2. Traffic Assignment: General Issues 6

SEVENTH FRAMEWORK PROGRAMME THEME [SST.2010.1.3-1.] [Transport modelling for policy impact assessments]

Grant agreement for: Coordination and support action

Acronym: Transtools 3 Full title: „Research and development of the European Transport Network Model – Transtools Version 3 Proposal/Contract no.: MOVE/FP7/266182/TRANSTOOLS 3 Start date: 1st March 2011 Duration: 36 months

Deliverable MS56 - “Notes on models for each mode (air, sea, road, and rail)” Document number: TT3_WP9_TEC_MS56_0a – til QA Workpackage: WP9 Deliverable nature: Short note Dissemination level: N/A Lead beneficiary: DTU, beneficiary number 1, Carlo Giacomo Prato Due data of deliverable: 31.12.2011

Date of preparation of deliverable: 31.01.2012 Date of last change: [31.01.2012] Date of approval by Commission: N/A

Abstract: This short note introduces the main concepts behind the development of traffic assignment for the different travel modes considered within TransTools 3 (TT3). As specified in the previous note MS55, traffic assignment models will be implemented on an ArcGis platform in the package Traffic Analyst, will be Mixed Probit models that are able to account for correlation across alternative routes and taste heterogeneity across the population, will be multi-class models that allow considering several trip purposes, and will use specific speed-flow curves that enable representing specific road types. This short note suggests cost and time components of utility functions and accordingly the use of origin-specific VoT. The short note updates the two directions mentioned in the previous note MS55 - ‘Short note on Traffic Assignment’ - that traffic assignment models should move toward, namely the implementation of fast algorithmic solutions and the design of models for specific modes.

Keywords: Traffic assignment, road assignment, rail assignment, air assignment, sea transport assignment Author(s): Carlo G. Prato

Disclaimer: The contents of this report reflect the views of the author and do not necessarily reflect the official views or policy of the European Union. The European Union is not liable for any use that may be made of the information contained in the report.

The report is not an official deliverable under the TT3 project and has not been reviewed or approved by the Commission. The report is a working document of the Consortium. Notes on models for each mode (air, sea, road, and rail)

Report version 1.a 2011

Copyright: Reproduction of this publication in whole or in part must include the customary bibliographic citation, including author attribution, report title, etc.

Published by: Department of Transport, Bygningstorvet 116B, DK-2800 Kgs. Lyngby, Denmark Content

1. INTRODUCTION 5

2. TRAFFIC ASSIGNMENT: GENERAL ISSUES 6 2.1 Matrix thinning 6 2.2 Implementation solutions 8

3. TRAFFIC ASSIGNMENT FOR TRAVEL MODES 9 3.1 Road assignment9 3.2 Rail assignment 10 3.3 Air assignment 12 3.4 Sea transport assignment 13

4. CONCLUSIONS 14

Deliverable MS55 - “Short note on traffic assignment” 1. Introduction

The present note introduces the main concepts behind the development of traffic assignment models within TransTools 3 (TT3), with an emphasis on the formulation of the models for each travel mode. It should be noted that the models are in their development phase, and that this phase suffers from the delay in the delivery of a sample of the data from ETIS+ that was originally expected in September 2011. The structure of the data has been received by the consortium and commented upon by the consortium leader (Professor Otto A. Nielsen), but contacts with the ETIS+ consortium are still on- going. Model design meetings focusing on passenger and freight models have in fact reiterated the need for these contacts with the ETIS+ consortium to be pursued further, since any delay in the delivery of the matrices will be reflected in a delay in the development, estimation and calibration of the models in TT3.

The traffic assignment models for each travel mode presented in this short note take inspiration from the traffic assignment models implemented by DTU and Rapidis within TransTools 1 (TT1) and TransTools 2 (TT2). As noted in the previous note MS55: ‘Short note on Traffic Assignment’, traffic assignment models will be implemented on an ArcGis platform in the package Traffic Analyst (Rapidis, 2011), will be Mixed Probit models that are able to account for correlation across alternative routes and taste heterogeneity across the population (Nielsen, 2000; Nielsen et al., 2002), will be multi-class models that allow considering several trip purposes (see Nielsen et al., 2002), and will use specific speed-flow curves that enable representing specific road types. Users will be able to select options within the traffic assignment models, thus tailoring them according to their needs in terms of number of iterations, solution methods, number of trip purposes, utility function specifications, and selection of random coefficient distributions. For an initial review of traffic assignment and solution methods see Sheffi (1985), and for an initial overview of utility-based analysis see Ben-Akiva and Lerman (1985).

Initially, the present note focuses on more specific details about the implementation of fast algorithmic solutions with respect to the initial assumptions proposed in the previous note MS55. Then, the present note concentrates on the model design for different travel mode by proposing a conceptual overview and hypothesizing utility function specifications with parameters to be estimated and calibrated through the interaction with the passenger and freight models.

5 2. Traffic assignment: general issues

General issues in the traffic assignment models within TT3 concern the reduction of the matrices from the passenger and the freight models, the calibration of the network and the fast implementation of the software. It should be noted that traffic assignment models within TT3 consider very large matrices that are delivered for four purposes (i.e., commuting, business, private, vacation) and five modes (i.e., car driver, car passenger, public transport, train, airplane). It should also be noted that traffic assignment models within TT3 deal with high level of stochasticity, related to the fact that the model accounts for taste heterogeneity across the population and for similarity across alternative routes, and high computational time because of the dimensionality of the problem. As illustrated in the previous note MS55, these issues may be tackled by means of matrix thinning and implementation solutions that are going to be implemented in task 9.1.

2.1 Matrix thinning

Traffic assignment models within TT3 deal with a high dimensionality problem that causes most cells in the matrices to be either extremely small or even empty because the combination of modes and distances is neither reasonable nor attractive to any traveller, given his/her time and budget constraints (e.g., a worker does not commute from Denmark to Portugal every day). The computational expenditure for these traffic assignment models is proportional to the number of cells in the matrices, and hence most computational costs are related to the assignment of cells with less than one trip. Moreover, the computational expenditure is proportional to the square of the distance searched because shortest path calculations are stopped when all destinations are reached and computational complexity is proportional to the area searched.

Accordingly, removing or reallocating cells with entries less than a threshold (i.e., a pre-determined number of trips) enables reducing the memory requirements and hence the calculation costs. Tests have shown that matrix thinning produces very efficient reductions of calculation costs when combined with an ad-hoc selection of a number of iterations dependent on the traffic volume. Tests have also shown that matrix thinning improves convergence when combined with some solution algorithms. These tests have proved that a reduction of the calculation time by 90% is possible for some trip purposes in the model. In fact, it is obvious to achieve a large time saving on calculation costs when cells connecting distant points are removed is obvious, given the quadratic relationship between distance searched and computational costs.

While the previous note MS55 mentioned the issue, the present note proposes solutions to the two questions that need to be answered when reducing the dimensions of a matrix: Which OD-pairs should be selected and which method should be applied for the redistribution of trips (see Kristofferson and Engelson, 2011).

The selection of OD-pairs could be threshold-based or stochastic-based.

6 A threshold-based method imposes a threshold for the demand over the analysed assignment period. OD-pairs over the defined threshold are selected for the thinned matrix. The selection of the threshold depends on the analysis of the distribution of the number of trips over the examined zones and on the level of tolerance the analyst accepts when removing cells. The advantage of the threshold-method in a large-scale model as TT3 is that a large number of OD-pairs may be removed while affecting only a small portion of the demand, given the rather large number of OD-pairs containing zeros or fractions of trips. The disadvantage of the threshold-method is that the removed OD-pairs are biased towards shorter trip lengths (Kristofferson and Engelson, 2011).

A stochastic-based method imposes a random draw of a pre-defined number of OD-pair with the probability of a certain OD-pair of being selected depending on its demand (similarly to the destination sampling method proposed by Miller et al. (2007). The number of random draws depends on the level of tolerance the analyst accepts when managing large matrices. The advantage of the stochastic- method is that OD-pairs with larger demand shares have higher probability of being drawn regardless of the trip length, thus removing the bias of the threshold-method. The disadvantage of the stochastic- method is that not all the small entries may be removed, and likely a large number of OD-pairs may be removed while affecting a larger portion of the demand than the one removed with a threshold- method. Experimental analysis in Sweden has revealed that the threshold-method is preferable because of the latter drawback of the stochastic-method (Kristofferson and Engelson, 2011).

Once the OD-pairs candidates for removal are selected by either methods, five methods are available to redistribute the removed demand to reach the original total demand: Uniform growth factor (UGF), area-specific UGF, cross-fratar, shortest-distance, and proportional (Kristofferson and Engelson, 2011).

After the OD-pair removals, the UGF-method scales up the remaining matrix by a constant. The area- specific UGF-method corrects the general UGF by operating separately on each area relation and hence preserving the geographical trip pattern. The cross-fratar method maintains the row and column totals in the OD-matrix and hence corrects the number of trips starting and ending in each area. The shortest-distance-method assigns half of the removed demand to the closest remaining destination in the same area while keeping the origin fixed, and then assigns the remaining half of the removed demand to the closest remaining origin in the same area while keeping the destination fixed. The proportional method assigns trips to destinations in a measure proportional to their original demand while keeping the origins fixed.

Methods will be tested and compared according to three criteria that compare before and after the matrix thinning procedure: (i) before/after evaluation of the distance distribution, (ii) before/after evaluation of travel duration and delay profiles, and (iii) before/after evaluation of the link flows. It should be noted that the number of trips does not vary with the redistribution, as the number is independent of the applied method.

2.2 Implementation solutions

7 The first issue in the implementation of traffic assignment models within TT3 is the transformation of the OD-matrices received from the ETIS+ consortium into GA-matrices in order to be able to use the appropriate value-of-time (VoT) for the origin zone of the back-and-forth tour represented in the GA- matrices. In fact, the utility function specifications are origin-specific.

The second issue concerns level-of-service (LoS) values that will be calculated per trip purpose and per travel mode by the assignment at the GA-level and hence sent to the demand models. Each cell of the matrices will have the LoS values averaged over the mode choice probabilities, while for each travel mode the LoS values will be averaged over the route choice probabilities. Passenger models are based on GA-matrices and hence will use the LoS values from the assignment models directly, while freight models are based on OD-matrices and hence will use cost matrices and a weighted utility measure.

The third issue is taste heterogeneity that will be expressed by the random coefficients in the Mixed Probit assignment models, but less stochasticity will be allowed by the national-specific VoT values that express some preference variability already. The reduction of the variance of the error term is one of the option on the table to reduce the stochasticity of the models, especially for long trips where error terms are additive across links. As anticipated in the previous note MS55, the simulation of the error terms should not rely on inefficient Monte Carlo simulations, but on alternative solutions such as Halton sequences, scrambled Halton sequences (Bhat, 2003) and Modified Latin Hypercube Sampling (Hess et al., 2006). Intelligent alternative solutions could drastically improve simulation efficiency that some tests have evaluated in 75% calculation cost reduction with Halton sequences applied to the simulation of taste heterogeneity and link error terms.

The fourth issue is the pseudo-dynamic approach to the assignment models. Heuristic distributions on the time of day may be implemented, and the concept is to follow a vehicle that starts its long distance trip in the morning and in the afternoon reaches a certain zone where it will be affected by the peak hour congestion. This approach allows increasing the level of detail of the traffic assignment models without increasing the computational costs.

The last issue is the effort necessary for the calibration of the network and the implementation of the software. One the one hand, a challenge consists in jointly calibrating networks that are specific to the various travel modes for which traffic assignment models are designed, in particular the cross-links (e.g., access and egress trips to airports are loaded on the road network) that need to be properly addressed for an efficient implementation. On the other hand, a challenge consists in the overall implementation of the software and the validation of the traffic assignment models to the 2010 network data that will be provided by the ETIS+ project and will be tested by WP5. The challenge lies in particular in the interaction with the demand models (e.g., transfer of level-of-service data) that need algorithmic enhancements (e.g., outer loop for the MSA) for an efficient implementation.

8 3. Traffic assignment for travel modes

Traffic assignment models will be designed for specific domains by departing from the existing models within TT2 and addressing areas of weakness. The interested travel modes are road, rail, air and sea.

3.1 Road assignment

Traffic assignment models for road traffic will adopt the Mixed Probit model proposed by Nielsen (2000) and Nielsen et al. (2002).

Intrazonal traffic will be accounted for in the road assignment model within TT3, also because of the short-distance demand model for trips below the selected threshold of 100 km that is estimated alongside the long-distance demand model for trips over the same threshold. Then, a set of time period factors will be used in order to describe congestion for trips below 100 km and a second set of time period factors to describe congestion for trips between 100 and 250 km.

The intrazonal LoS will be calculated prior to the assignment, and will stem from the consideration that most trips are short, but some trips are long. The intrazonal trip distance will be expressed as a function of the zonal area that will then be constrained between a minimum and a maximum distance. Given the average intrazonal trip distance, the travel time will be also averaged over the preloaded traffic at the single links within a zone that is weighted by length and traffic. The average travel time will take into account also the presence of tolls once a generalised cost function is constructed, and this feature is extremely useful in order to evaluate pricing policies. The preloaded traffic will be calculated in terms of passenger km as a function of average vehicle occupancy rate, number of vehicles and distance covered, and in terms of truck km as a function of number of trucks, distance covered and a correction factor accounting for the fact that likely trucks cover longer distances than cars. From the AADT for road links within a zone, intrazonal vehicle km will be calculated as a weighted average of passenger km and freight km, which will be able to be forecasted for future years according to growth factors.

The road assignment models will consider the difference between petrol and diesel vehicles on the basis of national factors describing the vehicle share between the two types. Filter criteria will allow considering the correct split of the nationality of the vehicle (e.g., a Danish vehicle in Germany uses Denmark’s split factors). Revenues from variations in the taxation will be calculated correctly by differentiating vehicles according to the fuel types, as well as revenues from variations in toll systems are computed by calculating the travel costs for ferries, bridges, etc.

The road assignment models will consider congestion, as average daily traffic flows will be generated by the demand model and then split into time periods. The level of detail of the split will be quite refined because the matrices are GA-based and not OD-based, and hence for example trips by commuters going to work in the morning will then be automatically and correctly linked to trips by commuters coming back home in the afternoon. The demand split factors will be defined for (i) type-of-

9 day within the week (i.e., four types of day per four trip purposes plus trucks), (ii) time-of-day within the day when considering short trips (i.e., 3 times-of-day per four trip purposes plus trucks), (iii) time-of- day within the day when considering medium trips (i.e., 3 times-of-day per three trip purposes that exclude commuting plus trucks), and (iv) time-of-day within the day when considering access to and egress from airports (i.e., 3 times-of-day per three trip purposes that exclude commuting).

Specifications of different utility functions will follow the differentiation across travel purposes and vehicle type. Generalized cost functions will be constructed by multiplying origin-specific VoT by the time components and then summing travel costs. Moreover, generalized cost functions will be defined at the link level and then summed over to obtain the costs at the route level. For vehicles traveling for all purposes, the time components will include free flow time, congested travel time, ferry waiting time, and ferry sailing time, while the cost components will comprise fuel costs and link costs (e.g., tolls, pricing schemes). Stochastic simulation will be used on the free flow time, the congested travel time, the ferry waiting time and the ferry sailing time. While the same time and cost components will be considered for all the purposes, the parameters of each component will be appositely calibrated, as will be the parameters for trucks that will particularly reflect the higher fuel costs. The cost components will be calculated prior to the assignment as toll costs, which will represent ferry prices and road tolls, and fuel costs, which will originate from fuel prices in 2010 for each country. In addition, a link cost will be specified to represent the generation of revenue for the public budget (e.g., toll revenues for the public budget, fuel taxes for the public budget).

It should be noted that the parameters of the utility functions and the cost components that are nation- specific (e.g., toll roads, fuel taxes) will be made available for users to modify in their application of the TT3 model.

3.2 Rail assignment

The rail assignment model assumes that the network will be considered jointly for passenger and freight rail traffic in order to assign a unique model. The consistency of the network will need to be addressed, in particular for the aspect concerning the railways serving both passenger and freight trains. The capacity of the network will need to be calculated, with heuristic solutions inspired by the UIC 406 capacity guidelines.

While it appears relatively easy to determine the capacity for the roads, where the number of vehicles per hour represents the capacity, it seems more difficult to calculate the capacity for the rail traffic, since both infrastructure and timetables are involved. Even the definition of capacity is not unique for rail traffic, as different definitions have been given over the year (see Landex et al., 2006): (i) ability of the infrastructure to operate the trains with an acceptable punctuality; (ii) capacity of the infrastructure to handle one or several timetables; capacity of the infrastructure does not exist as such, and depends on the way railways are utilized. The reason behind the different definitions is the presence of several parameters that are measurable and are dependent of each other: number of trains, stability, heterogeneity and average speed.

10 According to Landex et al. (2006), capacity is a balanced mix of the number of trains, the stability of the timetable, the high average speed achieved and the heterogeneity of the train system. For example, it is possible to reach a high average speed on a railway network by having a high heterogeneity through a mix of fast trains (e.g., InterCity Express, InterCity) and slow trains (Regional and Local) serving all stations. Notably, the cost of having high average speed with high service heterogeneity is the impossibility to run as many trains with high stability (punctuality) as in the case that all trains run with the same speed. For this reason for example, the suburban railway network in Copenhagen reduces the average speed by running more trains and mixing less trains to avoid this cost in term of stability (punctuality).

A possible method for the calculation of the capacity for the rail traffic is provided by the UIC (2004). According to the UIC 406 method, the capacity consumption on railways depends on both the infrastructure and the timetable, and hence its calculation depends on the actual timetables. It should be noted that the timetables are created for the entire network (i.e., not only for the line or the line section interested by the capacity analysis), and hence the capacity consumption depends not only on the infrastructure and the timetable within the area under examination, but also on the network effects. However, the UIC 406 method does not take into account these network effects and hence the capacity used will be inferior to the capacity consumption.

In order to calculate capacity utilization, timetable graphs are compressed according to the train order and the running times for a defined line or a defined line section. For each line section, all single train paths are moved to reach the minimum headway time in order not to have buffer times left. As the timetable graphs are compressed according to the train order and the running times, it is not possible to change running times, running time supplements, dwell times and block occupation times, and it is allowed to overtake and cross only when overtaking manoeuvres and crossings are scheduled. Once the timetable has been compressed, the calculation of the capacity consumption is performed by comparing the cycle times. Various timetabling pieces of software (e.g., RailSys) implement the UIC 406 capacity calculation method, and a Danish application of the method is provided by Landex et al. (2006).

Once the passenger and freight rail networks are matched and the capacity is calculated, the rail assignment faces two further problems, namely the limited number of traffic counts severely restricting the possibility of validating the rail assignment given that the rail matrices are not checked, and the limited availability of IPR free data greatly reducing the possibility of modelling services along the lines for modelling average frequency and speed per link. It is considered looking for publicly available timetables on railway websites; even though it is likely not possible to obtain a complete description of all the lines and services in Europe, a focused effort in that direction should provide relevant pieces of information for at least the majority of the international connections. This effort would allow modelling lines and services for passenger trains with an enormous benefit for the reliability of passenger railroad zone-to-zone travel times, which is critical for the quality of the level-of-service data provided to the passenger demand model.

Similarly to the road assignment, specifications of different utility functions will follow the separation across travel purposes and will be constructed by multiplying origin-specific VoT by the free flow time

11 component and then summing a distance component with purpose-specific parameters. As for the road assignment, it should be noted that the parameters of the utility functions and the cost components that are nation-specific (e.g., toll roads, fuel taxes) will be made available for users to modify in their application of the TT3 model.

3.3 Air assignment

The air assignment model within TT2 is a multi-modal choice model that represents the choice of airport, the choice of route in the air network, and the choice of feeder mode. This approach allows representing the choice between a flight originating in a local airport and having an intermediate stop (e.g., Lyon-Paris-Copenhagen) and a flight originating in a farther airport and not having an intermediate stop but having a feeder mode choice (e.g., Lyon-Paris by train and Paris-Copenhagen flight). This approach also allows representing the choice between main airports and competing airports served by low-cost airlines. The air assignment models are based on fairly good data sources, since detailed information is available about passenger volumes at the leg level, and since an update of the information to the year 2010 is available on the basis of the ETIS+ project.

The model in TT2 considers an upper and a lower level. At the upper level, the model represents access and egress links as zone connectors. At the lower level, the model splits the flows from a given connector into road and railway flows with a binary logit model, and then assigns these flows to the path from the origin zone to the airport (represented as a pseudo-destination zone). Short connectors are attached from the origin zone to the network (existing connectors for the road and railway assignment) and from the network to the airport (new connectors to the pseudo-destination zone). The LoS along the paths for road (connector, sequence of road links, connector) and railway are calculated as average values according to the likelihood from the binary logit model, and are used for the connectors in the main air route choice model that represents the average connection of the zone directly to the airport. This simplification could be replaced by a more realistic route choice model considering railway and road assignment for the origin-airport and the airport-destination trips, and then a mode choice model between rail and road alternatives, although this would mean to increase the complexity of the model that should model the choice of a specific route rather than the average across the possible alternative routes to reach and to depart from the airport.

The air assignment is run separately for each trip purpose, as utility functions are purpose-specific. An OD assignment of the GA matrices is performed, since outgoing and incoming flows are assumed to be symmetric and capacity is not considered. Generalized cost functions are defined for different purposes, namely private, business and vacation. Each function consists of a purpose-specific parameter, a purpose-specific cost component and time components multiplied by the origin VoT. The time components are the connector time, the flight time, the transfer time and the headway time, with the waiting time possibly added. Each time component is multiplied by the origin VoT and introduced stochasticity in the formulation, and in addition correction coefficients are specified for each purpose. The cost component could potentially not be limited to the fare, and hence be extended to (e.g.) costs for crossing borders that should make travellers preferring airports in their own country. Once the functions are defined, one assignment per purpose is run.

12 The air assignment model requires the consideration of intercontinental air transport that was ignored in TT2. To this extent, data from WorldNet and ETIS+ describing intercontinental flights will be considered and hence improvements from this perspective are achieved for the flight choice and the feeder mode choice. Moreover, the model requires the consideration of alliances in order to better represent the airport hubs, and since their numbers is somewhat limited, it seems feasible to handle them by coding manually the relationships in the case that the data provided by ETIS+ do not account for airline alliances. Technically, an option is the definition of alliances are “pseudo airports” within the same airport hub (i.e., terminals are coded as nodes), since the air assignment model within TT2 already represents transfers between airports in towns with several airports (e.g., Guadeloupe is served from Paris Orly, but many airports in Europe are only connected to Paris Charles de Gaulle).

3.4 Sea transport assignment

Sea transport has not been assigned within TT2 onto a dedicated network, and the TT3 model intends to perform the assignment of specific routes on the basis of data provided by WorldNet through the ETIS+ project. Specific effort is necessary with respect to assigning generalized cost functions on specific routes that consists in a cost component and a time component. The cost component is a function of the volumes moved multiplied by an origin-specific parameter, while the time component is multiplied by the origin VoT, and stochastic elements are considered within the formulation.

It should be noted that inland waterways are assigned separately. Ferries for passenger cars and trucks, as well as RoRo ferries for trucks, are modelled within the road assignment model through the specification of costs, frequency and other variables in the utility functions. Ferries for rail transport are included within the rail assignment model in the rare cases that the trains run on-board the ferries. Ferries and other vessels that carry passengers are included within the rail assignment model in the cases that harbours are close to train stations. Hence, the task focuses on the assignment of freight transport, which is not explicitly assigned in the traffic assignment models within TT2.

13 4. Conclusions

The present note elaborates on the concepts behind the design of traffic assignment models by travel mode within TT3. General issues are discussed for each mode, and possible solutions to issues emerged during TT2 as well as possible utility specifications are hypothesized.

Initially, the present note focuses on more specific details about the implementation of fast algorithmic solutions with particular emphasis on matrix thinning. Details are more specific when compared to the initial assumptions proposed in the previous note MS55. Then, the present note concentrates on the model design for different travel mode by presenting a conceptual overview and hypothesizing utility function specifications with parameters to be estimated and calibrated through the interaction with the passenger and freight models.

The areas of improvement with respect to the assignment in TT2 are: (i) the improvement of road assignment through the implementation of already successfully tested matrix thinning methods; (ii) the enhancement of rail assignment through the simultaneous maintenance of passenger and freight networks and the consideration of capacity constraints; (iii) the improvement of air assignment through the representation of intercontinental air transport and the improvement of the hub representation; (iv) the inclusion of sea transport assignment alongside ferry lines for passenger cars and trucks and ferries for trucks that are modelled within the road assignment model.

Hopefully, the note reaches the scope of facilitating the discussion about the design of traffic assignment models within meetings focusing on the related models of freight and passenger demand.

14 References

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