use the canal through Zuid-Beveland, from where they will travel over the Westerschelde. Ships going to Vlissingen from Volkerak can also use this route, the smaller ships can use the canal through Walcheren as well; this route is a bit faster. Ships traveling between Vlissingen, Terneuzen and Antwerpen can only travel over one route, over the Westerschelde. A graph (network) containing the different locks and bridges can be found in ﬁgure 7.2. Within this graph there are several endpoints included, these are some of the most used endpoints but there are other endpoints possible.

43 44 7.P RACTICALCASE -ZEELAND

Rotterdam Volkerak or other destination

Veere Zandkreek Krammer

Middelburg Postbrug

Kreekrak Vlissingen Vlakebrug Legend:

Lock Vlissingen Hansweert

Antwerpen End-point

Sea Terneuzen Gent Bridge

Figure 7.2: The graph of the practical case including end-points

Within this network there are several bridges and locks located. The details about the locks will be explained in section 7.1, followed by the details about the bridges in section 7.2. To be able to ﬁnd the correct schedule at the locks and bridges, it’s important to know when ships will arrive at the objects. Therefore an expected arrival time is calculated, more information about the expected arrival time can be found in section 7.3. In order to use the mesoscopic model on the practical case there are a lot of parameters that need to be determined. For the different edges (fairways), it’s needed to known the distance between the end-points and the maximum speed allowed there. For the locks and bridges one needs to know their dimensions, and the time needed for the different processes (traveling into/out of the lock, locking, opening the bridge, etc.). For all parts of the network you need to known what ship dimensions are allowed there. These values have all been collected and are explained in appendixB.

7.1.L OCKS For the different locks it’s important to known how many chambers they have; the number of chambers and the size of the chambers will ultimately determine what the capacity is of the lock and as a result how much delays there will be at a lock. In figure 7.3 all locks can be found with the number of chambers at each lock. The first number denotes the number of chambers that are used for commercial traffic, these are the chambers that are included in the model. The second number denotes the number of chambers used mostly for recreational traffic. These chambers are not included in the model, as they are not often used by commercial traffic. However, these additional chambers do give some important information. As there are two additional chambers for recreational traffic located at Krammer, there will be almost no recreational traffic through the other two chambers. Only those ships that cannot fit within the recreational chambers (for instance due to height) need to be locked in the commercial chambers. At Hansweert all recreational traffic will have to use the two chambers included in the model. This difference can be included by adjusting the percentage of the lock that is allowed to be filled. Lowering this percentage leaves more room in the lock for recreational traffic (that is not taking into account in the mesoscopic model). 7.2.B RIDGES 45

Rotterdam Volkerak or other 3-1 destination

Zandkreek Krammer 1-0 2-2

Kreekrak Veere 2-0 1-1 Hansweert 2-0

Vlissingen 1-1

Antwerpen

Terneuzen Sea Gent 3-0

Figure 7.3: The locks including the number of chambers

7.1.1.S UB-CHAMBERSINLOCKS Some of the chambers have the possibility to be separated, because they have an additional set of gates in the middle of the lock. Using only half of the lock would make the locking process faster. This is the case at Volkerak for the Midden and Oost chambers and at Terneuzen for the Oost and West chambers. Sub-chambers can only be used when there are two lockages after one another that would have fitted a sub-chamber. Therefore a check is added to see if this happens for the lockages that are now scheduled in the complete chamber. If there are often two lockages after another that could have fitted in a sub-chamber, this means that the sub-chambers should be included in the model (they are now only included in the model by adding this check, their use is not included). There is a second situation where the sub-chambers are used, again doing two lockages after another. Instead of doing one lockage in each direction, do them both in the same direction. This way one ’large’ lockage can be replaced by two ’smaller’ ones. An advantage of this is that the first lockage can be done before all ships in the second one have arrived at the lock. This method is (mis)used in the case of ships carrying dangerous cargo. As there are now two lockages, the rules set for these ships might now be satisfied while they would not be satisfied when there was only one lockage. For example: It’s not allowed to lock a ship carrying one cone along with a passenger vessel.[21] However, by using sub-chambers, it’s possible to first lock a ship carrying one cone, and with the second sub-chamber a passenger vessel, because these are now two separate lockages. When there are no sub-chambers then this rule would result in one of the ships having to wait until (one of) the chamber(s) comes back, which would result in higher delays.

7.2.B RIDGES On the fastest route from Volkerak to Antwerpen (Schelde-Rijn connection, passing Kreekrak) there are several fixed bridges. As these bridges cannot be opened to let high ships through, this results in a constraint for ships wanting to travel along this route. Therefore ships that can fit underneath these bridges can choose from multiple routes when they are traveling from Volkerak to Antwerpen. Ships that cannot pass under these bridges always need to travel along the route Krammer-Hansweert (canal through Zuid-Beveland) and are not allowed to travel along the route using the Kreekrak lock (Schelde-Rijn connection) instead. Besides fixed bridges, there are moveable bridges located in the model. For instance on the canal through Zuid-Beveland, where there are two bridges located (Vlakebrug and Postbrug). Both bridges open twice every hour to allow the higher ships to pass. Within Vlissingen and Middelburg there are several bridges located close to one another. As these bridges all have scheduled opening times (again twice an hour), the time the ship needs to pass all bridges is known when you know the time it passes the first bridge. Therefore the bridges are modelled within one node in the practical case. 46 7.P RACTICALCASE -ZEELAND

This merging does have a disadvantage, because it assumes that a ship needs all bridges to open. When a ship only needs some of the bridges to open, but can pass underneath the others, this merging would result in more time needed to pass the bridges than there is needed in reality. The bridges located in Middelburg have a height of 1.7 and 1.5 meter, therefore it’s unlikely that a ship can pass one, but not the other. However, the bridges in Vlissingen have height of 1.7, 2.4 and 4.9 meter, making it more likely that a ship can fit underneath one (two), but not underneath the other(s). There are bridges located at the locks, for instance located over (or close to) one of the gates. As the opening of these bridges depends on the use of the lock, they will be taken into account in the lock model. At the Zandkreeksluis and the locks at Terneuzen there is a bridge placed at both sides of the lock. This means that whenever one of the bridges is opened, (road-)traffic can still pass the lock using the other bridge. As a result these bridges will simply open whenever needed, without interrupting the road traffic. As these bridges are very low (having a height between 2.07m and 6.75m for Terneuzen and a height of 3.4m and 7m for Zandkreek), the opening of these bridges would be necessary in most of the (filled) lockages. At Terneuzen the bridges are even added to the standard locking procedure, so that they opened whenever there is a lockage. At Volkerak and Krammer there are also bridges located, in this case there is only a bridge at one side of the lock. There is only a moveable bridge over one of the chambers, over the other chambers there is a fixed bridge. As there is only one road (whereas at Zandkreek and Terneuzen there are two) opening the bridge means delaying the traffic on the road significantly. Due to safety it’s needed to open the bridge before any of the ships travel into the lock and it can only be closed again when all ships have entered (or when traveling out of the lock; open the bridge before the first ship travels out and close only after all ships have left the lock). This means that depending on the amount of ships traveling in the lockage, the bridge might even be opened for 20 minutes. Luckily these bridges are a lot higher than the bridges that are located at the other locks, as they are 14m (Volkerak) and 14.9m (Krammer).[24]This means that the bridge will not need to be opened that often. Because the bridge located at Volkerak lies within the A59/A29 it’s not allowed to open within the rush hour for the road (defined as 6.00-9.00 in the morning and 16.00-18.30 in the evening). This means that ships having a height over 14m are not allowed to pass in this time period. In reality ships exceeding this height will almost never arrive at the lock within this time period (during the whole day there are only a few ships with this height), instead choosing a different departure time or if that is impossible finding a berth before reaching the lock. In the mesoscopic model it might occur that high ships arrive in this time period, these ships should not be allowed to join a lockage until the rush hour has ended. Consideration should be given to ships arriving just before the start of the blocked time of the bridge, as they might need to jump ahead in order to be locked before the start of this blocked time. As a start simply block the ships within the blocked time, and record how often ships are blocked. This will show whether or not further modelling is necessary.

7.3.E XPECTEDARRIVALTIME At locks and bridges it is important to know which ships want to pass and when they arrive; this information is used to find a schedule. Not for all ships it’s known exactly how late they will arrive at the object. When the arrival time is unknown an expected arrival time is calculated. This is done by using an average travel time for the remaining part of it’s journey. All ships that arrive (or are expected to arrive) within the horizon (set for instance at one hour from the current time) will be taken into account when defining the schedule. An explanation of this horizon can be found in figure 6.1. In order to calculate the expected arrival time, first the average travel time needs to be defined for fairways, locks and bridges. On the edges the average travel time is calculated by assuming a speed of 15km/h, and adding an extra 5 15 minutes to the travel time to take into account that not all ships can reach this speed. − For the different objects an average passage time is set, this time is then added to the travel time found for the edge (this method is explained in chapter5). The passage time contains several elements, for the locks it can be divided into three parts. Firstly the time needed for the lockage itself: this includes the closing of the gates, leveling the water in the lock and opening the gates again. Secondly the time needed for ships to travel into the lock and out of it needs to be included. Thirdly it’s needed to include the delay obtained when a ship has to wait before being able to travel into the lock (the delays obtained at the lock). In the table below these times have been written out. For the larger locks the average delay is assumed to be higher, as there are more ships using these locks. This means that there will be more ships in each lockage (adding time needed for the other ships to travel into and out of the lock) and the time before the chamber is available at the correct side grows due to the fuller schedule. The time needed at the different locks is given in table 7.1. 7.3.E XPECTEDARRIVALTIME 47

Lock Lockage time Time for traveling in+out Average delay Average passage time Volkerak 15 4+2 15 35 Krammer 25 4+2 15 45 Hansweert 15 4+2 15 35 Kreekrak 15 4+2 15 35 Terneuzen 15 4+2 15 35 Vlissingen 15 4+2 5 25 Veere 15 4+2 5 25 Zandkreek 15 4+2 5 25

Table 7.1: Time needed for passing each lock

For the bridges the passage time is deﬁned similarly. Because all bridges are opened every half an hour, the average delays are (slightly less than) 15 minutes. For the bridges in Vlissingen and Middelburg the passage time needed should be added, this passage time is dependent on the direction the ship is traveling in. The passage time is determined based on the time each bridges opens, using this it’s possible to calculate the time needed to pass the bridges; for the model the bridges have been merged into one ’bridge’. The passage time at the different bridges can be found in table 7.2.

Traveling south to north Traveling north to south Bridge Passage time Average travel time Passage time Average travel time Vlakebrug 0 15 0 15 Postbrug 0 15 0 15 Vlissingen 40 55 20 35 Middelburg 10 25 20 35

Table 7.2: Time needed for passing each bridge Using the averages travel times on both the edges and the objects (locks and bridges) it’s possible to calculate an expected arrival time at the locks and bridges a ship still has to pass. Whenever a ship has passed an object, the expected arrival time is updated for all following objects. For ships that start their route at an object, this means their expected arrival time is simply their departure time.

IV RESULTS

8 BASISSIMULATION

In order to gather results a basis simulation was determined with close to the same amount of ships passing through each lock compared to the amount seen in the IVS90 records for the 17th of November 2015.1 When running these basis simulations it can be seen that the delays obtained at the different locks are approximately equal to the delays registered in the records. This means that it is possible to simulate the current situation. For this situation a partial investigation is executed (using the mesoscopic model) to the possible usage of sub-chambers, and to the bridges that are located at the locks. These elements where not included in the model, instead a check was added to see how much they were used. This is done so that it can be determined if these elements should have been included in the model. All simulations are done twice, the ﬁrst time the ships are divided over the simulated day and night equally. In reality there will be more ships traveling during the day as there are traveling at night, this is included during the second simulation. The differences in results between these two situations gives an insight in how much the distribution of the ships over the day inﬂuences the different elements measured (for instance the delays obtained at objects; locks and bridges).

8.1.S UB-CHAMBERS Sometimes a chamber of a lock can be used in parts (these parts are called sub-chambers) or as a complete chamber. By adding a gate in the middle of a chamber, it is possible to execute a lockage in part of the chamber, thereby limiting the time needed for the lockage (as there is less water that needs to move in or out of the chamber). A disadvantage of using a sub-chamber, is that the next lockage should again be done using this sub- chamber. This is due to the water level in the different sub-chambers after the lockage has been done. There- fore it is only possible to use a sub-chamber if there are two lockages following each other that fit in this sub-chamber. Another possibility is to use the second sub-chamber in the same direction as the first sub- chamber. This way the complete chamber has the same water level again.2 In the practical case there are two locks at which there are sub-chambers located. At Volkerak there are sub-chambers within the Oost and Midden chambers. At the locks of Terneuzen there are sub-chambers within the chambers West and Oost. In all four chambers there are two sub-chambers, at Volkerak the sub- chambers are exactly the same size, at Terneuzen one of the sub-chambers is slightly bigger than the other (because the middle set of gates is not placed exactly in the middle of the chamber). In the mesoscopic model a check was added for the ships scheduled in those chambers, to see whether they would have fitted in one of the sub-chambers. If two lockages after another could have fitted in the same sub-chamber it would have been possible to use the sub-chamber instead of the complete chamber. As

1The IVS90 records of this day where analysed to gain insight in the current situation for the locks. This was done for Volkerak, Krammer, Hansweert, Kreekrak and Terneuzen. The records contain information about the time lockages take place, which ships are contained in them, and how much time they have waited before being locked. Furthermore, dimensions of the ships, origin, destination of their journey and some information about the cargo they are transporting can be found in the record.[25] 2When there are sub-chambers, most of the time there are are only two sub-chambers. It is possible to have three or even more sub- chambers. In this report only the situation of two sub-chambers is explained, because within the practical case only the situation with two sub-chambers occurs.

51 52 8.B ASIS SIMULATION explained in section 4.2.7 this check doesn’t take into account the possibility of separating a lockage into two lockages in sub-chambers.

When looking at the lockages scheduled in these four chambers, most of them would not have fitted within a sub-chamber. For the chambers at Volkerak none of the lockages fit in either of the sub-chambers, meaning it’s not possible to use the sub-chambers. At Terneuzen only one of the lockages fits the sub- chamber, because this lockage is followed by an empty lockage this means that the sub-chambers can be used for two of the 46 lockages (meaning in less than 5% of the lockages). This indicates that it’s not possible to use the sub-chambers by locking one sub-chamber first in one direction, and then in the other. It might be possible to first do a lockage in one sub-chamber and then a lockage in the other sub-chamber. A check cannot be included to check for the possibility of this, because it might result in different ships being included in the lockages (for instance ships which were not allowed to be locked due to dangerous cargo can now be included because two lockages are created). Therefore to include this possible use of sub-chambers the use of sub-chambers needs to be taken into account when determining the schedule for locking, instead of only doing a check afterward. However, this was outside the scope of this project. Before being able to include sub-chambers in the model more information needs to be collected. The time needed for lockages in sub-chambers needs to be known, along with the method used to decide between a lockage in a complete chamber or in a sub-chamber. Furthermore, it should be investigated how often sub- chambers are used to split one lockage into two smaller ones. If the sub-chambers are not used this way in reality, adding this to the mesoscopic model is unnecessary.

8.2.B RIDGESATLOCKS There can be bridges located over or close to the gates of a lock, the opening of this bridge will then depend on the operation of this lock. Within the practical case four of the locks have such bridges. At the locks of Terneuzen and Zandkreek there are bridges located at either end of the chamber. This means that when one of the bridges is opened, the other will be closed allowing road-trafﬁc to pass (almost) unhindered. This is necessary, because these bridges are low and they will have to open often for ships to pass through the lock. At Terneuzen the opening of the bridges has been included in the normal locking procedures.

At the Krammer and Volkerak locks there are also bridges over the gates of the lock. However, there is only a bridge at one side of the lock, this is a fixed bridge for all chambers except one, where a moveable bridge is located. As a result all ships for which the bridge needs to be opened, need to use this chamber. Because there is only one bridge, traffic on the road will be delayed significantly when the bridge needs to be opened. The bridge located at Volkerak lies within the A59/A29 and is therefore not allowed to open within the rush hour.

Because of the high delays for traffic on the road when opening these bridges, it is important to look into how often the bridges at Krammer and Volkerak need to be opened. Luckily these bridges are high, so they only have to be opened for ships with a height over 14 meter. Within the basis simulation this results in around 20 ships for which the bridge has to open in a day. Because these bridges cannot use the Schelde-Rijn connection, they pass both the Volkerak and Krammer locks. This is approximately 6% of the ships passing Volkerak and around 20% of the ships passing Krammer. As a result around 25% of the lockages need a bridge opening at Volkerak and around 38% at Krammer (percentage taken with respect to the number of lockages in the chamber with a moveable bridge). Important to realize is that these percentages are the result of the assumptions made with respect to the ship sizes. These ship sizes are defined from the ship sizes registered in the IVS90 records for Volkerak.[25] However, the height of a ship is rarely registered. The heights that are given are used to fill in the missing heights. This way a complete set of ship sizes can be generated. A consequence of this might be that the heights of the ships differ from the heights in reality. Most likely the heights that are registered are for the higher ships, because the height is not interesting for the lower ships that can easily pass all bridges. This would mean that the heights used are on average overstated and as a result the percentages given before will be overstated as well. 8.3.D ANGEROUSCARGO 53

8.3.D ANGEROUSCARGO Within the simulation, there are different percentages set that define the amount of ships carrying dangerous cargo. An investigation was done to see the effect of changing these percentages, specifically the effect this has on the delays obtained. The new percentages used can be found in the following table; Different percentages Category Original 1 2 3 4 5 6 7 8 Dangerous cargo, one cone 4% 4% 6% 6% 4% 4% 6% 4% 4% Dangerous cargo, two cones1 1% 2% 0% 1% 2% 1% 2% 1% 1% Dangerous cargo, single lockage2 1% 0% 0% 1% 1% 2% 2% 1% 1% Passenger-ships 5% 5% 5% 5% 5% 5% 5% 5% 5% Ships having a certificate 55% 55% 55% 55% 55% 55% 55% 35% 75% The first two situations simulate the relaxing of rules, this can for instance be because of better con- structed ships. In the first simulation all ships that, in accordance to the current rules, have to be locked alone2, are now allowed to be locked as if they have two cones1. In the second simulation all ships carrying dangerous cargo will now be locked as if they only carry one cone. The simulations 3-6 are done to investigate the effect of an increased amount of ships carrying dangerous cargo. Lastly, simulations 7 and 8 are done to investigate the effect of more (less) ships having a certificate.

When looking at these percentages it’s important to realize that the simulations are done for only one day. This means that the total amount of ships (in the basis simulation) is 520. This number of ships has been determined using the IVS90 records for the 17th of November 2015.[25] As a result in the original simulation there are only 21 ships with one cone, 5 with two1 and 5 that are forced to be locked alone2. In each run these ships are divided randomly over the different routes. Because of the low amount of ships with dangerous cargo this randomness has a huge effect. This can be seen in the results of the simulations. Even when averaging over ﬁve runs it’s still not possible to take any conclusion out of the data. While one lock will get less delays another will get more. It’s also not possible to separate the locks into groups based on their response. This is most likely due to the fact that while in one run a lock might have several ships with dangerous cargo passing it, in another run there could be no ships with dangerous cargo. Because of this no conclusions can be made about the effect of the amount of ships carrying dangerous cargo on the delays that are obtained at the different locks.

8.4.I NCREASINGTHEAMOUNTOFSHIPS With the construction of the Maasvlake 2, the policy has become to increase the vessel traffic (and reduce the transportation over the road); therefore an analysis was made to see what the effect of such an increase would be. Starting with the basis situation, ships where added up to 50% additional ships, compared to the situation in the basis simulation (determined based on the standard records obtained from IVS[25]). The delays obtained at the locks are displayed in figures 8.1 and 8.2 for the different percentages of ships added to the original amount. Looking at figure 8.1 it can be seen that for Volkerak and Kreekrak the delays increase when there are more additional ships. This increase of delays indicates that the capacity of the lock is reached. Interesting is to see the difference between the situations. When the ships are divided equally over the day and night, the delays are a lot lower and more acceptable than in the situation where more ships travel during the day. This means that the capacity of the lock can be used more efficiently when the ships are divided over both the day and the night. To give a value to this efficiency; assuming average delays until 30 minutes are acceptable, how much increase in traffic is possible? At Volkerak in the case of ships divided equally over the day and night, it is possible to increase until 35% without the delays exceeding 30 minutes. However, when there are more ships during the day, it’s only possible to increase the traffic until 15%. At Kreekrak it’s possible to increase the amount of traffic until 25% when the ships are divided equally over day and night. When there are more ships during the day, even in the original situation a delay of just over 30 minutes is seen. This shows that the lock is used much more efficient when the ships are divided over the day and night; as a result the capacity of the lock is higher when dividing ships equally. This shows that in situations where capacity might become a problem, stimulating the equal distribution of ships equally over the day and night can reduce the problems.

1Ships carrying two cones, that are allowed to be locked with other ships, when satisfying additional rules. 2Ships carrying three cones and ships carrying two cones, that are not allowed to be locked with other ships in any situation. 54 8.B ASIS SIMULATION

(a) Ships divided equally over the day (and night) (b) More ships during the day

Figure 8.1: The delays at Volkerak and Kreekrak with additional ships

Figure 8.2 shows a more stable value for the delays obtained at Krammer and Hansweert. This means that the capacity of these locks is not yet reached, even when there are 50% additional ships compared to the basis situation. At these locks there is not that much difference between the two situations. When there are more ships during the day the delays are a bit higher, but the effect is much smaller then it was at the other locks. Both in ﬁgure 8.1 and 8.2 it can be seen that the ships in one direction have more delays than the ships in the other direction. This is due to the difference in the arrival patterns between both sides of the lock. Further on their journey ships will have spread more over time due to the differences in speed. The locks ships have already encountered will change the arrival pattern of the ships as well. This can result in more delays in one direction than there are in the other direction. 8.4.I NCREASINGTHEAMOUNTOFSHIPS 55

(a) Ships divided equally over the day (and night) (b) More ships during the day

Figure 8.2: The delays at Krammer and Hansweert with additional ships

8.4.1.C APACITY USAGE Next to the delays there are other methods that can be used to determine how efﬁcient the capacity of a lock is used. For instance the number of ships in a lockage. Expected would be that there will be more ships in a lockage when the capacity of a lock is used better. To investigate this, compare the results of the basis simulation, to the results of the basis situation including 5, 10 or 25 % additional ships. It can be seen that the amount of lockages stays the same for the different locks, even though more ships have to pass the lock. As a result the number of ships in each lockage increases. This indicates that in the basis situation the reason for the lockage being started is due to the waiting times allowed for the ships being exceeded and not because there is not any space left. This might of course not be true for all lockages, but at least for some of them (this makes it possible for the average number of ships per lockage to increase).

9 MAINTENANCEAT KREEKRAK

Within the fairway network the most important route is between Antwerpen and Volkerak (from there ships can either go toward Rotterdam, other places in the Netherlands or toward Germany). The fastest route for ships is over the Schelde-Rijn connection, for which ships have to pass the Kreekrak locks. A second route exists, using the Krammer and Hansweert locks going over the canal through Zuid-Beveland, but traveling over this route takes more time. Because the two routes arrive in Antwerpen at a different point, there are Belgian locks within Antwerpen (Berendrecht or Zandvliet) that need to be passed (therefore the difference in travel time between the two routes grows further). This means that under normal circumstances ships that can use the Schelde-Rijn connection (the height and draft of the ship need to satisfy a bound here, because they need to be able to use one of chambers at Kreekrak) will always use this route. However, in the case of (planned or unplanned) maintenance at Kreekrak delays might make the second route a more acceptable alternative. In order to investigate this, several simulations were done for the Kreekrak locks. Firstly the situation where one of the chambers cannot be used for the complete day is investigated. This is of course an extreme situation. Secondly different types of shorter maintenance are investigated as well; restricting the usage of one of the chambers for several hours. Lastly an investigation is done between two (possible) alternatives. Comparing the effect of closing the chamber for a short period several times, to the effect of closing the chamber once for a longer period.

9.1.C HAMBERCLOSEDCOMPLETELY If one of the chambers is not available for the entire day, a huge increase in delays can be expected. When looking at the results of the simulations in ﬁgure 9.1 a huge difference in passage time can be seen. This difference can be explained using the queues seen at the lock. In the situation using both chambers, the queues do increase, but are continually lowered to zero. The queue being zero indicates that at this point all ships that were waiting are now locked. When only one chamber can be used, it’s not possible to take all ships that are waiting. This makes the queues increase a lot (till almost 30 ships are waiting to be locked) and thereby the delays (and passage time) grow till almost 10 hours for some ships. The queue only diminishes when there are no more ships generated within the simulation. Luckily not all ships will need so much time to pass the Kreekrak locks, but the delays still average at more than 3 hours. In the situation with two chambers a ship only gets delayed for just over 15 minutes on average. The route over the canal through Zuid-Beveland takes about two additional hours the three hours delay might make this route become interesting. However, it is important to keep in mind that the ships will have to be locked within Antwerpen by the Berendrecht- or Zandvlietlock when taking this route. The time needed for this increases the additional two hours needed for the route even further. In this case when the passage time in Antwerpen is less than one hour, the route over the canal through Zuid-Beveland would be faster. However, when the passage time in Antwerpen takes longer the route over the Schelde-Rijn connection would still be best to use.

57 58 9.M AINTENANCE AT KREEKRAK

(a) Using both chambers (b) Using a single chamber at Kreekrak

Figure 9.1: Passage time and queues at Kreekrak when divided over day and night

When there are more ships traveling during the day than there are at night, the passage time needed will become even higher, as can be seen in ﬁgure 9.2. The passage time is higher both when using both chambers and when only one chamber is available. When both chambers are used this increases the average delay with approximately 5 minutes compared to the situation where ships are divided equally over the day and night, resulting in a 20 minute delay. When only one chamber is used the average delays are now over 5 hours, where divided over the day this was 3 hours. With these delays at Kreekrak it might becomes faster to travel over the canal through Zuid-Beveland, depending on the time needed to pass the Berendrecht or Zandvliet locks. In ﬁgure 9.2 it can be seen that there are times at which the delays are low again (the passage time equals the minimum passage time needed), this is caused by the inter-arrival time between ships being over an hour at this point. Another interesting factor is the number of lockages scheduled and the number of ships using each lockage. The single chamber executes approximately the same number of lockages as either of the chambers in the situation with two chambers. This results in the number of ships in each lockage being higher when only one chamber is available. The single chamber needs to continue locking longer before all ships have past the lock (with two chambers all ships have been able to pass the lock after 26 hours, with one lock only after 35 hours), this can be explained by the fact that a queue that has formed. This queue keeps growing throughout the simulation, indicating that there is not enough capacity at the lock when only one chamber can be used. 9.2.S HORTMAINTENANCE 59

(a) Using both chambers (b) Using a single chamber at Kreekrak

Figure 9.2: Passage time and queues at Kreekrak when more ships are traveling during the day

9.2.S HORTMAINTENANCE Next to the possibility of having a chamber unavailable for the complete day, it is possible to have a shorter period in which the chamber is not available. This can be due to (planed) maintenance, but can have any other reason. To effectively see what delays where caused by the maintenance, the situation where the chamber is unavailable is compared to a run of the basis simulation, using the exact same ships. This way it’s possible to determine which delays where caused by the fact that the chamber in unavailable, and which delays would have be obtained in the original situation as well.

First looking at the possibility of the chamber not being available for one, two or three hours. In ﬁgure 9.3 the delays obtained in the original situation are plotted, these delays will be compared to the delays when the chamber is not available for either one, two or three hours (all starting at 12.00).

(a) Ships are divided equally over day and night (b) More ships during the day

Figure 9.3: Passage time at Kreekrak without any maintenance 60 9.M AINTENANCE AT KREEKRAK

In ﬁgure 9.4 the additional delays are plotted for in the case that the ships are divided equally over the day and night. It can be seen that although in all three cases it takes till around 24.00 till the additional delays are solved, the amount of additional delays grows when the chamber is closed for a longer time.

Figure 9.4: Difference in passage time at Kreekrak when ships are divided equally over day and night The same can be seen in ﬁgure 9.5 for the case where there are more ships during the day. Note that the additional delays seen occur in the same period and have the same height as they did in the situation with the ships divided equally. This means that the difference between the two situation only comes from the basis situation (where the delays are slightly higher in the case with more ships during the day). Logically the average delays at Kreekrak grow when the chamber is closed longer, this growth is approximately the same in both the situation with ships divided equally over day and night and the situation with more ships during the day. 9.2.S HORTMAINTENANCE 61

Figure 9.5: Difference in passage time at Kreekrak when there are more ships during the day

The same simulations were executed with the chamber being unavailable for two, four or six hours. Again the passage time needed in the situation without the chamber closing (shown in ﬁgure 9.6) is compared to the passage time needed when the chamber is closed.

(a) Ships are divided equally over day and night (b) More ships during the day

Figure 9.6: Passage time at Kreekrak without any maintenance When looking at figure 9.7 it can be seen that again it takes till around 24.00 before the additional delays are solved. This is similar to the situation when the chamber was closed for one, two or three hours. Inter- esting is to see that in figure 9.7a there are negative additional delays in almost the complete time-period. This can be seen in other situations, but there only for shorter time-periods. These negative additional delays are mostly caused by the different lockage times. Because of the maintenance done the lockages will now be executed at a different time, this can result in additional delays for some ships, but will be beneficial for others. When comparing the results in figure 9.8 to the results in figure 9.7 it becomes obvious that when there are more ships during the day this results in more additional delays (note the difference in axis limit). This due to the different inter-arrival time of the ships during the day. 62 9.M AINTENANCE AT KREEKRAK

(a)

Figure 9.7: Difference in passage time at Kreekrak when ships are divided equally over day and night

Figure 9.8: Difference in passage time at Kreekrak when there are more ships during the day 9.3.D IFFERENT MAINTENANCE OPTIONS 63

9.3.D IFFERENT MAINTENANCE OPTIONS Besides looking at a single period of maintenance an investigation is done into different scheduling options for maintenance at a lock. Chamber closed at Depending on the type of maintenance it might be possible to do Option 1 10.00-13.00 the maintenance in several shorter periods. Therefore the following 10.00-11.00 options for maintenance are compared to the situation without any Option 2 12.00-13.00 maintenance (exact time periods can be found in table 9.1): 14.00-15.00 1. Closing one of the chambers at Kreekrak for three hours. 10.00-11.00 Option 3 13.00-14.00 2. Closing one of the chambers at Kreekrak three time for one 16.00-17.00 hour, opening the chamber for one hour in between. Table 9.1: The different maintenance options 3. Closing one of the chambers at Kreekrak three time for one hour, opening the chamber for two hours in between.

The different options are used on the exact same ships (same route, dimensions, speed and departure time), so that the passage time of the locks can be compared to the passage time without any maintenance. This is done for the situation where ships are divided equally over the day and night and for the situation where there are more ships traveling during the day.

(a) Ships are divided equally over day and night (b) More ships during the day

Figure 9.9: Passage time at Kreekrak without any maintenance In figure 9.9 the passage time without any maintenance can be found. To see the delays that result from the maintenance, the difference between the passage time with maintenance and without any maintenance is plotted in figures 9.10 and 9.11. This makes it possible to determine how much time is needed for the passage time to recover, meaning the passage time is (almost) equal to the situation without maintenance again. In figure 9.10 it can be seen that for option 1 the passage time has recovered around 15.00, this is two hours after the maintenance is finished (maintenance was done from 10.00 till 13.00). Interesting to see is that for option 2 the passage time has recovered around 15.00 as well, at the exact time maintenance is finished (maintenance was done from 10.00 till 11.00, from 12.00 till 13.00 and from 14.00 till 15.00). In option 3 the passage time doesn’t recover till after 18.00, this is only one hour after the maintenance was finished (maintenance was done from 10.00 till 11.00, from 13.00 till 14.00 and from 16.00 till 17.00). For both options 1 and 2 the additional delays due to the maintenance are in the time-period between 10.00 and 15.00, but the delays in option 2 are lower and more spread out over the time-period. In option 1 the maximum additional delay is higher than it is in option 2. In average delays the different options are equal. Because a peak in delays as seen in option 1 and a long period of hindrance as seen in option 3 are not wanted, it would be better to use option 2.

When looking at the situation with more ships traveling during the day, the differences between the options become more apparent. In ﬁgure 9.11 it can be seen that the additional delays appear in the same time-period for all three options (in the period from 10.00 till 24.00), meaning a long recovery time needed for all options. However, the amount of additional delays in option 2 is much lower than for the other two options. This can be seen in the average delays obtained at Kreekrak as well; these are much lower for option 2 than they are in the other two options. 64 9.M AINTENANCE AT KREEKRAK

Figure 9.10: Difference in passage time at Kreekrak when ships are divided equally over day and night

Figure 9.11: Difference in passage time at Kreekrak when there are more ships during the day 10 OPTIMIZINGTHEALLOCATIONOFSHIPS

If skippers know that huge delays will occur at a lock, then they will try to avoid this lock. This can be done by taking another route, or by simply changing the departure time. Because there are not often different routes between endpoints (or routes with a huge difference in travel-time), only the last case will be taken into account. Of course not all ships can choose their departure time, in these simulation it’s assumed that 25% of the ships have this possibility. As explained in section 6.4 changing the departure time of the ships will result in the model becoming iterative. The process of changing the departure time of ships can be done in different situations. Firstly an investigation is done into the effect in the basis simulation. Secondly the effects are investigated for the situation where there is more trafﬁc. Lastly the situation with maintenance at Kreekrak is investigated as well. When changing the departure time, a constraint set is that there should be an advantage of at least 30 minutes. This means that a ship only changes it’s departure time if the expected travel time indicates an advantage of 30 minutes or more compared to previously best travel time (the best travel time realized for the ship). The expected travel time is calculated using the averages of the different passage times at the objects. Because of this the actual travel time of ships might lie higher or lower than this value. Because the travel time might not be accurate changing the departure time of a ship will not always result in the travel time of the ship becoming lower. The following steps determine the departure time:

• If there is a departure time for which the expected travel time indicates an advantage of at least 30 minutes, then this departure time will be chosen.

• If not: choose the departure time from the departure times already used. The departure time that has the lowest travel time will be used.

With this method it is still possible that a ship changes it’s departure time even though with this new departure time the travel time increases. This can be because the travel time for the ship has grown because of other ships changing their departure time. Another possibility is that the travel time for this ship simply is higher than the expected travel time. (Or that the travel time for the original departure time was lower than would be expected from the travel time function.) This is simply a consequence of the travel time being calculated from averages.

10.1.B ASISSITUATION In the basis situation (the situation used in chapter8; based on data from the IVS90 records for the 17th of November 2015[25]) an investigation is done into changing the departure times of ships. For 25% of the ships the possibility of changing the departure time is investigated, assuming that compared to the original departure time a deviation of maximal 2 hours is possible. When looking at the results, a huge difference can be seen between the situation with the ships divided equally over the day and night and the situation where there are more ships during the day. When the ships are divided equally over the day and night the average delays at locks are not that high (none exceeding 15 minutes). The travel time might ﬂuctuate a bit over time, but it is still stable. As a result changing the departure time of some ships might have a positive inﬂuence on the travel time of the

65 66 10.O PTIMIZINGTHEALLOCATIONOFSHIPS ships changing their departure time, but the effect on the average delays is negligible. This comes partly because only a few ships change their departure time (only seven ships, most traveling between Volkerak and Antwerpen, some between Volkerak and Terneuzen). For these ships the time saved on the route averages at 50 minutes, not taking into account the ships for which the travel time grows (in this case only with a few minutes). In the situation where there are more ships during the day there are some higher values in the average delays at the locks (for Volkerak and Krammer). When changing the departure time of some ships, these extremes become lower, while the other values stay approximately equal. This is partly due to the fact that there are now a bit more ships for which the departure time changes. Of the 13 ships almost all are traveling from Volkerak to Antwerpen; this is due to the additional delays at Volkerak (North toward South) and Krammer (East toward West). These ships save on average approximately 70 minutes on their route, again not taking into account the ship (only one) for which the travel time grows (the travel time increases with 45 minutes in this simulation). These results indicate that there is only an effect when the trafﬁc is not divided equally over the time- period. This is as can be expected as it’s only reasonable to change the departure time of ships, when the amount of ships deviates over time (because as a result the passage time will deviate over time).

10.2.I NCREASEDAMOUNTOFSHIPS The results might become different if the amount of trafﬁc on the waterways grows, therefore the simulation is redone for the case with 30% more trafﬁc on the fairways. Remember from section 8.4 that this means that at Volkerak and Kreekrak the capacity will be exceeded, as a result the delays at these locks might be high.

In the case of ships divided equally over the day and night, the capacity of Kreekrak is exceeded (having average delays just over 30 minutes) whereas the capacity of Volkerak is only just enough (average delays just below 30 minutes). Similar to the basis situation the average delays do not truly improve when some ships change their departure time. There are a bit more ships changing their departure time (now 12 instead of 7 in the basis situation, again almost all on the routes between Volkerak and Antwerpen), they again save 50 minutes on average on their route. Interesting is to look at the two ships that now need more time to travel their route. For the first ship, different departure times were set, one of them resulting in more than two additional hours needed. The additional travel time in the last iteration was only 55 minutes (this is less than 8% of the total travel time on the route). The second ship needing more time after changing it’s departure time clearly shows a case of bad luck. The departure time of this ship is set equal to another ship traveling the exact same route. This other ship, that in the original situation needed approximately the same time to finish the route, takes more than an hour less to finish the route. Most likely the reason for the additional delay for the ship is that with the two ships departing at the same time, they arrive at almost the same time at the lock. If they cannot fit into the lock together, this will result in the ship arriving last to get additional delays as it has to wait for a later lockage. Another possibility is that there is a ship that is carrying dangerous cargo. The rules set for these ships can increase the passage time needed at a lock drastically compared to the passage time needed for a ’normal’ ship.

The simulation done with more ships during the day shows almost the same result. The average delays obtained at Kreekrak and Volkerak (due to exceeding the capacity) cannot be lowered by changing the departure time of ships. However, the delays at Krammer are lowered by the process; all other locks have almost no difference. There are more ships that change their departure time (now 30 instead of 13 in the basis situation) and they still save on average 70 minutes on their route. This average doesn’t take into account the three ships that now need more time to travel their route. One of these three ships departs now on the same time as another ship on the same route (that ship has less travel time because of it). The reasons for one of the two ships having a higher travel time while they depart at the same time was explained before. The other two ships that need longer to ﬁnish their route, are departing at the same time and follow the same route. They only shift their departure time with 5 (10) minutes, but as a result need 25 (45) additional minutes to ﬁnish their route. This is most likely due to the other ships that need to pass the lock as well. Due to all ships that have changed their departure time, these ships now arrive at a lock at a time that it will take longer to pass the lock. This can be based on the amount of ships at the lock at that time, or because of a ship carrying dangerous cargo. If a ship needs to be locked without any other ships, this will result in high passage times for this lock. 10.3.M AINTENANCE AT KREEKRAK 67

10.3.M AINTENANCEAT KREEKRAK When there is a short period of maintenance you want less ships to arrive during this period. If the maintenance is known, this might be possible (by communicating this maintenance to skippers). The method of changing the departure time of ships is applied to this situation to simulate this. The maintenance will take place between 12.00 and 14.00, during that time-period only one chamber will be available at Kreekrak. When the ships have been divided equally over the day, there are not that much delays (when looking at the averages). The average delays at Kreekrak are a bit higher, but still not extreme (now 20 minutes instead of the 10 minutes in the basis simulation). Similar to the basis simulation, these average delays cannot be lowered much by the simulation. The ships that do change their departure time loose a lot of travel time, on average 70 minutes, there is even a ship with over 4.5 hours less travel time. When there are more ships during the day, the delays obtained at Kreekrak become higher, starting at 45 minutes up until 75 depending on the run and direction looked at. In this case it’s possible to lower these delays seen at Kreekrak (by 10-20 minutes). The delays seen at the other locks have increased slightly from the situation with the ships divided equally over the day. Changing the departure time of the ships makes it possible to lower these delays till they are approximately the same as they where in the situation with the ships divided equally. For the ships that change their departure time a decrease of the travel time is seen of approximately 60 minutes. The reason for this value being lower than the situation with ships divided equally over the day and night is that there are less extremes. In previous case there was a ship saving 4.5 hours (with ships divided equally over the day and night), now the maximum decrease in travel time only just exceeds 2.5 hours.

10.4.I NCREASING DELAYS Even though changing the departure time is done to reduce the travel time needed, this might not always be the result that is obtained. Another possibility is that by changing the departure time of some ships, the travel time of these ships decrease, while the average delays at locks still increase. The reason for this is that by changing the departure time of ships, the order in which the ships arrive at a lock is changed (and the time at which the ships arrive changes as well). As a result it might not be possible anymore to lock all ships (for instance because there is too much time between two ships or because it simply doesn’t ﬁt within the lock). If a ship cannot be locked immediately this will result in delays as it has to wait for the next lockage. This shows that a method can give an advantage to some ships, but will not necessarily result in less delays for all ships (or even less average delays).

CONCLUSION

Rotterdam Volkerak or other In this chapter the results obtained destination from the simulations with the mesoscopic model are summarised. First Zandkreek Krammer the conclusion about capacity usage of the locks is given in section 11.1. Sec- ond the conclusions found when sim- Kreekrak Veere ulating maintenance at Kreekrak are Hansweert given in section 11.2. Third the conclusion about the sub-chambers is given

Vlissingen in section 11.3. Lastly the conclusion about optimizing the allocation of Antwerpen ships is given in section 11.4. Once the results of the simulations Sea Terneuzen Gent have been summarised the contribution obtained from this research will be summarised as well in section 11.5. Figure 11.1: The locks in the mesoscopic model

11.1.C APACITY USAGE OF LOCKS

In the current situation most of the Increase possible with Increase possible with Lock locks have not yet used all their ca- ships divided equally more ships during the day pacity. From the simulations ex- Volkerak 35% 15% plained in section 8.4 (results are Kreekrak 25% 0% summarized in table 11.1) it can be Krammer More than 50% seen that the amount of ships can Hansweert even be increased by 50% with respect to the basis simulation with- Table 11.1: Increase of ships possible when accepting a 30 minute delay out the delays at Krammer and Hansweert becoming much higher. However, at Volkerak and Kreekrak it’s not possible to increase the amount of traffic that much. The increase these locks can handle depends on how the traffic is divided. When the traffic is divided equally over the day and night, the delays are much lower than when there is more traffic during the day. When accepting a delay of 30 minutes, the increase possible at Volkerak is 35% when the traffic is divided equally over the day and night, but only 15% is possible when there is more traffic during the day. At Kreekrak the capacity is fully utilized earlier; when there are more ships traveling during the day there are already delays of 30 minutes in the original situation, when the ships are divided equally over the day and night then a 25% increase is possible. This difference in capacity means that when traffic does increase, it’s important to look at methods to spread the traffic over day and night, thereby lowering the delays.

69 70 11.C ONCLUSION

11.2.K REEKRAK Within the practical case, the Kreekrak locks hold an important position. There are two routes going between Volkerak and Antwerpen, the shortest of the two routes goes over Kreekrak. Ships that have a height of over 9.1 meter cannot take this route because of the fixed bridges on the route, and must take the second route; passing the Krammer and Hansweert locks. This route takes approximately two additional hours to travel. (And additional time might be needed to pass locks within Antwerpen, Berendrecht or Zandvliet, those were not included in the mesoscopic model.) This means that under normal circumstances ships will not take the route over the canal through Zuid-Beveland if they can use the Schelde-Rijn connection as well. However, when something happens at Kreekrak, for instance some type of maintenance, it might become interesting to take the second route. In order to investigate this several simulations were executed using the mesoscopic model. First the situation where one of the chambers is unavailable for the complete duration of the simulation is investigated. This situation has already happened in reality, when in 2015 the lock was adapted so that it can be operated remotely. In this period first one and then the other chamber was adapted during which time the chamber could not be used by vessel traffic. Second the situation in which one of the chambers is unavailable for a shorter time period (up until 6 hours) is investigated, mainly in order to determine the effect on the delays. Lastly three options for maintenance are compared (either closing the lock once for a longer time-period, or closing the lock several times for a shorter period). This is done to see if there is a difference in the amount of delays obtained for these options, and if so which option would be best to use.

11.2.1.C HAMBERCLOSEDTHEWHOLEDAY When one of the chambers at Kreekrak is closed for a complete day, the effect on the delays is enormous. Delays up until 10 hours (even 13 hours when there are more ships during the day) can be seen. Even when looking at the average the delays are still enormous, on average there was a delay of 3 hours, growing to 5 hours when looking at the situation with more ships during the day. The queues of ships waiting at the lock is constantly growing, until the point where no more ships are generated within the simulation. This shows that there is simply not enough capacity at Kreekrak to lock all ships with only one chamber. The different passage times and the delays obtained at Kreekrak can be found in table 11.2, a huge difference is seen between the situation with two and the situation with only one chamber available. Number of Maximum Situation Average delay chambers available passage time Ships divided equally Two One hour 15 minutes over the day and night One 10 hours 3 hours Two Two hours 20 minutes More ships during the day One 13 hours 5 hours

Table 11.2: Delays seen at Kreekrak With these delays at Kreekrak it might become faster to travel over the canal through Zuid-Beveland, assuming that it’s possible to pass the Berendrecht or Zandvliet locks in less than 3 hours. This rerouting is exactly what was advised when one of the chambers was unavailable for a period of time in 2015.

11.2.2.S HORTMAINTENANCE Average delays at Kreekrak (min) It’s possible that one of the chambers needs Ships divided equally More ships to be closed for a shorter time-period (sev- over the day and night during the day eral hours). From investigation reported Basis situation 18 22 in section 9.2 some interesting results were Chamber closed obtained. For the really short maintenance 20 22 for one hour (up to 3 hours), a small difference is seen between the situation where ships are di- Chamber closed 26 27 vided equally over the day and night and for two hours the situation where there are more ships Chamber closed 34 34 during the day. The additional delays due for three hours to closing the chamber are not affected by Table 11.3: Delays at Kreekrak when chamber closed for 1, 2 and 3 hours the way the ships are divided over the day and night. 11.2.K REEKRAK 71

When comparing the average delays at Kreekrak (seen in table 11.3) this becomes even clearer. With both chambers being open during the whole day, there is a difference of approximately 4 minutes between the average delays in the two situations (ships divided equally and more ships during the day). When closing the chamber for 1, 2 and 3 hours this difference becomes less until the average delays of the two situations are equal.

Average delays at Kreekrak (min) This is not true when closing the cham- Ships divided equally More ships ber for a longer time-period (2, 4 or even over the day and night during the day 6 hours). To investigate these situations, Basis situation 17 18 another simulation is done separately from Chamber closed the simulation used to investigate closing 15 34 for two hours the chamber for 1, 2 and 3 hours. The maximum delays are almost twice as high for Chamber closed 24 51 the situation where there are more ships for four hours during the day compared to the situation Chamber closed 39 66 where ships are divided equally over the for six hours day and night. These effects occur not only Table 11.4: Delays at Kreekrak when chamber closed for 2, 4 and 6 hours in the delays over time, but also in the average delays at Kreekrak for the whole day. The average delays can be seen in table 11.4, because simulations are done separately the basis situation is slightly different from the basis situation in table 11.3. The average delays in the situation with more ships during the day are almost twice as high as the average delays seen in the situation with ships divided equally over the day and night.

11.2.3.D IFFERENT OPTIONS FOR MAINTENANCE Depending on the type of maintenance that needs to be done it might be an option to schedule several shorter time-periods instead of one larger period. To see the effect of separating the maintenance in several smaller time-periods three options for closing a chamber are simulated. The result of these simulations is explained in section 9.3 and a summary can be found in table 11.5. Ships divided equally More ships during the day Chamber Maximum additional Average Maximum additional Average closed at delays (min) delays (min) delays (min) delays (min) Option 1 10.00-13.00 70 22 80 50 10.00-11.00 Option 2 12.00-13.00 60 23 60 40 14.00-15.00 10.00-11.00 Option 3 13.00-14.00 50 22 90 49 16.00-17.00

Table 11.5: The different maintenance options First the three options are simulated in the situation where the ships are divided over the day and night equally. There is not much difference seen between the three options, all resulting in almost the same average delays. When looking at the way the delays are spread over the day, option 2 would be preferred because the delays are spread only over a small time-period without having large peaks. Looking at the situation with more ships during the day, there are more differences between the options. The maintenance done results in additional delays obtained within the same time-period, in all three options. However, in the options 1 and 3 the additional delays are much higher compared to the additional delays seen when implementing option 2. This can be seen in the average delays as well; in the second option they are much lower than in the other two options. 72 11.C ONCLUSION

11.3.S UB-CHAMBERS When there are sub-chambers located at a lock, this results in less time needed for a lockage (as there is less water that needs to be moved). Because of the water-level, there always need to be two lockages after another with a sub-chamber. This can be two times the same sub-chamber, or once in either sub-chamber.1 In the basis simulation a check was added to determine if using the sub-chamber is possible, more explanation about this check can be found in section 8.1. This check shows that it’s almost never possible to use one sub-chamber twice. It is not possible to add a check for using both sub-chambers after another, instead of using the complete chamber.

Number of locks Number of chambers 309 355 OCCURRENCEOFSUB-CHAMBERS Chambers having a sub-chambers Important to realize is that sub-chambers do not oc- Has a sub-chamber? Number of chambers cur that often. Not all locks have a chamber with sub- Yes 33 chambers, or if they have, only one of their chambers has No 322 sub-chambers. The amount of sub-chambers within the Locks having a chamber with sub-chambers Netherlands can be found in table 11.6, it can be seen that Has a sub-chamber? Number of locks sub-chamber are only available at locks in less than 10% of Yes 31 the locks. This indicates that including the sub-chambers No 278 in the mesoscopic model might not be necessary.

Table 11.6: Amount of sub-chambers in the Netherlands2

11.4.O PTIMIZINGTHEALLOCATIONOFSHIPS When traveling on the road there are situations when choosing a different route will result in less travel time. On the fairway there are not often two routes, because the fairways a ship is allowed to use can be restricted by the size of the ship. When there are multiple routes there is often a huge difference in travel time between the routes. However, for some ships it might be possible to choose a different departure time. This makes it possible to spread ships over the day more equally, reducing the delays obtained at the objects (locks and bridges). From the simulations explained in chapter10 it can be concluded that this approach can result in less delays. The ships that change their departure time can save between 50 and 70 minutes on their route taken in the mesoscopic model. The exact advantage for the ships can be different; there are ships that can save more than 4 hours and ships that need the same time to travel their route. It is possible that some ships even need more time for their route; because the departure time of ships is changed the order ships arrive in is different as well. This can lead to more time needed at a lock than was expected when scheduling the departure times (based on calculated travel times the best departure time was determined). Changing the departure time of some ships will not always result in less average delays. Looking at the simulations done it can be seen that the process of changing the departure times can remove extremes from the average delays. Whenever (one of) the average delays show a higher value than seen in other simulations, this value can be reduced by changing the departure time of some ships. However, this does not mean that all extreme delays can be removed by changing the departure time of ships. Looking for instance to the simulations done with more traffic (using 30 % more traffic than seen in the basis simulation). In this situation the capacity of both Kreekrak and Volkerak is exceeded, resulting in high delays at these locks. The delays at Kreekrak and Volkerak cannot be lowered much by changing the departure time of some ships. However, when one of the other locks has a significant delay, that delay can be lowered.

1When there are sub-chambers, most of the time there are are only two sub-chambers. It is possible to have three or even more sub- chambers. In this report only the situation of two sub-chambers is explained, because within the practical case only the situation with two sub-chambers occurs. 2Determined from ViN (Vaarwegkenmerken in Nederland) 11.5.C ONTRIBUTION 73

11.5.C ONTRIBUTION The research goal set for my graduation project is to define a model that can simulate the traffic on fairways and use this model to optimize the allocation of this traffic. With the defined mesoscopic model a basis has been made for simulating fairway traffic. To achieve my research goal I have investigated the existing traffic models. This way a model was found that could be extended to fairway traffic, the mesoscopic model. The original mesoscopic model was adapted such that it can model fairway traffic. Within the mesoscopic model there is a possibility to incorporate a more detailed microscopic model for the objects (locks and bridges). Several microscopic models were defined for the locks and bridges. Optimization models were set up based on previous work done into lock modeling.[13] However, optimization models cannot include all rules used in reality; this makes heuristic models more efficient. For bridges the optimization model can be defined starting from the lock optimization. This optimization model can determine what the best time to open a bridge is. In the case of bridges the situation decides which model is best to use. When no information is available, the best result comes from an optimization model. Some bridges have fixed opening times; simply using this schedule gives the same result in less time.

I have implemented the mesoscopic model on a practical case in Zeeland. Using simulations of this model it is possible to gain insight into several elements:

• Give a value to the efﬁcient use of objects when trafﬁc is spread over the day and night equally.

• Effect of different situations that can occur when maintenance reduces the capacity of the network.

• Effect of stimulating skippers to travel at a time when there is less trafﬁc, optimizing the allocation of trafﬁc.

V DISCUSSION

12 RELIABILITY OF RESULTS

It’s important to investigate the reliability of the results that are obtained from the simulations. Therefore the reliability of several aspects of the model will be discussed here.

12.1.O BJECTMODELS Some choices were made in deﬁning the object models, for instance the choice between using an optimization or a heuristic method. A comparison will be given here of the different methods that can be used, their advantages and their disadvantages.

12.1.1.L OCKMODEL Within the lock model two separate models are combined. The time-dependent part of the model determines when the lockages take place and which ships will be within each lockage. The second part determines the place of each ship within the chamber.

TIME-DEPENDENT PART There are three possible models for finding a solution to the time-dependent part of the lock model. The first possibility is an optimization model, this optimization model is explained in section 4.2.1. The second possibility is a double optimization method, explained in section 4.2.2. The third possibility is a heuristic method, explained in section 4.2.3. This third method is implemented in the mesoscopic model. The main disadvantage of both the optimization and the double optimization method is that they cannot include the First Come First Sever (FCFS) rule as it is currently used. In reality the ships are locked based on their arrival time. However, if a ship cannot join a lockage (due to size or cargo constraints) the ship arriving after it is allowed to join the lockage. In the optimization model this exception cannot be added, resulting in either a strict FCFS or none at all. Both situations do not simulate the reality. In the double optimization model there is a different FCFS applied. Here a reordering of ships is allowed, but there is a limit to the disadvantage a ship can have from this reordering. Similar to the optimization this does not simulate the reality. With the heuristic method it is possible to include the FCFS as it is currently used. Because this is one of the main characteristics of the traffic at locks this method can better simulate the reality. This is seen in the basis simulation explained in chapter8, where the delays obtained using the heuristic method equal the delays seen in reality.

PLACEMENT The placement method used within the mesoscopic method is one that has been investigated in a dissertation about lock scheduling methods.[13] Within this dissertation a heuristic (multi-order best fit) has been developed that can find a placement for ships with an accuracy of over 99%. The solutions obtained from an optimization (it is possible to determine an optimization method that can find the best placement) can be more difficult to check for lock operators. This combined with the stable calculation time of the heuristic method result in the conclusion that it is better to use the heuristic instead of the optimization.

77 78 12.R ELIABILITY OF RESULTS

Within in the VCM trafﬁc planner similar choices are made. For the time-dependent part a heuristic (based on rules originating from SIVAK) is used and for the placement of ships the multi-order best ﬁt heuristic is used.

12.1.2.B RIDGEMODEL There are two methods possible for modeling traffic at moveable bridges. The best method to use depends on the information available about the bridge. When no scheduling information is known about a bridge, the best (and only) method to use is an optimization. This optimization, explained in section 4.3.1, can find the best time(s) at which to open this bridge. It determines how late a bridge will open, and which ships can pass the bridge at that time. For some bridges a schedule has already been set, in this case using an optimization is not useful. Instead use the set schedule; ships will pass the bridge the first time it opens after the ship has arrived.

12.2.D ANGEROUSCARGO When looking at the rules set for dangerous cargo in section 4.2.5 there are still some points where the model can deviate from the way the rules are implemented in reality. For instance concerning the ships having a certiﬁcate, the law states the following ([21] artikel 3.14 zevende lid):

Een schip, dat in het bezit is van een certiﬁcaat van goedkeuring, als bedoeld in het ADN, nr. 8.1.8, en dat voldoet aan de veiligheidsvoorschriften die gelden voor een schip als bedoeld in het eerste lid, mag, indien het gelijktijdig met een schip, dat de tekens bedoeld in het eerste lid moet voeren, wil worden geschut, bij het naderen van een sluis, de tekens bedoeld in het eerste lid voeren.

This has been implemented literally in the model: a ship that has such a certiﬁcate, can choose to carry a cone even though it’s not carrying cargo that makes it mandatory to carry this cone. When the ship doesn’t carry a cone, it’s seen as a ’normal’ ship and needs to follow all rules set for these ships. However, when it does carry a cone it’s seen as a ship carrying dangerous cargo and therefore has to follow all rules for these ships. The question is how this is implemented in reality, it’s possible that instead of truly having to carry a cone, the ship is simply allowed to join a lockage that a ’normal’ ship is not allowed to join (but a ship with a cone, and therefore a ship with a certiﬁcate, is allowed). If this is the case this does change some elements when considering other rules. [21]

Op een wachtplaats van een sluis en in een sluis moet een schip een zijwaartse afstand van ten- minste 10 m in acht nemen ten opzichte van een schip of een samenstel dat het teken bedoeld in artikel 3.14, eerste lid, voert. Deze verplichting geldt evenwel niet voor een schip of een samenstel dat eveneens dit teken voert, alsmede voor een schip bedoeld in artikel 3.14, zevende lid.

When implementing this rule the two versions explained above will give different results. If the first method is used (ships actually need to carry a cone), then the ships can be split into two groups. The ships that do carry a cone, and the ships that don’t. The ships that have a certificate need to choose in which group they belong. Between the two groups a distance of 10 meter needs to be kept, within each group the ’standard’ safety distances need to be satisfied. With the second method (no cone is necessary for the rule to apply) the ships can be divided into three groups. The ’normal’ ships, the ships carrying a cone and the ships that have a certificate. Now only between the first two groups there needs to be a distance of 10 meter, the ships with a certificate just need to satisfy the ’standard’ safety distances toward all other ships. Within the mesoscopic model the first method has been implemented, using the rules literally. 12.3.B RIDGES AT LOCKS 79

12.2.1.S UB-CHAMBERS The rules set for ships carrying dangerous cargo give another application for the sub-chambers located at Volkerak and Terneuzen. Instead of executing one lockage in the complete chamber, another possibility is to execute two lockages; one in each sub-chamber. The advantage in this is that now there are two separate lockages, meaning it will be easier to satisfy all rules set for ships carrying dangerous cargo.

12.2.2.E FFECT OF QUANTITY OF SHIPS CARRYING DANGEROUS CARGO In section 8.3 an investigation was done into the effect of changing the amount of ships that are carrying dangerous cargo. However, the percentage of ships carrying dangerous cargo is not that high (only 6% divided over three categories). Because the ships carrying dangerous cargo are chosen randomly, this low amount has a high inﬂuence. Where there could be several ships carrying dangerous cargo passing a lock in one simulation, there can be none in another simulation. This randomness is seen in the results of the simulations done. Even when averaging over ﬁve simulations, there is no pattern in the results. A larger simulation should be done to see the effects of changing the amount of ships carrying dangerous cargo. For instance modeling a week, or even several weeks within a simulation. An investigation should be done into the ships carrying dangerous cargo as well. Do these ship travel along all possible routes, or are there routes on which the percentages are higher or lower than average? Giving an answer to these questions might make it possible to remove some of the randomness now seen.

12.3.B RIDGESATLOCKS It can be investigated how often the bridges located at the locks need to be opened. However, the results determined in section 8.2 depend on the heights set for the different ships. This information was obtained based on IVS data, in this data the heights are rarely given.[25] Better information about the ship sizes is needed to obtain a reliable result about the opening of bridges at the locks (over or close to the gate).

12.4.T ERNEUZEN The locks located at Terneuzen cannot be modelled correctly with the model as it is now. There are several reasons for this. A first reason is that whereas the model is focused at inland navigation, the locks at Terneuzen are heavily used by seagoing vessels. This means that there are larger ships using this lock compared to the other locks in the model. Some of these ships might be bound to a tide slot, when their draft is such that they can only travel into the harbour and through the lock when the water level is high enough. A second reason for the locks not being modelled correctly is that depending on the water levels some of the chambers might be needed to let water through toward the sea (flushing), resulting in this chamber not being available for locking ships during that time. The third and last reason is that the BPR[21] is not valid for this lock. Instead there has been made a different set of regulations for the canal from Gent to Terneuzen; these regulations are valid for the locks of Terneuzen. As a result there are different rules for this lock when handling ships carrying dangerous cargo, the differences between the regulations are explained further in appendixF. Because of these differences from the model the results obtained for the locks at Terneuzen will not come close to the situation in reality. This can be seen in the results of the basis situation explained in chapter8. Instead of the 25 minutes average delays seen in reality, there is only an average delay of 5 minutes. The first reason can be removed by adding ships of a different size on the routes used often by seagoing vessels. How- ever, in order to remove the second reason, the model should include water levels, this was outside the scope of this graduation project. Due to the unreliability of the results in the basis situation, no further investigation was done into the locks of Terneuzen (such as capacity investigation). 80 12.R ELIABILITY OF RESULTS

12.5.C ANALTHROUGH WALCHEREN Along the canal through Walcheren compared to the other fairways, there can be more recreational traffic. As this traffic is not taken into account this means that the results for this part of the network can deviate from the truth. Because the locks located on this route are small the ships can obtain large delays (it is not possible to lock two ships at the same time). However, this route is not heavily used by commercial traffic, a reason for this is the possibility of high delays on this route. Instead of passing one lock and two bridges (when using the canal trough Zuid-Beveland) with this route three locks and five bridges have to be passed. Because of this there is a higher change of obtaining delays, what can result in skippers choosing another route. This unreliability can be seen in the results obtained from the basis situation; at some times the passage time doubles compared to the ’normal’ passage time.

12.6.H UMAN BEHAVIOUR A reason some of the delays at objects will be higher than they are in reality is that in the model human behaviour is not taken into account. The blocked times of a bridge are known, therefore it would not often happen that ships have to wait for 25 minutes at a bridge. In these instances a ship would (if possible) simply increase its speed, so that it can make the previous opening of the bridge (by arriving 5 minutes earlier). If increasing the speed is impossible, then the speed of the ship will most likely be lowered to the speed that is the most energy efﬁcient for this ship. In both cases the delay that is obtained at the object decreases. Another part of human behaviour is the speed in which ships can execute several actions. For instance in the case of entering or leaving the lock; while some ships can do this quickly others might need more time. 13 PARAMETERSCHOSEN

The results of the model depend on the parameters chosen for the practical case in Zeeland, they can be found in appendixB. In order to deﬁne these parameters different sources where used in order to set the values accurately.[17, 18, 24] Luckily a lot of people at Rijkswaterstaat were open to help determining the parameters needed, either by giving the exact parameters or by directing me to the right source. For the different parameters an explanation of the method used for deﬁning this value is given here.

13.1.S IMULATION PARAMETERS To run the simulation, there are some parameters that need to be set. The number of time steps and time step size can be changed depending on the situation on which the simulation is run. In the simulations done (explained in chapter6) the time step size was set at 5 minutes, with the maximum amount of time-steps being 600. This makes it possible to continue simulating for up to 50 hours. However, ships are only added to this model within the ﬁrst 24 hours. When all ships have ﬁnished their journey, the simulation is stopped, therefore this high number of time-steps doesn’t hinder the model. The horizon decides which ships to take into account in the object models; currently the horizon is set at 60 minutes. The lock model is done every 20 minutes(once in 4 time-steps). This means that a schedule is made with all ships arriving in the following 60 minutes, but this schedule is updated after 20 minutes.

In the object models described in chapter4 there are parameters that need to be set. For instance when using the lock heuristic, values must be set determining how long to wait on ships. These values, as well as other parameters used in the object models have been deﬁned based on several simulations. The values for the parameters chosen are those that gave the best result, when looking at the delays obtained at the objects. The values set for the lock heuristic can be found in table B.2. When simulating bridges some parameters are needed as well; for instance the time needed for opening and closing the bridge. The values used to simulate the bridges can be found in table B.3.

13.2.F AIRWAYS On the fairways several values have been defined that are fixed, these are the length of the fairway and the maximum speed that is allowed here, these values have been determined as exact as possible.1 The average travel time used in finding the expected arrival time of ships is calculated using an average speed of 15 km/h. To make sure this travel time is an overestimation of the actual travel time an additional 5 minutes is added (15 minutes on the longer edges). The travel time needs to be an overestimation to make sure that a ship actually arrives before it’s scheduled to be locked.

1Different sources are used to determine the distances. Where possible using the route points denoted in ViN[24], this is only possible if the endpoints are deﬁned on the same route(for instance both on the canal through Walcheren). Where needed adaptions where made using a route planner for fairways to ﬁnd the distance between points[26]. Maximum speeds on the waterways are set by law and are extracted from this law.[27]

81 82 13.P ARAMETERSCHOSEN

13.3.L OCKS For the locks there are several parameters set. Most important are the size of the lock chambers, and the size of the ships that are allowed to use each chamber. This information is extracted from a database ViN[24]. Besides these values, the time needed for a lockage is determined. This time is in reality dependent on the water level, but a good approximation is 10 minutes for changing the water level. When there needs to be done a separation between freshwater and saltwater this adds an additional 10 minutes. In the practical case this is only needed at Krammer. There needs to be time for the opening and closing of the lock gates, this takes about 2 3 minutes. This averages at 5 minutes for both opening and closing of the gate. These values − lead to the values found in table B.6.

13.4.B RIDGES Besides the simulation parameters used for the bridges, also the dimensions of the bridges need to be included in the model. These dimensions are recorded and have been used for simulating the practical case. A bridge can give a height, width and draft restriction for ships passing it. Combined these restrictions de- ﬁne the clearance of a bridge. Height, width and draft restrictions that result in a ship not being able to pass a bridge are taken into account in the dimensions allowed on the fairway. This is done such that any ship entering a fairway can actually pass all objects on the route it takes. For the bridges (only moveable bridges are denoted here, for further explanation see section 4.1.2) the most important value is the height because this value determines whether or not the bridge needs to open for a ship to pass it. The dimensions of each bridge are denoted in table B.8. Within this table the draft is not given, because the draft at the bridge does not limit the draft possible on the fairway. All bridges in the practical case have ﬁxed opening times. Only in exceptional circumstances will the bridge open outside of these periods. These time-periods are given in table B.9. Both the information about the clearance of the bridge and the opening-times (block-times) are extracted from the ViN database[24].

As there are several bridges close to another in Vlissingen and in Middelburg, these bridges will be com- bines into one ’bridge’. The height of this bridge is deﬁned as the height of the lowest bridge. The passage time needed is determined from the opening times of the separate bridges. The merging of the bridges and the corresponding passage time calculated is only valid for the ships that need all bridges to open. With the combination of the height of these bridges and the dimensions of the ships currently used (more explanation about the ship dimensions will be given in section 13.5) every ship needs all bridges to open. Therefore this merging of the bridges will not result in any inaccuracies.

Also at the locks some bridges are located; the opening of these bridges is dependent on the schedule of the lock. However, the height of these bridges is known and used to determine whether or not it’s needed to open the bridge. The heights of the bridges can be found in table B.11.

13.5.S HIPS In order to model ships several values need to be defined for each ship. First the speed of ships is set between 12 and 18 km/h. The dimensions of the ships are defined based on the IVS90 records obtained at Volkerak.2 Most of the inland navigation ships need to pass Volkerak, in the simulations done over 60% of the ships has Volkerak either as origin or destination. The number of ships traveling between endpoints is defined such that the amount of ships passing each lock is approximately equal to the amount of ships passing the lock in the IVS90 records. For ships carrying dangerous cargo some values need to be set. There are percentages used, that is used to assign this dangerous cargo to random ships. The percentages used (can be found in table B.13) are similar to the ones used in a previous investigation into the traffic at Krammer and Kreekrak.[17]

2The IVS90 records for the 17th of November where analysed to gain insight in the current situation for the locks. The records contain information about the time lockages take place, which ships are contained in them and how much time they have waited before being locked. Also dimensions of the ships, origin and destination of their journey and even some information about the cargo they are transporting can be found in the record. 14 FURTHERRESEARCH

There are some elements that can further improve the model, during this work not enough information and/or time was available to implement those elements.

14.1.R ELIABILITY Besides the time needed for traveling over a route the reliability of this route is important as well. A route with a higher expected travel time, but a low chance of additional delays, might be preferred over a route with a lower expected travel time and a high chance of additional delays. This because the arrival time is now known with more certainty (although it might be slightly later). In order to use this it is needed to determine the chance of additional delays. These additional delays can come from different sources. For instance because overtaking a ship having a lower speed is not possible. Any delays that are obtained might result in a ship not being able to make the lockage it was scheduled in. For instance because the lockage has already taken place before the ship arrives, or due to another ship that now arrives at the lock earlier. Because of the First Come First Serve (FCFS) constraint this other ship will be included within the lockage instead (assuming this ship can join the lockage). This can further increase any delays already obtained by the ship. More investigation needs to be done to ﬁnd out all parameters needed to implement this. In order to accurately give the reliability of the travel time several elements of the model should be made stochastic. This means that for all parameters now set constant, an investigation should be done to see if this value is truly constant or if it’s in reality a stochastic value (this way including the possible delay).

14.2.S UB-CHAMBERS A check was made in the model to include the possible use of sub-chambers. With this check it was possible to determine that it’s almost never possible to lock with one sub-chamber twice. However, there is another possibility; using first one sub-chamber and then the other, both in the same direction. When using both sub-chambers after another, this means that a lockage with the complete chamber is separated into two smaller lockages. As a result there might be more ships within the lockage (an additional ship can now join the second lockage), or there can be less ships within the lockage (by separating into two parts, there are now less ships that fit within the space). Because the amount of ships joining the lockage is not known, it’s not possible to add a check to determine if this specific use of sub-chambers is possible. It’s possible to take the usage of sub-chambers into account within the model. Instead of always doing a lockage in a complete chamber, now lockages are done either in the complete chamber, or in one of the sub- chambers (the water level decides which sub-chamber can be used). In order to make a model that can decide which choice to make, more information should be collected. For instance the time needed for a lockage in a sub-chamber, and the rules set to determine whether to lock in the complete chamber or in a sub-chamber. It should be investigated how often these sub-chambers are used. When the sub-chambers are almost never used in reality, modeling the sub-chambers is not very useful.

83 84 14.F URTHERRESEARCH

14.3.F IRST COME FIRST SERVE Loosing the First Come First Serve (FCFS) rule could result in the average delays being lower. A reason for relaxing the FCFS rule lies in the situation where the chambers of a lock have different sizes, you want to use these chambers optimally. With the FCFS rule it could happen that a "small" ship is locked in the largest chamber resulting in a huge delay for the larger ship arriving after it. This ship will now have to wait until the chamber has returned to this side again. In practice you would want the ships that can only travel through one of the chambers to get a priority at this chamber. In the practical case chosen the different chambers have equal size, but there are bridges situated over some of the chambers (at Volkerak and Krammer). Because only one of the chambers has a moveable bridge, all high ships have to travel through this chamber. In the simulation if is seen that there are only a few ships for which the bridge actually has to open, therefore making this idea not useful to implement.

Even without differences between chambers there can still be an advantage when loosing/relaxing the FCFS constraint. Reordering the ships can make sure that the space within the chambers is used more optimal. However, this can give a disadvantage to some ships (mostly the larger ones) because they will now be scheduled later (to make room for smaller ships that can ﬁll the chamber more optimally). This idea of reordering is not yet accepted, and has therefore not been included in the model. By implementing the loss of FCFS into the model it might be possible to give a value to the advantage of loosing the FCFS constraint. This might then become the reason for accepting the reordering of ships.

14.4.T IDES, CURRENTSANDWATER-LEVEL An important factor in a network of waterways is the water level (for instance caused by the tides). Depending on the water-level some ships might not be able to use a fairway (because there is not enough draft) or they might need a bridge to open (due to the water-level being high). The water-level inﬂuences the time needed for locking because this time is dependent on the difference in water-level between the two sides. The tides not only inﬂuence the water-level, they also introduce currents that might slow down some ships. When including the tides within the model, it is important to include the restrictions that might be valid for some ships. Some ships might not be able to pass a lock at all times due to the water height included. In reality this can lead to less ships arriving at a lock when the water-level is low. For instance because a ship cannot pass the lock at all or because the ship cannot travel along the fairway (before or after the lock) with this water height. An investigation should be done into the restrictions resulting from the water level and the arrival patterns seen at the different objects (locks and bridges).

14.5.H UMAN BEHAVIOUR Something that has not yet been taken into account in the model is human behaviour. Depending on the situation a skipper might speed up or slow down, instead of traveling on the same speed (now a ﬁxed speed is used). This makes it possible for a skipper to speed up in order to arrive at the lock on time for the lockage. Another possibility is that a skipper slows down when it is already clear the ship will not arrive at an object on time (can be a lock or a bridge). Slowing down to the most energy-efﬁcient speed reduces the time a ship spends waiting at an object. Not only when traveling over the fairway, but also at the objects human behaviour is a factor. Not every ship will need the same amount of time to travel into or out of the lock. The time needed is depended on the ship, but can also depend on the combination of the ship with the chamber (size of the ship compared to the size of the chamber).

Besides the skippers, the lock operators show human behaviour as well. When using the heuristic lock model, there is a limit set for how long to wait on ships that still have to arrive. Implemented this limit is strict, whereas in reality there is some ﬂexibility used. Whenever a ship arrives just after the set time limit, a lock operator can decide to wait on this ship. Similar even if a ship arrives within the time limit, it is still possible for the lock operator to exclude the ship from the lockage. The decision of whether or not to wait on ships that still have to arrive is a complex one. More investigation should be done into the factors inﬂuencing this decision. 14.6.W AITINGBERTH 85

14.6.W AITINGBERTH A journey can not always be completed in one time, instead it might be separated into two or more parts. Depending on the crew on a ship it might be allowed to complete the journey in one time (working in shifts), or the ship might not be allowed to travel during the night. In this case the ship can decide to wait at a berth, in order to give the crew the demanded rest (or even to stay the night there). It’s decided by law whether or not a ship is allowed to continue 24/7 or is required to rest for several hours (or even a whole night). These waiting times can not yet be taken into account, instead several journeys should be created for such a ship. The rules set for the waiting time result in some ships traveling 24/7, while others only travel during the day. Looking back to the two situations investigated in the simulations: ships divided equally over the day and night or more ships traveling during the day. The ﬁrst situation would only happen if all ships where traveling 24/7, the second also incorporates the ships demanded to rest during the night (therefore traveling only during the day). The demanded waiting times have a huge inﬂuence on the journey of some ships. Therefore this can be a useful addition to the model. In order to include this in the model information needs to be gathered on the exact rules set (and how many ships there are that need to satisfy them). For all berths the exact place needs to be determined as well; along with the ships that are allowed to use this berth.

14.7.R ECREATIONAL TRAFFIC Recreational traffic has not been taken into account in the mesoscopic model defined. At locks they can have an influence on the delays obtained by other ships. Some locks have separate chambers dedicated solely to recreational traffic. If this is the case only ships that cannot use these chambers (for instance due to limitations to the size of ships allowed to use the recreational chamber) will need to be locked in the chambers used for commercial traffic. Unfortunately not all locks have such a chamber. When no separate chamber is available all recreational traffic will use the same chambers as the commercial traffic. The recreational traffic can be taken into account by reserving a percentage of the chamber for recreational traffic. This is implemented by lowering the percentage of the chamber allowed to be used by the commercial ships (now all ships in the mesoscopic model are commercial ships). Another possibility would be to include recreational traffic within the mesoscopic model. To be able to include recreational traffic more investigation should be done. The recreational ships will not follow the same patterns as the commercial ships, because of this information specific to recreational traffic should be gathered. What should be determined is for instance origin and destination of the ships, speed and dimensions of the ships. 86 14.F URTHERRESEARCH

14.8.E XTENDINGTHEMODEL The mesoscopic model has now been implemented for a small region (the practical case in Zeeland), when developing this model further it might be implemented on a larger region. Computational heavy elements in the mesoscopic model are the microscopic models deciding the best schedule to use at locks (or bridges). Within the mesoscopic model those models are run after one another, another possibility is to run these parallel. It is possible to execute elements of the model parallel, when there is no direct interdependence. A ship has to travel over a fairway (the edge) between two objects. This means that there is no direct interdependence between the object models and these models can be executed parallel. A decision that influences the computation time needed is the choice of the microscopic models used. For the locks the choice is made to implement a heuristic method because this method is able to include the First Come First Serve (FCFS) rule as it’s currently used. The computation time would increase significantly when using one of the optimization methods. The optimization methods are written as a MILP that is known to be NP-hard1, combining that with a quickly rising number of variables makes the computation time increase. This computation time gives another reason not to use the optimization model. A possibility might be to use the double optimization technique from section 4.2.2 combined with the heuristic method from section 4.2.3. Instead of doing two optimizations, the first is replaced by the heuristic method. The solution determined from the heuristic can then be used to define the constraints in the optimization. This makes it possible to compare the FCFS as it’s currently used, to the situation where reordering of the ships is allowed (with a restriction to the disadvantage a ship can have). This combination will need less computation time than the situation where two optimizations were included, but one MILP still needs to be solved. Before implementing this method it should be investigated if the computation time is acceptable and what possibilities there are in different programming languages.

TERMS

An explanation of different terms is given in this chapter. First a list of nautical terms used in this project will be given along with their explanation(when needed). As some are better known in Dutch, the Dutch translation will also be given here. This list will be followed by a list of abbreviations used in the report.

A.1.S PECIFIC TERMS

English term Dutch term Explanation Fairway Vaarweg Part of the waterway on which ships can travel. Vastliggen Can be either at a berth or within a lock to the side of To moor /afmeren the chamber or to another ship. Berth Ligplaats A place where a ship can moor. Kruispunt/ Any place where more than two fairways come to- Crossing splitsing gether. Can be defined in several ways, the definition used in Vertraging Delay this project is: The time between the arrival of a ship (verliesuren) and the time it passes a bridge or starts a lockage. Bridge Brug Fixed bridge Vaste brug Beweegbare Moveable bridge brug Railway bridge Spoorbrug Blocked times Bloktijden Times at which a bridge is not allowed open. The size of that part of the bridge a ship can travel Doorvaart- through. In the case of a closed (or fixed) bridge, this Clearance opening clearance has a width, height and draft. For a moveable bridge this height can equal infinity.

89 90 A.T ERMS

English term Dutch term Explanation Lock Sluis Lock chamber Sluiskolk ¾ See figure A.1 for en explanation of lock elements Sub-chamber Deelkolk Lock gate Sluisdeur Operates the lock, also makes the decision of who will Lock operator Sluiswachter be allowed in which lockage. Lockage Schutting The lock changes sides, either with or without ships A lock is used to let water through, most of the time To drain/flush Spuien toward open water (sea). This is done to keep the water level steady on the other side of the lock. Within a lock, the water level is changed to equal the Leveling Niveleren other side of the lock. Entering the lock Invaren Leaving the lock Uitvaren Ships do not fit in the lockage and will have to wait for Delay time Overliggen the next lockage, this results in additional delays. Inland navigation Binnenvaart Maritime navigation Zeevaart Draft Diepgang Has been defined as: A ship on which twelve or more Passenger vessel Pasagiersschip passengers are allowed.[21] Ship carrying dangerous cargo Kegelschip Has to carry a cone to signal this to other ships. One cone Flammable substances ⇒ Cones Kegels Two cones Substances detrimental for the health ⇒ Three cones Explosive substances[21] ⇒

Lock chamber

Water level Water level A B

Sub- Sub- Lock gate chamber chamber

Figure A.1: Schematic top view of a lock A.2.A BBREVIATIONS 91

A.2.A BBREVIATIONS A list of abbreviations used in the model Abreviation Explanation MILP Mixed Integer Linear Programming FCFS First Come First Served BPR Binnenvaart Politie Reglement[21] Conférence Européenne des Ministres de Transport CEMT (Classiﬁcation of European Inland Waterways) SIVAK SImulatie VAarwegen en Kunstwerken VCM VerkeersmanagementCentrale van Morgen ViN Vaarwegkenmerken in Nederland European Agreement concerning the International ADN Carriage of Dangerous Goods by Inland Waterways AIS Automatic Identiﬁcation System IVS90 Informatie- en Volgsysteem voor de Scheepvaart Normal water-level in Amsterdam (Normaal Amster- NAP dams Peil)

B PARAMETERSFORTHEPRACTICALCASE

For the practical case in Zeeland there are a lot of parameters needed, these will be described here. Where possible values were determined from several sources[17, 18,24]. However, when there are no sources available there were luckily enough people with the right knowledge at Rijkswaterstaat.

B.1.S IMULATION PARAMETERS To execute the simulation itself there are also some parameters needed. These parameters will be explained in table B.1.

Variable Value Explanation Time steps 600 Maximum amount of time-steps to do in the simulation. Time step size 5 Time step size in minutes. Horizon 60 Ships expecting to arrive within this time (in minutes) from the end of the current time-step will be taken into account in the different object models. Lock modeling 4 Once every 4 iterations (20 min) a run of the lock model is done, to determine which ships will be locked in the next two lockages, and at which time these lockages take place.

Table B.1: Simulation parameters used For the lock heuristic there are values needed for how long to wait on trafﬁc still coming and how long should be waited on trafﬁc before doing an empty lockage. Testing has been done to determine the values that result in the lowest average delays.

Lock Wait ﬁlled(a) Wait empty(b) Volkerak 11 9 Krammer 18 15 Hansweert 13 10 Kreekrak 13 8 Terneuzen 11 9 Vlissingen 21 18 Veere 21 18 Zandkreek 21 18

Table B.2: The values for a and b used in the heuristic model of section 4.2.3

In the microscopic model for the bridges there are also some values set, the values needed concern the time needed for opening an closing the bridge. Also some time is reserved for changing between the two directions(first traffic from one side is allowed to pass the bridge, then traffic in the other direction). The values used are given in table B.3; all values denoted are in minutes. The time needed for opening an closing the bridges within Vlissingen and Middelburg are set differently due to the fact that the denote a combination of bridges. Therefore it was not possible to find a true value.

93 94 B.P ARAMETERSFORTHEPRACTICALCASE

Time needed for Time needed for Time needed for Bridge opening the bridge closing the bridge changing direction Vlake(spoor)brug 3 3 2 Postbrug 3 3 2 Bridges Vlissingen 1 1 2 Bridges Middelburg 1 1 2

Table B.3: The values needed for the microscopic bridge models explained in section 4.3

Also needed in the bridge model is the time needed for each ship to pass the bridge. This value could be set for each ship separately, because not enough information is available this value is currently set at one minute for each ship.

B.2.F AIRWAYS For all edges (fairways) the distance between the two end-nodes is needed. This distance is used in order to determine the travel time needed for each ship to pass the edge. Also the maximum speed allowed at each route is denoted. For the Westerschelde no maximum speed is set, however as there are (almost) no ships that can reach a speed over 20 km/h, this is set as a maximum speed here. When this speed is restricting some ships from reaching their maximal speed, this can be set higher or even be removed. For some of the points an additional explanation is added in a footnote, any points with the same number naturally denote the same point. For the different fairways also an average travel time was determined, this travel time uses a speed of 15km/h on all fairways. As it’s needed in the model for the average travel time to be an overestimation an additional 5min is added to this (for the longer edges another 10 minutes is added). This additional time is added to the time calculated with the assumed speed of 15km/h. This average time is used when determining the expected arrival time of ships at the objects the ship has yet to reach. B.3.L OCKSIZES 95

Distance Maximum Average Fairway From To (km) speed (km/h) time (min) Kanaal door W1 Terneuzen2 17.9 20+ 77 Westerschelde Terneuzen2 Kanaal door ZB3 18.2 20+ 78 Kanaal door ZB3 Antwerpen 26.3 20+ 120 Buitenhaven Westerschelde2 Locks Terneuzen 1.5 20 11 Terneuzen Westerschelde1 sluis Vlissingen 1.2 15 10 Sluis Vlissingen Keersluisbrug 1.3 15 10 Canal through Souburg Schroebrug 3.6 15 19 Walcheren Stationsbrug Sluis Veere 6.5 15 31 Sluis Veere Veerse Meer4 1 15 9 Kanaal door W4 Zandkreek sluis 17.2 15 74 Veerse Meer Zandkreek sluis Oosterschelde5 2.1 15 14 Westerschelde3 Hansweert 2 20 13 Canal through Hansweert Vlakebrug 1.4 20 11 Zuid-Beveland Vlakebrug Postbrug 3.1 20 18 Postbrug Oosterschelde6 3.8 20 21 Kanaal door ZB6 Veerse meer5 7.6 20 35 Oosterschelde Veerse meer5 Krammer sluizen 25.4 20 117 Noorder Krammer Krammer sluisen Schelde-Rijn7 6.4 20 31 Volkerak Schelde-Rijn7 Volkarak sluizen 13 20 57 Schelde-Rijn Noorder Krammer7 Kreekrak sluizen 23.9 20 117 connection Kreekrak sluizen Antwerpen 20.2 20 102

Table B.4: Fairways in the practical case

B.3.L OCKSIZES For all the locks it’s important to known their size. The length and with of each lock is used to determine whether or not a set of ships can be locked together. The locks are in the model assumed to be rectangular, if this is not the case either the set length and width or the placement model should be adjusted accordingly. In the practical case, some of the locks consist of several chambers. Some also have additional chambers dedicated to recreational trafﬁc, these are not taken into account in the model. Note that for the draft all values are with respect to a certain water level (this water level can be NAP, but can also be the water level in the canal, or the most common water-level measured at the lock). This means that whenever there is an unusually low water-level at either side, the draft allowed (possible) at the lock will decrease. These values are registered within ViN and can be found on the site visualizing this database[24]. When the lockages are modeled, there is a lockage time set. However this time doesn’t include time for the ships to travel into or out of the lock. How much time a ships needs to travel into or out of the lock depends on the size of a ship, but also on the ratio between the width of the ship and the width of the (entrance to the) lock.[18] As an average 4 minutes is taken for ships traveling into the lock, and 2 minutes is needed for a ship traveling out of the lock. Now that the time for traveling into or out of the lock is set, time needed for a lockage must also be determined. As traveling into and out of the lock is modelled separately the time needed for a lockage should include only the time between the doors on one side closing, changing the water level and then the doors on the other side opening. This means that the time needed for an empty lockage is equal to the time needed for a lockage that includes ships. This time has been determined and can be found in table B.6.

1The point where ships leave the Westerschelde to go to the canal through Walcheren. 2The point where ships leave the Westerschelde to go to the locks at Terneuzen. 3The point where ships leave the Westerschelde to go to the canal through Zuid-Beveland. 4The point where ships leave the Veerse meer to go to the canal through Walcheren. 5The point where ships leave the Oosterschelde to go to the Veerse meer. 6The point where ships leave the Oosterschelde to go to the canal through Zuid-Beveland. 7The point the Noorder Krammer, the Volkerak and the Schelde-Rijn connection meet. 96 B.P ARAMETERSFORTHEPRACTICALCASE

Size (m) Dimensions ships allowed (m) Lock Chamber Length Width Draft Height Length Width Draft Height Hansweert Oost 270 23.6 4.75 38 200 23.5 4.75 38 West 270 23.6 4.75 38 200 23.5 4.75 38 Krammer Zuid 270 23.6 4.75 14 200 23.5 4.75 14 Noord 270 23.6 4.75 200 23.5 4.75 ∞ ∞ Kreekrak West 318 23.6 4.3 9.1 225 23.5 4.3 9.1 Oost 318 23.6 4.3 9.1 225 23.5 4.3 9.1 Terneuzen West 285 36 12.3 265 34 12.3 ∞ ∞ Oost 280 23.9 4.3 200 23 4.3 ∞ ∞ Midden 140 24 6.5 140 16 6.5 ∞ ∞ Veere 135 24.6 3.7 130 18 3.7 ∞ ∞ Vlissingen 141 23.4 7.9 140 20.5 7 ∞ ∞ Volkerak West 300 23.6 4.75 14.8 225 23.5 4.75 12 Oost 300 23.6 4.75 225 23.5 4.75 ∞ ∞ Midden 300 23.6 4.75 14.8 225 23.5 4.75 12 Zandkreek 121 19.6 4.5 121 18 ∞ ∞ ∞ Table B.5: Locks in the practical case

Lock Lockage time Volkerak 15 Krammer 25 Hansweert 15 Kreekrak 15 Terneuzen 15 Vlissingen 15 Veere 15 Zandkreek 15

Table B.6: Time used in the mesoscopic model B.4.B RIDGEDIMENSIONS 97

B.4.B RIDGEDIMENSIONS Within the practical case, there are seven bridges, their heights and widths are given here. However the bridges within Vlissingen (Keersluisbrug, Sloebrug and Souburg brug) are combined together within the model, the same is done with the bridges within Middelburg (Schroebrug and Stationsbrug). Therefore the dimensions of these bridges are combined as well. The reason for combining these bridge is that they are located really close to another, more details about this merging can be found in section 7.2. The dimensions of the original bridges and their combined dimensions can be found in table B.7. At the Souburg bridge and the Stationsbrug recreational and commercial trafﬁc are separated, only the clearance valid for commercial trafﬁc is used in the model.

Moveable part Combined bridge Contains Width (m) Height closed (m) Height opened (m) Bridges Vlissingen 19.3 1.7 ∞ Keersluisbrug 19.84 2.4 ∞ Sloebrug 20 4.9 ∞ Souburg brug 19.3 1.7 ∞ Bridges Middelburg 19.85 1.5 ∞ Schroebrug 20 1.5 ∞ Stationsbrug 19.85 1.7 ∞ Table B.7: Merged bridges in the practical case1 The dimensions of the two bridges located on the canal trough Zuid-Beveland can be found in table B.8.

Fixed part (m) Moveable part (m) Bridge name Width (m) Height (m) Width (m) Height closed (m) Height opened (m) Vlake(spoor)brug 10.5 120 25 9.5 ∞ Postbrug 10.5 120 25 9.5 ∞ Table B.8: Bridges in the practical case2

B.4.1.S CHEDULEDOPENINGTIMESOFTHEBRIDGES These bridges all have a scheduled opening time twice in an hour, at this time the bridge is allowed to open (if there are ships that are waiting to pass this bridge). These scheduled opening times can be found in table B.9. Using these opening times it’s possible to determine how much time is needed to pass the combined bridges Opening 1 Opening 2 Bridge From Till From Till Vlakebrug .56 .05 .26 .35 Postbrug .00 .15 .30 .45 Keersluisbrug .15 .24 .45 .54 Sloebrug .06 .14 .36 .44 Souburg brug .54 .02 .24 .32 Schroebrug .12 .20 .42 .50 Stationsbrug .52 .01 .22 .31

Table B.9: Opening times of the bridges in Vlissingen and Middelburg, as has been denoted in table B.10. It’s assumed that all bridges need to open in order to let the ship pass. If ships can pass underneath some of the bridges, the passage time denoted in the table will be higher than the passage time in reality. The time slots denoted in the table are for the opening of the ﬁrst bridge, then after the passage time the ship will have passed the last of the bridges.

1Height with respect to the ’normal’ water level in the canal. 2Height with respect to NAP. 98 B.P ARAMETERSFORTHEPRACTICALCASE

Traveling south to north Traveling north to south Bridge Passage time Passage time Time slot 1 Time slot 2 Time slot 1 Time slot 2 (min) (min) Vlissingen .15 - .24 .45 - .54 39 .54 - .02 .24 - .32 21 Middelburg .12 - .20 .42 - .50 10 .52 - .01 .22 - .31 20

Table B.10: Time needed for passing each bridge

B.4.2.B RIDGESLOCATEDATLOCKS There are also bridges located at the locks; they are located over or close to the gates of a lock (chamber). In table B.11 the bridges are located, along with the side of the chamber they are on. Only the moveable bridges are denoted here; when a ﬁxed bridge is located close to or over the gates of a lock this results in a height restriction for the ships using this chamber. In most situations these bridges are simply opened whenever this is needed due to the ships being locked. The only exception is at Volkerak, where the bridge is not allowed to open during rush hour (determined as 6.00-9.00 in the morning and 16.00-18.30 in the evening). More information about the method used for modeling these bridges can be found in sections 4.2.7 and 7.2. Lock Chamber Side Height when closed (m) Volkerak Oost South 14 Krammer Zuid East 14.9 Terneuzen West South 2.22 Terneuzen West North 4.35 Terneuzen Oost South 3.19 Terneuzen Oost North 6.75 Terneuzen Midden South 2.07 Terneuzen Midden North 4.2 Zandkreek West 3.4 Zandkreek East 7

Table B.11: Bridges located at the locks B.5.S HIPS 99

B.5.S HIPS The ship sizes are determined from the IVS90 records for Volkerak, as most ships have to pass this lock, these are a good measure for the ships on the network. The ships all get a maximum speed between 12 and 18 km/h which they cannot exceed. For each set of endpoints, a total number of ships to travel between them is determined. When multiple routes between these endpoint exist, the size of the ship will determine which of them is used (ships will always choose the route that takes the least amount of time, that they are allowed to travel on). The departure time of the ships is determined using a random variable, this means that the ships can be divided evenly over the day (one day is simulated), or giving more weight to one time-period than to the other.

B.5.1.S HIPSONROUTES For each set of endpoints, the number of ships traveling between them. Using this amount of ships, the number of ships that pass each lock are approximately equal to the number of ships passing a lock in the situation seen in the IVS90 records.

Start point End point Number of ships Volkerak Vlissingen 8 Vlissingen Volkerak 8 Volkerak Terneuzen 20 Terneuzen Volkerak 20 Volkerak Antwerpen 132 Antwerpen Volkerak 132 Terneuzen Antwerpen 20 Antwerpen Terneuzen 20 Vlissingen Terneuzen 20 Terneuzen Vlissingen 20 Vlissingen Antwerpen 60 Antwerpen Vlissingen 60

Table B.12: Number of ships traveling on each route

B.5.2.D ANGEROUSCARGO In order to determine ships carrying dangerous cargo, percentages of the total amount of ships are determined. Based on previous work in this area the percentages are determined as follows;[17] Category Percentage Dangerous cargo, one cone 4% Dangerous cargo, two cones1 1% Dangerous cargo, single lockage2 1% Passenger-ships 5% Ships having a certiﬁcate 55%

Table B.13: Percentage of ships in the different categories

B.6.S HIPSALLOWEDONROUTES Depending on the size of a ship, the routes it’s allowed to travel on can be determined. It’s assumed that all ships have a size smaller than 4.75/23.5/200 (draft/width/length), as this makes it possible to travel between all endpoints(in the current simulation the ship sizes are independent of the route). As this is the size allowed at Volkerak, the ship sizes used all satisfy this. On some routes there are larger ships allowed, most importantly on the Westerschelde where also maritime navigation ships are allowed. Even when the ships satisfy this size, there are still several separations that can be made; based on this the network that the ship can travel on can be determined. This means that there are four groups for the ships based on their dimensions in meter, based on the group they are in the network of fairways they are allowed to travel on can be found in ﬁgure B.1. When multiple dimensions are given (for instance draft, width and length) all need to be satisﬁed.

(a) Ships having a smaller size than 3.7/18/120/9.1 (draft/width/length/height), these ships can travel on the complete network.

(b) When ships are smaller than 3.7/18/120 (draft/width/length) but have a height higher than 9.1m they cannot use the Schelde-Rijn(blue part of the network), but can travel the rest of the graph.

(c) Only the Canal of Walcheren(green part of the network) is unavailable for ships exceeding 3.7/18/120 (draft/width/length), but having a height lower than 9.1 and a draft lower than 4.3

(d) If ships fall in one of the following categories only the black part of the network can be used;

• The draft exceeds 4.3m • Or exceed 3.7/18/120 (draft/width/length) and a height higher than 9.1

Rotterdam Volkerak or other destination

Zandkreek Krammer

Kreekrak Veere Hansweert

Vlissingen

Antwerpen

Sea Terneuzen Gent

Figure B.1: The network for the practical case including the locks and endpoints The advantage of this separation, is that only four different graphs need to be saved, how this method can be extended to a larger network, will depend on the network itself. Also it will depend on the complexity of the bounds set at the different fairways (and/or locks). C OBJECTMODELSDETAILS

In this appendix a more detailed explanation of the object models can be found. The models described here are those that have not been used within the mesoscopic model. For the global explanation of the models and the detailed description of the models used in the mesoscopic model see chapter4.

C.1.L OCKS Here a detailed explanation of the optimization can be found. For the optimization method(s) the exact equations used are written out, along with the variables and parameters used in the optimization. Information about the conditions set (the constraints follow from these conditions) and information about the objective function used can be found in section 4.2.1. For the lock models there are several input values. • A queue of ships that want to pass the lock. For each ship in the queue an arrival time is given (can be in the past or future).

– It might not be possible to lock all ships within this queue.

• The number of chambers at this lock, for each chamber the following information is needed:

– Number of lockages allowed to be scheduled with this chamber. Depending on the situation not all might be used (when there are not that many ships that need to be locked). – Time and direction of the ﬁrst lockage in this chamber. This is decided by the lockages that have already taken place. The time is not allowed to be in the past, but can be later than the current time (for instance when the chamber is still locking at the current time).

C.1.1.O PTIMIZATIONMODEL The optimization model determines which ships will be locked together, and at which time this lockage takes place. When looking at a lock having multiple chambers, this gives an added difﬁculty, as the ships need to be divided over the different chambers. The optimization model is set up to be able to handle any number of chambers.

DEFINITIONS In the model different variables and parameters are used. The values of the parameters need to be deﬁned before starting the optimization, the values of the variables are determined by the optimization. Variables zi,k Binary value stating if lockage i of chamber k is used or not. Ti,k Continuous value stating the time at which lockage i of chamber k is used. fi,k,j Binary value stating if ship j uses lockage i of chamber k. p j Binary value stating if ship j will be scheduled. t j Continuous value stating the time at which ship j is allowed to pass the lock. Tmax The maximum delay obtained by the ships.

101 102 C.O BJECT MODELS DETAILS

Parameters K The amount of chambers available at the lock. M The maximum number op lockages available for each chamber. This number can be equal for all chambers or a vector-wise parameter can be used containing different values. dk Binary value stating whether the first lockage of chamber k is in the first (0) or second (1) direction. next_thk The time at which the first lockage of chamber k is allowed. lock_timek The lockage time needed for chamber k. timein The time needed for ships to travel into the lock. timeout The time needed for ships to travel out of the lock. n1 The number of ships that wants to pass the lock in the first direction. n2 The number of ships that wants to pass the lock in the other direction. n The total number of ships that want to pass the lock (n n n ). = 1 + 2 mpk The maximum percentage of the surface of chamber k that can be used by the ships. MT A value set higher as both Ti,k and t j . Sc A scaling variable. A j The time that ship j arrives at the object. B j Set containing the chambers that ship j is allowed to use. W Array containing the widths of the lockage chambers. L Array containing the lengths of the lockage chambers. S_W Array containing the widths of the ships. S_L Array containing the lengths of the ships. T _ski p Added ’delay’ for ships that are not scheduled. Additional parameters (calculated from the others) Area Array containing the area of the lockage chambers(W L). ∗ S_Area Array containing the area of the ships(S_W S_L). ∗ The scaling variable Sc is used to reduce the difference between the binary values of zi,k and fi,k,j and the values of Ti,k and t j that can take higher values. By dividing the continuous variables by this scaling value, the different values are closer together, making the optimization more stable.

CONDITIONS If a lockage is not used (z 0) then the following lockages of the same chamber are not allowed to be used i,k = either.

zi 1,k zi,k 0 k 1...K (C.1) + − ≤ ∀ ∈ Set the time the ﬁrst lockage can be done (needs to be done for all chambers). Also time needs to be reserved for the ships to travel into the lock.

X T1,k next_thk timein f1,k,j if z1,k 1 (C.2) ≥ + j =

Between two lockages of the same chamber there needs to be time for the ships of the previous lockage to travel out of the lock, the lockage to take place and for the ’new’ ships to travel into the lock.

X X Ti 1,k Ti,k lock_timek timeout fi,k,j timein fi 1,k,j if zi 1,k 1 (C.3) + − ≥ + j + j + + =

Each ship will be in a lockage exactly one time when the ships is scheduled, or not at all if the ship is not scheduled. Only lockages in the right direction are allowed to be used.

X X fi,k,j p j ships for which j n1 (C.4) k B i d odd = ≤ ∈ j + k = X X fi,k,j p j ships for which j n1 (C.5) k B i d even = > ∈ j + k = C.1.L OCKS 103

The lockages in the wrong direction are not allowed to be used by a ship, because the elements need to equal zero, also the sum should equal zero (remember fi,k,j is a binary value). X X fi,k,j 0 ships for which j n1 (C.6) k B i d even = ≤ ∈ j + k = X X fi,k,j 0 ships for which j n1 (C.7) k B i d odd = > ∈ j + k =

The ships can only be locked in a chamber they are allowed to use (this are the chambers that are in B j ). Again if the elements need to equal zero this is equivalent to the sum equalling zero. X X fi,k,j 0 for all ships (C.8) k B i = ∉ j Ships are only allowed to use a lockage if that lockage itself is used.

f z 0 k 1...K , i 1...M(k) (C.9) i,k,j − i,k ≤ ∀ ∈ ∀ ∈ In any lockage, the area the ships occupy cannot exceed the set maximum percentage of the chamber area.

n X S_Area j fi,k,j mpk Areak (C.10) j 1 ≤ · = The time at which a ship is allowed to pass the object, has to satisfy several constraints. First a ship cannot pass an object before the ship has arrived at an object.

t A (C.11) j ≥ j Second the time should be when the lockage the ship uses is set. Again the part M (f 1) makes sure that T i,j − when f 1 the condition is always satisﬁed. Note that the last two conditions only have to be added for i,j 6= those lockages a ships is allowed to be part of, as these lockages are the only ones that could have f 1. i,k,j = This means that only for the lockages in the right direction these constraints need to be added. Whenever a lockage is used f will equal 1, as a result these two constrains will then combine to t T . i,k,j j = i,k t T M (f 1) j − i,k ≥ T i,k,j − t T M f M (C.12) j − i,k − T i,k,j ≥ − T t T M (1 f ) j − i,k ≤ T − i,k,j t T M f M (C.13) j − i,k + T i,k,j ≤ T The third constraint that is needed is the First Come First Serve (FCFS) constraint; it only needs to be added between ships traveling in the same direction. Note that the ships are already ordered by arrival time. Ships 1 till n are the ships in the ﬁrst direction, ordered by arrival time. Ships n 1 till n are the ships in the other 1 1 + direction also ordered by arrival time. Also important is the choice to not schedule the ship. If a ship is not scheduled, then all following ships in the same direction are also not scheduled. The

p j 1 p j 0 when j, j 1 n1 or j, j 1 n1 (C.14) + − ≤ + ≤ + > t j 1 t j MT p j 1 MT when j, j 1 n1 or j, j 1 n1 (C.15) + − − + ≥ − + ≤ + > Besides the average delays, also the maximum delay obtained is taken into account when optimizing. There- fore the maximum delay is also added as a variable Tmax . In order to determine it’s value, the following constraints are added.

T t A j, if p 1 (C.16) max ≥ j − j ∀ j = T min(next_th) A T _ski p j, if p 0 (C.17) max ≥ − j + ∀ j = The second equation is added to also include the delays that occur for the ships that are not scheduled. These ships might have a delay already, if they arrived before the ﬁrst lockage is scheduled, that delay equals min(next_th) A . The parameter T _ski p simulates the additional delays, as the ship is not scheduled (and − j therefore has to wait until one of the chambers returns). 104 C.O BJECT MODELS DETAILS

DANGEROUSCARGOANDPASSENGERVESSELS Speciﬁc rules apply to ships carrying dangerous cargo. Depending on their cargo a ship might be required to carry one or more (maximal is three) cones. Ships that carry cones are not allowed to be locked along with a passenger vessel. Ships having two or three cones might even have to be locked separately depending on the circumstances. When ships carrying cones are allowed to be locked together with other ships, they still have to adhere to increased safety-distances. That means that in order to include these rules the following variables and parameters need to be included.

Variables dli,k Binary value stating if option i of chamber k contains a ship carrying dangerous cargo. psi,k Binary value stating if option i of chamber k contains a passenger vessel. dl sli,k Binary value stating if option i of chamber k contains a ship that needs to be locked alone. nori,k Binary value stating if option i of chamber k contains a ’normal’ ship (any ship not carrying dangerous cargo, having a certiﬁcate or being a passenger vessel). dl2i,k Binary value stating if option i of chamber k contains a ship carrying dangerous cargo, having 2 cones. Parameters Dl Set containing the ships that carry dangerous cargo. ndl The amount of ships in Dl. Ps Set containing the passenger vessels. nps The amount of ships in Ps. Dlsl Set containing the ships that need to be locked alone. nsl The amount of ships in Dlsl . Nor Set containing the ’normal’ ships. nnor The amount of ships in Nor . Dl2 Set containing the ships that carry dangerous cargo, having 2 cones. ndl2 The amount of ships in Dl2. With these variables and parameters the separation between ships carrying dangerous cargo and passenger vessels can be forced using the following constraints.

X fi,k,j ndl dli,k i,k (C.18) j Dl ≤ · ∀ X∈ fi,k,j nps psi,k i,k (C.19) j Ps ≤ · ∀ ∈ dl ps z i,k (C.20) i,k + i,k ≤ i,k ∀ The ﬁrst two constraints forces the value of dl (or ps) to equal 1 when there is a ship carrying dangerous cargo (or a passenger vessel) contained in the lockage. The third constraint makes sure that it’s not possible to have both passenger vessels and ships carrying a dangerous cargo in one lockage. When the lockage is not used, it’s not allowed for any ships to use the lockage. When the ships not only have to be separated from passenger vessels, but even have to be locked alone, this means that there are more constraints needed.

X fi,k,j nsl dl sli,k i,k (C.21) j Dl ≤ · ∀ ∈ sl n X fi,k,j 1 n(1 dl sli,k ) i,k (C.22) j 1 ≤ + − ∀ = The ﬁrst constraint forces the value of dl sl to equal 1 when there is a ship that needs to be locked alone contained in the lockage. The second constraint makes sure that in that case the maximum amount of ships equals 1. An additional constraint is needed for ships that carry 2 cones. These ships might need to be locked alone, however this is not the case for all ships. Even if these ships do not need to be locked alone, they can only C.2.B RIDGES 105 be locked with ships that either have one or two cones or have a certiﬁcate. It’s not allowed to lock ’normal’ ships along with these ships having two cones. Therefore some additional constraints are needed.

X fi,k,j nnor nori,k i,k (C.23) j Nor ≤ · ∀ ∈X fi,k,j ndl2 dl2i,k i,k (C.24) j Dl2 ≤ · ∀ ∈ nor dl2 z i,k (C.25) i,k + i,k ≤ i,k ∀ The ﬁrst two constraints forces the value of dl2 (or nor ) to equal 1 when there is a ship carrying dangerous cargo with two cones (or a ’normal’ ship) contained in the lockage. The third constraint makes sure that it’s not possible to have both ’normal’ ships and ships carrying dangerous cargo (with two cones) in one lockage. When the lockage is not used, it’s not allowed for any ships to use the lockage. It’s also possible that because of the cargo ships are carrying there are additional rules for the ship placement. For instance there could be an additional safety distance. These additional rules will need to be added in the heuristic placement problem explained later. The example of additional safety distances can also be taken care of without having to change the code. This can be done by adding the safety distances to the size of the ship, and then determine the placement for this ’larger’ ship.

ITERATIVEPROCESS After the optimization has been done, the placement heuristic needs to be run to see if there is a placement for these ships possible. If not, a constraint will be added (so hat these ships cannot be placed together), and the optimization will be run again. This process will continue until an optimal result is fount where for all lockages a placement is possible.

C.1.2.D OUBLEOPTIMIZATIONMODEL When using the double optimization model, the first step is to run the previously defined optimization model. After that model is run a second optimization model needs to be run (resulting in the name). This model is similar to the previous one, however it doesn’t include the First Come First Serve (FCFS) constraints from equations C.14 and C.15. Instead a now constraint is added using the solution of the first optimization. The parts of the solution that are used are the values of p j and t j . Denoting the ’old’ values as p˜j and t˜j , the new values p j and t j and adding a parameter W ai tlim the additional constraints are

p p˜ (C.26) j ≥ j t t˜ W ai t if p˜ 1 (C.27) j ≤ j + lim j = This means that the order of arrival doesn’t need to be the order in which the ships are let through the lock. However there is a set limit (W ai tlim) as to how much disadvantage a ship can have from this reordering. The advantage a ship has from the newly used order is not limited (except for by the arrival time, as a ship cannot be locked before it arrives at the lock).

C.2.B RIDGES Scheduling of ships at bridges is simpler than for locks, one reason is that there are not as many ships that need to be taken into account. There are ships that can fit under the bridge, without it having to open. These ships are not taken into account in these models, instead they get a fixed delay, as they might have to slow down, and are let past the bridge. The ships for which the bridge has to open are taken into account in the models. This model determines when the bridge will open and which ships are allowed to pass the bridge then. To do this a simplified version of the lock optimization is used to find the optimal solution. Also possible is to use a heuristic model that has been made for the case that the bridges are operated using a schedule.

C.2.1.O PTIMIZATIONMODEL The optimization model for bridges determines at which time the bridge opens and which ships will then be allowed past the bridge. This way a decision is made whether to wait on the next ship or not. It’s also possible to include blocked times, for instance when a bridge is not allowed to be opened during rush hour. 106 C.O BJECT MODELS DETAILS

Variables zi Binary value stating if bridge opening i is used or not. Ti Continuous value stating the time at which bridge opening i is used. Li Continuous value stating the time the bridge is open in bridge opening i. fi,j Binary value stating if ship j uses bridge opening i. p j Binary value stating if ship j will be scheduled. t j Continuous value stating the time at which ship j is allowed to pass the object. gi,k Binary value stating if bridge opening i is before blocked time k or after it. Parameters M The maximum number op options available for the bridge. to The time the bridge needs to open (no ships are allowed to pass through in this time). tc The time the bridge needs to close (no ships are allowed to pass through in this time). ts The time the bridge needs to ’switch sides’. n1 The number of ships that want to pass the bridge in the ﬁrst direction. n2 The number of ships that want to pass the bridge is the other direction. n The total number of ships that want to pass the bridge. (n n n ) = 1 + 2 next_th The ﬁrst time the bridge is allowed to open. d j The direction that ship j is traveling in. MT A value set higher as both Ti,k and t j . C The minimum time the bridge needs to be closed between two times it opens. maxopen The maximal time the bridge is allowed to be open at once. Sc A scaling variable. A j The time that ship j arrives at the object. l j The time that ship j needs to pass the bridge, when it’s opened. K The total (separate) blocked times. Bl_star tk The time that blocked time k starts. Bl_endk The time that blocked time k ends.

The scaling variable Sc is used to reduce the difference between the binary values of zi and fi,j and the values of Ti and t j that can take higher values. By dividing the continuous variables by this scaling value, the different values are closer together, making the optimization more stable. When a bridge opens ﬁrst all ships in the ﬁrst direction are let through, then there are ts minutes needed so that also the last ship has completely past the bridge, then the ships in the other direction are allowed past.

BOUNDS Besides the constraints, there are also some bounds added. Both make sure that the variables do not take too high values. When a bridge opens, it’s only allowed to stay open for maxopen minutes. Therefore a bound is added, L max to make sure of this. i ≤ open The schedule made only looks ahead for 3 hours, therefore the bound t 120 is added (all time-elements j ≤ are in minutes). By restricting the variables t j this automatically makes sure that the values Ti will also satisfy this bound (because of the interdependency between the two).

CONSTRAINTS If an bridge opening is not used (z 0) then the following bridge openings are not allowed to be used either. i =

zi 1 zi 0 (C.28) + − ≤ There is a limit set for when the ﬁrst opening is allowed to be scheduled.

T next_th if z 1 1 ≥ 1 = T next_th M (z 1) (C.29) 1 ≥ + T 1 − C.2.B RIDGES 107

Between two bridge openings there needs to be at least C time (if they are both used).

Ti 1 (Ti Li ) C if zi 1 1 + − + ≥ + = Ti 1 Ti Li C MT (zi 1 1) (C.30) + − − ≥ + + − Ships that are scheduled are taken along in exactly one of the times the bridge opens. Ships that are not scheduled are not taken along in any of the options.

M X fi,j p j (C.31) i 1 = = A bridge opening that is not used, can not be used by any of the ships

f z (C.32) i,j ≤ i Ships need to arrive on time to be allowed to pass the bridge. The time it’s allowed to pass the bridge (is the time it starts to pass it) should be such that it falls in the time the bridge is open, and ships are allowed through.

t A M (p 1) j ≥ j + T j − t M p A M (C.33) j − T j ≥ j − T t (T t ) M (f 1) j − i + o ≥ T i,j − t T M f t M (C.34) j − i − T i,j ≥ o − t (t l ) (T L t ) M (1 f ) j + j − i + i − c ≤ T − i,j t T L M f M l t (C.35) j − i − i + T i,j ≤ t − j − c The last constraint that is needed is the First Come First Serve (FCFS) constraint needs to be added between ships traveling in the same direction. Note that the ships are already ordered by arrival time. Ships 1 till n1 are the ships in the ﬁrst direction, ordered by arrival time. Ships n 1 till n are the ships in the other direction 1 + also ordered by arrival time. Also important is the choice to not schedule the ship, if a ship is not scheduled, then all following ships in the same direction are also not scheduled. This results in the following constraints

p j 1 p j 0 when j, j 1 n1 or j, j 1 n1 (C.36) + − ≤ + ≤ + > t j 1 t j MT p j 1 MT when j, j 1 n1 or j, j 1 n1 (C.37) + − − + ≥ − + ≤ + > Another constraint is needed to make sure that the ships pass the bridge in the right order. The ships in the ﬁrst direction are allowed past, only after they have past, are the ships in the other direction allowed past.

t t if j n , j n and f , f 1 (C.38) j2 ≥ j1 1 ≤ 1 2 > 1 i,j1 i,j2 = t t M (f f 2) if j n , j n (C.39) j2 − j1 ≥ T i,j1 + i,j2 − 1 ≤ 1 2 > 1 BLOCKINGTIMES Most bridges have blocking times, in which the bridge is not allowed to open. This can for instance be during rush hour, or because there is a train traveling over the bridge at that time. This results in additional variables, parameters and constraints. The variables gi,k is added to decide if the opening should be timed before or after the blocked time. This means that two constraints are added

T L Bl_star t if g 0 (C.40) i + i ≤ k i,k = T Bl_end if g 1 (C.41) i ≥ k i,k = At any time only one of these will be satisﬁed, a trick is used to make the constraint true in any case.

T L Bl_star t M g i + i ≤ k + T i,k T L M g Bl_star t (C.42) i + i − T i,k ≤ k T Bl_end M (g 1) i ≥ k + T i,k − T M g Bl_end M (C.43) i − T i,k ≥ k − T Note that there are in total M K variables added along with 2M K constraints, this will increase the ∗ ∗ complexity of the optimization, and thereby the calculation time that is needed.

D USING R

For programming the R program is used, this is an open-source program for which packages exist that can handle several applications. It also contains a package that makes it able to combine this program with Neo4j, which is the database that is used at Rijkswaterstaat. As this programs main goal is to have tools for data analysis (using statistics) it can easily handle importing data from several ﬁle formats. Also basic mathematics functions as using arrays, matrices, for, while and if loops have been implemented in it.

D.1.P ACKAGES For more speciﬁc usage packages have been written, that can be imported in R. The packages that have been used will be explained below.

D.1.1.G RAPHALGORITHMS The igraph package is used because it contains several functions for graph handling and algorithms. Also a method for plotting a graph is contained in this package. Main functions that have been used from this package are;

• Finding the neighbors of an node

• Finding the corresponding number connected to an edge

• Determining the shortest path between two nodes (only for the time-independent case)

• Plotting a graph

D.1.2.S OLVING MILP There are several packages that make it possible to solve a MILP using R. Two examples are Rsymphony and Rglpk. Both are interfaces to an open source optimizer. As these packages need similar input (if not equal) both where investigated on there use. When using Rsymphony on larger problems, an error was returned that seemed to be originating from a fault in the underlying C code in the package. As Rglpk was able to solve these problems without returning error, this is the solver that was used in this project.

D.1.3.I MPORTINGDATA Additional functions that can be used to import data can be found in the gdata package. One of its functions was used to import excel data of the fairway network

D.1.4.RN EO4J This package makes it possible to combine the functions of R with the Neo4j graph database. For instance the speciﬁc shortest paths can be used (shortest path over a certain relation). This package is not used for the mesoscopic model.

109 110 D.U SING R

D.1.5.E XPORTINGDATA In order to save tables or matrices it’s possible to export them to excel using the xlsx package.

D.2.D ATATYPES In R it’s not only possible to use matrices and arrays to save data, but also to use lists. These list have as an advantage that it’s allowed to contain data of different lengths. This is useful because it makes it possible to combine similar data, without it needing to have the same length. This is the case when comparing the paths of the different ships, one might take a ’shorter’ route as another (visiting less nodes), but it’s useful to save the paths of all ships in one variable.

D.3.P ROGRAMSWRITTEN Several programs are written in R, a short explanation of these programs can be found here.

D.3.1.M ESOSCOPICMODEL A mesoscopic model has been made, applied to the practical case further detailed in chapter7. This practical case contains both bridges and locks, that are modelled using the programs described below.

LOCKSWITHPARALLELCHAMBERS An optimization model that can determine the best schedule when dealing with multiple chambers at one lock. This problem includes an iterative process for the ship placement problem, using the heuristic to determine if there is a feasible solution. This heuristic is also modelled in R. All ships are allowed to moor to the sides of the lock, or to other ships, with the demand that this ship must be located along the total length of the ship(ship you are mooring to needs to be longer). Also included are the constraints set for ships carrying dangerous cargo, as explained in section 4.2.5.

BRIDGES Bridges are modelled in different optimization model. This model also includes a set of blocked times in which the bridge is not allowed to open. Also there is a limit set to how long the bridge is allowed to be closed for trafﬁc when it opens. For all ships there is a known time they need in order to pass the bridge. Before ships can pass the bridge, there is time needed to open the bridge, after all ships have passed the bridge it needs time to close again. After the bridge has been opened and has closed again, there is a set time period in which the bridge is not allowed to open again.

D.3.2.C HANGING DEPARTURE TIME Once the complete mesoscopic model has been run, it’s possible to determine if ships would need less time to travel it’s route when it chooses a different departure time. That is of course not possible for all ships, as they have set time-slots at their departure point. However when some ships change their departure time, this also has an effect on all the other ships. Therefore the complete mesoscopic model should be run again.

D.3.3.C OMPARING SITUATIONS It’s important to know what is the result of certain situations. In order to ﬁnd this out, the mesoscopic model should be run for twice(or more) with the same ships. This makes it possible to determine the effect of the difference between these two situations. First a basis run is done with the normal situation, then one (or more) chamber(s) is made unavailable for a time period(resulting in the second situation). This way the consequences can be determined of a chamber being unavailable, for instance due to an accident or because maintenance needs to be done on this chamber. This program can for instance be used to determine the best strategy for scheduling maintenance. De- pending on the maintenance done it might not be needed to do everything at once. This makes it possible to choose closing the chamber several times for a short period instead of closing the chamber one time for a longer period. This program can determine the effect on the travel time for both situation, thereby determining which is the best method for the maintenance. E CEMT CLASSES

The currently used ship groups, including their length width, draft and where known also the load capacity they carry can be found in table E.1. The load capacity is given in tons or where applicable either in cars or in TEU (Twenty Foot Equivalent Unit, determined from twenty foot containers).

Class Dutch name Length Width Draft Load capacity I Spits(barge) 38.5 meter 5,05 meter 2,20 meter 350 tonnes II Campine vessel (Kempenaar) 55 meter 6,60 meter 2,59 meter 655 tonnes Dortmund-Eems canal vessel III 67 meter 8,20 meter 2,50 meter 1.000 tonnes (Dortmunder) IV Rijn-Herne canal vessel 85 meter 9,50 meter 2,50 meter 1.350 tonnes (Europe ship) Va Large Rhine vessel 110 meter 11,40 meter 3,00 2.750 tonnes Vb Large Rhine vessel 135 meter 11,40 meter 3,5 meter 4.000 tonnes VIa Push-tug with two barges 172 meter 11,40 meter 4 meter 5.500 tonnes VIb Four barge convoy 193 meter 22,80 meter 4 meter 11.000 tonnes VIc Six barge convoy 193 meter 34,20 meter 4 meter 16.500 tonnes Va Standard tanker 110 meter 11,40 meter 3,50 meter 3.000 tonnes Vb Large tanker 135 meter 21,80 meter 4,40 meter 9.500 tonnes Va Car carrier vessel 110 meter 11,40 meter 2,00 meter 530 cars Container ship Campine vessel III 63 meter 7 meter 2,50 meter 32 TEU (Kempenaar class) Va Standard container ship 110 meter 11,40 meter 3,00 meter 200 TEU Vb Large container ship 135 meter 17 meter 3,50 meter 500 TEU Va Ro-ro vessel 110 meter 11,40 meter 2,50 meter Coupled formation (vessel with VIb 185 meter 11,40 meter 3,50 meter 6.000 tonnes dumb barge) ≈ VIb Coupled formation (ship to ship) 185 meter 11,40 meter 3,50 meter 6.000 tonnes ≈ Table E.1: The already-deﬁned ships including their names and characteristics[3]

111 112 E.CEMT CLASSES International Importance importance regional fairway yeof Type inland Of Of navigable ls of Class fairway VIb VIa VIc VII Vb Va III IV II I ag Rhine Vessels Large Welker Johan ings Koen- Gustav, Campine-Barge Cast-Caminois, Barge Péniche, Designation yeo esl eea characteristics general vessel: of Type oo esl n barges and vessels Motor eghWdhDatTonnage Draft Width Length 5101. .028 1500-3000 2.50-2.80 11.4 95-110 08 . . 1000-1500 2.5 650-1000 400-650 2.50 9.5 2.50 8.20 80-85 67-80 6.60 50-55 85 .518-.0250-400 1.80-2.20 5.05 38.50 m m m (t) (m) (m) (m) 4 50 3.90 15.00 140 al .:Tecasﬁaino aras[ 4 ] fairways of classiﬁcation The E.2: Table 7 7 8-9 30-42 .045 14500-27000 6400-12000 2.50-4.50 2.50-4.50 33.00-34.20 3200-6000 22.80 285-195 33.00-34.20 2.50-4.50 22.80 193-200 270-280 11.4 185-195 172-185 eghWdhDatTonnage Draft Width Length 5102.025-.0320-6000 2.50-4.50 1600-3000 22.80 2.50-4.50 95-110 11.4 95-110 m m m (t) (m) (m) (m) 595 .028 1250-1450 2.50-2.80 9.50 85 yeo ovy eea characteristics general convoy: of Type uhdconvoys Pushed .045 9600-18000 2.50-4.50 iia height Minimal ne bridges under .0o 9.10 or 7.10 9.10 or 7.10 7.00 or 5.25 7.00 or 5.25 4.00-5.00 4.00-5.00 r9.10 or 9.10 9.10 4.00 F DANGEROUSCARGO

The rules concerning ships carrying dangerous cargo that can be found in section 4.2.5 are derived from the Binnenvaartpolitiereglement[21]. However these regulations are not valid on all fairways in the Netherlands. For instance there is a separate one for the canal from Gent toward Terneuzen[28], there is also a separate one for the Rhine[29] and a separate one for the Westerschelde[30]. The basis of all these regulations are similar, however the rules concerning ships carrying dangerous cargo are not equal in all of them. In order to implement rules for ships carrying dangerous cargo, ﬁrst different groups of ships are deﬁned.

• Ships carrying ﬂammable cargo; these ships need to carry one cone.

– Cones are only specified for the inland navigation, for the maritime navigation a flag is mandatory when carrying dangerous cargo. The ships carrying this flag need to satisfy the same rules as the ships carrying one cone. – Rules for maritime navigation are only defined for the area’s that these ships travel. They are included on the canal from Gent toward Terneuzen and on the Westerschelde.[28, 30]

• Ships carrying cargo that can be detrimental to health; these ships need to carry two cones.

• Ships carrying explosive cargo need to carry three cones.

• Ships that have a certiﬁcate to carry dangerous cargo but are not carrying cargo as explained above. These ships are allowed to carry one cone anyway.

These groups are the same for all regulations, and using these groups the rules are deﬁned.

First the regulations valid on the Westerschelde only contain rules concerning the signs ships need to have when carrying dangerous cargo(as explained above). As there are no locks located on this domain, rules for locking are not included here. The other three sets of regulations do include rules for locking ships carrying dangerous cargo [21, 28, 29]. Some rules for these ships can be found in all three:

• Ships have to keep a distance of at least 10 meter from ships carrying one cone. However this is not needed for another ships having this sign or ships with a certiﬁcate.

• A ship carrying one cone is not allowed to be locked along with a passenger vessel.

• Ships carrying two or three cones need to be locked separately.

The difference between the regulations is found in the exceptions on this last rule.

• On the Rhine: No exceptions at all. [29]

• On the canal from Gent toward Terneuzen: Exception for ships carrying the same signs. [28]

113 114 F.D ANGEROUSCARGO

• On other fairways (included in the ’Binnenvaartpolitiereglement’): Exception for ships having two cones if they carry dry cargo, solely containers, ICB’s, bulk containers, multiple element gas containers (MEGCs), portable tanks or tank containers. These ships are allowed to be locked together or along with ships carrying one cone, or ships having a certiﬁcate. There needs to be a distance between the ships of at least 10 meter, both in the length and width direction. [21]

It’s important to determine how these rules are implemented, mostly for ships having a certiﬁcate. If the rules are taken literally, these ships have to carry a cone in some situations, if they want to fall in an exception. This can be when not wanting to keep the 10 meter distance to a ship having one cone. But also in the case of the last exception explained above. However when these ships carry this cone, they automatically have to satisfy all rules for ships that carry one cone. BIBLIOGRAPHY

[1] Rijkswaterstaat, “Rijkswaterstaat works on keeping the Netherlands safe, liveable and accessible,” June 2015.

[2] “Netwerkanalyse voor binnenhavens en vaarwegen Zeeland (source ﬁgure: Rijkswaterstaat Zeeland).”

[3] Rijkswaterstaat, “The locks at Hansweert in the South Beveland Canal,” February 2016.

[4] Rijkswaterstaat, “Waterway Guidelines 2011,” December 2011.

[5] E. Cristiani and S. Sahu, “On the micro-to-macro limit for first-order traffic flow models on networks.”

[6] P.ir. L.H. Immers, dr. ir. C. Tampère, and dr. ir. S Logghe, “Verkeersstroomtheorie.”

[7] W. Burghout, “Hybrid microscopic-mesoscopic trafﬁc simulation,” 2004. PhD thesis, Royal Institute of Technology Stockholm.

[8] W. Burghout, H. N. Koutsopoulos, and I. Andreasson, “A discrete-event mesoscopic trafﬁc simulation model for hybrid trafﬁc simulation,” 2006.

[9] R. M. Goverde, N. Besinovic, A. Binder, V. Cacchiani, E. Quaglietta, R. Roberti, and P.Toth, “A three-level framework for performance-based railway timetabling,” 2015.

[10] J. Verstichel, J. Kinable, P.D. Causmaecker, and G. V. Berghe, “A combinatorial benders’ decomposition for the lock scheduling problem,” 2014.

[11] W. Passchyn, S. Coene, D. Briskorn, J. Hurink, F.Spieksma, and G. V.Berghe, “The lockmaster’s problem,” December 2015.

[12] L. Hall, “Computational complexity (Encyclopedia of Operations Research and Management Science).” The John Hopkins University, Baltimore, MD, USA.

[13] J. Verstichel, “The lock scheduling problem,” November 2013.

[14] L. D. Smith, R. M. Nauss, J. F.Campbell, and D. C. Sweeney(II), “Triangulation of modeling methodologies for strategic decisions in an inland waterway transportation system,” 2009.

[15] L. Chen, J. Mou, and H. Ligteringen, “Simulation of trafﬁc capacity of inland waterway network,” 2013.

[16] O. de Gans, “Scheepvaartsimulatie ten behoeve van de verkenning maritieme toegang Kanaal Gent–Terneuzen in het licht van de logistieke potentie,” 2007.

[17] “Duurzaam Stremmen, Simulatiestudie naar effecten van een gedeeltelijke stremming van de Krammer- sluizen en de effecten van mogelijk te nemen maatregelen.”

[18] “Pilot VerkeersmanagementCentrale van Morgen Trajectplanner, Modelspeciﬁcatie,” 2014. Rijkswater- staat WVL.

[19] A. Grund, “Informatiebehoefte Nautisch Verkeersmodel,” 27 november 2009.

[20] Rijkswaterstaat, “Bedienhandboek versie 5.0,” 11 november 2015.

[21] “Binnenvaartpolitiereglement.”

[22] “Europese overeenkomst voor het internationale vervoer van gevaarlijke goederen over de binnenwa- teren, european agreement concerning the international carriage of dangerous goods by inland waterways (adn).”

115 116 BIBLIOGRAPHY

[23] B. Ding, J. X. Yu, and L. Qin, “Finding time-dependent shortest paths over large graphs,” 2008.

[24] “Vaarwegen in Nederland.” https://vaarweginformatie.nl/fdd/main/infra/downloads.

[25] Rijkswaterstaat, “IVS - Standard records Volkerak, Krammer, Hansweert and Kreekrak from 17th of November 2015.”

[26] “Route planner for fairways.” http://webapp.navionics.com/.

[27] “Regeling snelle motorboten Rijkswateren 1995.”

[28] “Scheepvaartreglement voor het Kanaal van Gent naar Terneuzen.”

[29] “Rijnvaartpolitiereglement.”

[30] “Scheepvaartreglement Westerschelde.”