Implementing Crowding in SL's Transit Assignment Model

EXAMENSARBETE INOM CIVIL ENGINEERING AND URBAN MANAGEMENT, AVANCERAD NIVÅ, 30 HP STOCKHOLM, SVERIGE 2020

Implementing crowding in SL’s transit assignment model. Case study: Stockholm Public Transport Network

ALAA ELTAYEB

KTH SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT TRITA TRITA-ABE-MBT-2039

www.kth.se

Thesis Title: Implementing Crowding in SL’s transit assignment model Case study: Stockholm Public Transport Network Degree Project in Transport planning Master thesis

By Student: Alaa Eltayeb KTH supervisor & Examiner: Erik Jenelius: SL supervisor: Erik Almlöf November 2019

Acknowledgements

I want to express my gratitude to all the people who helped along this way. Without their support, the work that went into this thesis would not be possible. First of all, I am grateful for Trafikförvaltningen for trusting me and allowing me to have this unique experience with them, I have learned so much for just by being there, I would like to thank Erik Almlöf. I would also like to thank Gerasimos Loutos for his time, ideas, and help with Visum. A great thanks to my supervisor at KTH, Erik Jenelius, for his supervision and enlightenment throughout this thesis. To the department of transport science at KTH. To my lecturers at KTH, thank you for being understanding and helpful. A great thanks to My previous supervisor and friend Ilaf Hashim, Ilaf has been a tremendous supporter from day one; she taught me so much, and I am thankful to her for the opportunities even after she left the industry. My mother, Sana, and my father Hashim, my siblings, to the soul of my brother Salah and my precious grandparents. I am grateful for the support, love, and without you, I wouldn't make it. To the people who lost their souls in Sudan during the 2018 revolution while I was here, safe in Sweden. Thank you. To my country, Sudan, every step I took forward, every hardship I encountered and overcame is for the people of my country; you deserved better. And better is coming. And finally, to Swedish institute SI, this journey would become just a dream without your support and help throughout the master period I am forever in your debt. You have changed my life. Thank you To God … thank you, I am so grateful.

Table of Contents Table of Figures: ...... 5 Table of Equations: ...... 6 Table of Tables: ...... 7 Glossary of Terms: ...... 1 1. Background ...... 1 1.1. Study Area Stockholm city: ...... 1 1.2. Objectives ...... 4 2. Literature review ...... 4 2.1. An overall look at Crowding: ...... 4 2.1.1. Crowding definition: ...... 5 2.1.2. Crowding measurements ...... 5 2.1.3. Effect of crowding: ...... 5 2.1.4. Crowding in Transit Assignment Models: ...... 6 2.1.5. Static STA vs Dynamic Transit Assignment DTA ...... 6 2.1.6. Assignment procedures for Base and Crowding scenarios: ...... 8 3. Data Sources ...... 8 4. Modelling approach: ...... 9 4.1. PTV Visum:...... 9 4.2. Sampers: ...... 9 4.3. Stockholm public transport assignment model: ...... 9 5. Implementing Crowding: ...... 10 5.1. Perceived journey time PJT...... 10 5.2. Modeling steps (technical application on Visum PTV): ...... 11 5.2.1. 1st step: Calculate the Travel time component and OD matrix: ...... 11 5.2.2. 2nd step: ...... 11 5.3. Choice models for boarding decisions: ...... 13 5.4. Methodology: ...... 14 6. Evaluating the outputs of the crowding scenarios: ...... 15 6.1. Comparison Between the Complete Information and the Departure from stop area model choice: ...... 15 7. Crowding analysis:...... 17 7.1. RTW Spårfaktor: ...... 17 7.2. Crowding Vs, No Crowding: ...... 19

7.2.1. Result from implementing crowding at the network: ...... 19 7.2.2. Tunnelbana:...... 20 7.2.2.1. Conclusion about volume increasement in metro: ...... 25 7.2.2.2. The effect of crowding in boarding and alighting: ...... 25 7.3. Pendeltåg: ...... 26 7.4. Buses:...... 27 7.5. Light rail: ...... 28 8. Statistical validation of the model outputs: ...... 29 8.1.2. Greenline: ...... 31 8.1.3. Redline: ...... 32 8.2. Pendeltåg: ...... 33 8.3. Light rail ...... 34 8.4. Conclusion about the Validation: ...... 36 9. Model Calibration: ...... 38 9.1. Methodology:...... 39 9.1.1. Data filtering: ...... 40 9.2. Model analysis: ...... 42 9.2.2. 2nd model: ...... 45 9.3. Result from Visum Implementations:...... 49 9.4. Discussion and Conclusion: ...... 50 10. Recommendations: ...... 52 11. Bibliography ...... 53 12. Appendix ...... 55 12.2. Model-2 ...... 58

Table of Figures: Figure 1: Stockholm's municipalities ...... 1 Figure 2: Public transport network of Stockholm city [2] ...... 2 Figure 3: Crowding at the platform and while boarding in Tekniska högskolan metro station ..... 3 Figure 4: equilibrium procedure ...... 7 Figure 5: route assignment model Procedure...... 12 Figure 6; The complete information and departure from stop area choice model in Visum window ...... 14 Figure 7: SL (boarding + alighting) – each scenario (Boarding+alighting) ...... 16 Figure 8: the boarding percentage of base model to the SL observation in random station from the tunnelbana ...... 18 Figure 9: Differences between crowding to no crowding scenarios ...... 19 Figure 10: the difference between crowding to no crowding in Stockholm’s network ...... 20 Figure 11: crowding - no crowding volume in metro network ...... 21 Figure 12: crowding -no crowding in boarding values and percentage for stations between Hässelby strand and Ängbyoplan ...... 22 Figure 13: crowding -no crowding boarding values and percentages for terminal stations ...... 23 Figure 14: crowding -no crowding boarding values and percentages for terminal station at red line,...... 24 Figure 15: crowding to no crowding values and percentages at terminal stations ...... 24 Figure 16: Ropsten station (crowding to no crowding) ...... 25 Figure 17: Pendeltåg boarding values (crowding - no crowding)...... 26 Figure 18: Pendeltåg volume (crowding - no crowding) ...... 26 Figure 19: different Buses types increasement after implementing crowding ...... 27 Figure 20: Tvärbanan, Lidingöbanan, Nockebybanan volumes crowding to no crowding ...... 28 Figure 21: Spårvagn volume (crowding -no crowding) ...... 28 Figure 22: a comparison between the Crowding and base model to SL, Blue line Boarding percentage ...... 29 Figure 23: a comparison between the Crowding and base model to SL, Green line Boarding percentage ...... 31 Figure 24: a comparison between the Crowding and base model to SL, Red line Boarding percentage ...... 32 Figure 25: A comparison between the Crowding and base model to SL, Pendeltåg Boarding percentage ...... 33 Figure 26: A comparison between the Crowding and base model to SL, Spårvagn Boarding percentage ...... 34 Figure 27: A comparison between the Crowding and base model to SL, lokal Boarding percentage ...... 34 Figure 28: Calibration procedures ...... 41 Figure 29: Comparison between the outputs of Model-1, Model-3, Crowding before calibration and SL observations for Boarding values ...... 50 Figure 30: Comparison between the outputs of Model-1, Model-3, Crowding before calibration and SL observations for Alighting values ...... 50 Figure 31: discrete choice model in Visum PTV ...... 52 Figure 32: Future expanstion for stockholm's metro lines Model-1 ...... 56

Table of Equations: Equation 1: average crowding (ACM)...... 10 Equation 2: weighted crowding (WCM )...... 10 Equation 3: The generalized travel time ...... 11 Equation 4: Crowding perceived time journey ...... 11 Equation 5: Regression equation used to calibrate the boarding and alighting ...... 38 Equation 6: Crowding Journey time ...... 39 Equation 7: Journey time Linear regression ...... 39 Equation 8: Model-1, simplified linear regression model for calibration purposes ...... 42 Equation 9: Journey time in Visum ...... 45 Equation 10: Model-2 equations with attributes ...... 45 Equation 11: Model-3 equations with attributes ...... 47

Table of Tables: Table 1: Crowding Multipliers...... 10 Table 2: The generalized travel time weights ...... 11 Table 3: The 2 scenarios boarding and alighting values for different modes in addition to SL values ...... 15 Table 4: The 2 scenarios boarding and alighting percentages to SL ...... 15 Table 5: Base scenario with and without RTW value (boarding and alighting values for different modes in addition to SL values)...... 17 Table 6: Base model with RTW and without in percentages value to SL ...... 17 Table 7: assignment output for crowding and no crowding scenarios ...... 20 Table 8: decreasing and increasing in boarding and alighting in metro (crowding - no crowding) ...... 21 Table 9: boarding and alighting values and percentages (crowding - no crowding) ...... 27 Table 10: boarding and alighting values and percentages (crowding - no crowding) ...... 28 Table 11: Descriptive analysis of blue line for different scenarios ...... 30 Table 12: correlation between the base model and crowding with respect to SL (blue line) ...... 30 Table 13: Descriptive analysis of green line for different scenarios ...... 31 Table 14: correlation between the base model and crowding with respect to SL (green line) .... 31 Table 15:) A comparison between the Crowding and base model to SL, Red line Boarding percentage ...... 32 Table 16: correlation between the base model and crowding with respect to SL (red line ...... 32 Table 17: A comparison between the Crowding and base model to SL, Pendeltåg Boarding percentage ...... 33 Table 18: correlation between the base model and crowding with respect to SL (Pendeltåg) ..... 33 Table 19: A comparison between the Crowding and base model to SL, lokalbana Boarding percentage ...... 35 Table 20: A comparison between the Crowding and base model to SL, Spårvagn Boarding percentage ...... 35 Table 21: correlation between the base model and crowding with respect to SL (light rail) ...... 35 Table 22: Bus crowding multipliers ...... 36 Table 23: the differences between the SL observation to the crowding model boarding and alighting percentages and values ...... 36 Table 24: the differences between the SL observation to the crowding model boarding and alighting percentages and values ...... 37 Table 25: data used for model calibration that’s contained Journey time from the observation to the crowding journey time attributes ...... 40 Table 26: example of the data that used in the simplified linear regression model ...... 42 Table 27: Regression output using 1hr data filtering for model-1 ...... 42 Table 28: 1&2 Descriptive analysis + correlation for model-1 1 hr method ...... 43 Table 29: Regression output using IQR data filtering for model-1 ...... 44 Table 30: Regression output using 1hr data filtering for model-2 ...... 45 Table 31: Regression output using IQR data filtering for model-2 ...... 46 Table 32: example of the data that used in linear regression for model-3 ...... 47 Table 33: Regression output using IQR data filtering for model-3 ...... 48 Table 34: Descriptive analysis + correlation for model-3 ...... 48 Table 35: Result from implementing Model-1 and Model-3 ...... 49

Table 36: Comparison between the outputs of Model-1, Model-3, to SL observations for Alighting values ...... 51 Table 37: Descriptive analysis + correlation for model-1 IQR ...... 57 Table 38: Descriptive analysis + correlation for model-2 1hr method ...... 58 Table 39: Descriptive analysis + correlation for model-2 IQR ...... 58 Table 40: Calibration using weight 0.73 + RWT ...... 59 Table 41: Calibration using weights equal to 1 + RTW value (1.3) ...... 59 Table 42: Calibration using weights equal to 1.4 + RTW value (1.3) ...... 59 Table 43: Calibration using weights equal to 2 ...... 59

Glossary of Terms: SL : Storstockholms Lokaltrafik BI: Inner-city buses BY: Outer-city buses SBY: Stockholm outer-city trunk bus lines ('stombusslinjer') SBI: Stockholm inner-city trunk bus lines ('stombusslinjer') DB: Double Decker bus PT: Public transport JRT: Journey Time WCM: weighted crowding ACM: Average Crowding STA: Static Transit Assignment DTA: Dynamic Transit Assignment DTA Inv : In-vehicle time Acc : Access time Egr : Egress time OWT : Origin wait time Walk : Transfer walk time Wait : Transfer wait time Not : Number of transfers

1. Background: 1.1. Study Area Stockholm city:

Stockholm is the capital of Sweden. Geographically, the city stretches across fourteen islands. The town has a total of 26 municipalities (kommuner), as shown in Figure 1, with a sum of 2.3 million inhabitants. Stockholm is known as Sweden’s most populated region and the most densely populated as well.

Figure 1: Stockholm's municipalities

The Public transport network of the city comprises Buses (inner-city – outer city), Metro lines (Tunnelbana), long-distance, regional rail, commuter train (Pendeltåg), light rail (Stockholm County has four light rail lines, Tvärbanan, Lidingöbanan, Nockebybanan, and Spårväg City) and the archipelago boats as shown in Figure 2. Buses and tunnelbana are managed by Storstockholms Lokaltrafik (SL) throughout several contractors, and Waxholmsbolaget manages boat traffic. During the next ten years, and approximately 350,000 people expected to move to Stockholm [1]. According to a report in Dagens Nyheter, by 2027, the population will reach 2.6 million, an increase of 15 percent compared to 2018, making Stockholm the fastest growing city in Europe.

Figure 2: Public transport network of Stockholm city [2] The city is expecting changes in travel demand due to development in the transport infrastructure, the projects that Stockholm is considering for the next years, according to Region Stockholm [3] included: • The extension of the Blue line till Nacka by 2025, this line will connect Nacka to the T- Centralen with expectations to increase the capacity in the network. • The yellow line to Arenastaden, from Odenplan, the Metro, will go north to Arenastaden in Solna. The line will have three stations, Södra Hagalund and Arenastaden, connecting to the Greenline at Odenplan, planned construction would start in 2020. • Blueline to Barkarby: the extension will be started from Akalla to Barkarby via Barkarbystaden, the construction started in 2019. • The new metro line between Fridhmsplan and Älvsjö, the proposed line will have six stations: Fridhemsplan, Liljeholmen, Årstaberg, Årstafältet, Östberga, and Älvsjö. This line will create more transfer points to other public transport, such as Light Rail and commuter trains. [3] Another project finished by 2019 is the major expansion for Stockholm’s Tram Network, the line is linking the center of Stockholm city to the suburb of Lidingö and Stockholm royal seaport, this line is adding to the passenger’s exchange between the different modes at the central stations (WSP Tramway city, 2017). These projects will increase the demand, usability desirability for transportation within the region of Stockholm. As the population grows, the demand for transportation grows in correspondence. In the current situation, during the morning peak hours (7:00-9:00 am), evidence in several stops shown the

2 demand exceeds the available capacity of the wagons to the point that it posed a challenge for entering and exiting passengers. Figure (3) demonstrate the crowding at a platform and while boarding during a morning peak at Tekniska högskolan metro station, other examples of critical overcrowding at inner-city buses (4,6) during morning and evening peak periods. People commute during peak hours due to work commitment, which requires them to work within specified hours; it is unrealistic to expect changes at peak hours. However, it is possible to redirect commuters among different modes.

Figure 3: Crowding at the platform and while boarding in Tekniska högskolan metro station Furthermore, in Stockholm, the government encourages citizens to use public transportation and cycling at the expense of private cars; the establishing of Stockholm’s congestion charge highlights this topic. The fact drivers pay to reach the center of Stockholm provoked many to use the public transport system instead. The system has accomplished its objectives leading other cities in the country, i.e., Gothenburg, to adopt the congestion charge policy. This scheme gives the best result if the existent public transport system gives advantages over personal vehicle uses in order to handle this shift in modes. The transport system needs to be reliable, faster, comfortable and solve parking problems [4], a survey conducted in London to study overcrowding found the effect of overcrowding might outweigh the effect of reliability and speed if occurred, according to them, commuters find the effect of crowding not only uncomfortable but frightening [4].

During 2017, Ilaf [5], in cooperation with The transport administration (SL), conducted a study to calculate the values of the on-boarding crowding factors in different modes of the public transit network. The resultant crowding factors tested in a small geographical scale of Stockholm consist of 300 zones as a representative of the network, a cost-benefit analysis conducted which compared between two scenarios the base scenario (no crowding) against the new scenario which included the crowding factors in the model. The research [5] conducted gave evidence on the optimistic potential of crowding in a cost-benefit analysis study. However, [5] study has several limitations; the resultant values only limited to specific geographical coverage, and without a validation process to the output data or to the assignment model itself, this might not be sufficient to reflect both current and future situations accurately. Therefore, SL proposed this study to obtain an adequate model that includes the crowding in its calculation across the Stockholm entire public transit network which can contribute to appropriate decision-making on policies that are related to determine the future investment, reduce crowding as well and prevent the existing network from reaching the overcrowding stage. The department of strategic planning in SL is responsible for the public transport future strategies for the Stockholm area including the strategies for managing demand and capacity of the PT system, to be able to elaborate PT planes, SL needs to come up with a robust estimate of the economic value of reducing crowding on the transit system. This research is aiming to develop a realistic travel assignment model. Mainly applying the previously calculated crowding multipliers into the existent Stockholm’s network that included all the modes of transport with more than 1382 zones, the process included validation of the boarding and alighting results from the crowding, also, calibrating the model of 2014 (base year), the goal is to prepare the transport administration model for future year scenario testing that includes crowding on it.

1.2. Objectives

• Develop a route assignment model that includes crowding and can simulate the present and future network supply and demand. • Validate method to the results (output from the crowding model) concerning the observed travel data (statistical data from SL [6]. • Calibrate the model and suggest a new process that should work with transport modeling. 2. Literature review 2.1. An overall look at Crowding:

The usual empirical assessment methods assume that the utility of transport users and mode choice are primarily calculated based on the time and cost as main characteristics affecting people’s traveling behaviors [7] [8]. Recently, new methods indicated the impact of different attributes that affect the users’ experience of the Public transport such as the number of passengers that needed to share the vehicle at the same time, the condition of seats and vehicles, how comfortable and smooth is the ride and other influencing factors. These indicators summed

4 up as trip reliability, environmental preferences, safety, comfort, and crowding. On-board crowding in our primary concern in this study. 2.1.1. Crowding definition:

The term ‘’Crowding’’ itself has several meanings, levels, and measurements; in conventional practices, it refers to people and space ratio in terms of density [9]. However, recent researches ‘’David Stokols’’ has an argument that distinguishes between the density and crowding based on an article titled as ‘’On the distinction between density and crowding: some implications for future research’’ [10], Stokols concluded that crowding is: ‘’subjective, a psychological state in which one’s expectation of space exceeds the available supply’’ (Stokols, 1972). Other researchers such as [11] argued the use of the load factor in favor of the numbers of passenger per square meter as they expressed crowding as the number of standing passengers per square meter at their researches, they explained using this method provides the more realistic result of how passenger perceived crowding rather than the prior mentioned method. This thesis, the crowding, is defined as the occupancy rate or load factor, which is the number of passengers to the number of available seats, which associated with a high occupation and intensity of commuters on vehicles.

2.1.2. Crowding measurements

The crowding is a quantitative measurement. However, other researches indicate it can be classified as a qualitative measurement as well depending on the nature of the observed values [12], also [13] carried out a qualitative investigation to understand the attitude of the commuters while crowding in alleviating the effect of crowding in rail users particularly.

2.1.3. Effect of crowding:

Crowding could add a positive or negative influence on the commuting experience and their travel choices; some researchers concluded that crowding in public transport can be a crucial influence on passenger’s travel experience and affect both route and mode choice [14]. Researchers such as [7] stated that not considering the crowding in the demand estimation as a reason for disutility will lead to overestimation of the demand services. Crowding is associated with the feeling of discomfort and exhausting to the travelers [7] It limits personal safety and security and increases harmful health consequences related to crowding [9]. Some researchers related between the frequency of the services and crowding, by explaining how crowding contribute to an increment of dwell times at the stops during the boarding and alighting and thus service time due to the accumulative delay at the stops or stations, the reliability of timetable and the frequency of the service and accordingly the satisfaction of the commuters [15], some researchers concluded that the crowding is a threat not only for the system users but can even hold the rail industry development [9]. Researchers as [16] have stated that not taking into concern crowding in public transport before the network reaches a saturation limit will reduce the utility and attractiveness for the transit system even if the travel time is kept

5 constant. Also, applying policies to limit the use of privet vehicles might not be effective without considering upgrading the public transport system. The literature delivers obvious indications that are crowding matters to users; and should be considered besides the traditional travel time and cost to represent the broader set of benefits from investment in public transport.

2.1.4. Crowding in Transit Assignment Models:

The Transit assignment models (TAM) are focusing on the selection of routes and assigned passengers to them. They used to forecast the share of the commuters over a transit network [17]. The model used mainly to calculate the number of passengers that used a transit route in a transit network as a function of transit level of service LOS. The input for the model is the Origin- Destination Matrix (O-D matrix), which represents the demand, the supply is the transit network, the output is the expected number of travelers who choose each route in the transit network which required in the evaluation process of transit infrastructure projects.

The distribution of passengers over the routes follows the equilibrium procedure. It based on Wardrop's first principle. The principles based on the assumptions that the route users are as stated as "identical, non-cooperative and rational" in selecting the shortest path and are aware of the travel time of each of these paths if these conditions met, the route network has reached an equilibrium state, [18] the equilibrium process is described in details in a further section. However, the term "travel time" has been converted to a significant comprehensive term, which is the "Generalized Travel Cost," which include sets of travel time and cost attribute, these collectively called GTC see Equation 1.

The TAM is a vital tool when it comes to evaluating, assessing, and planning the public transit networks schemes and investment. As mentioned, the primary function of TAM is assigning passengers on the transit network; the crowding effects will be tested throughout this tool to capture the performance of the systems, how commuters will choose, and switch between routes after the system gets crowded. In general, the Transit assignment model can be categorized into two types: Static and Dynamic transit assignment model in which each will be disused further.

2.1.5. Static STA vs Dynamic Transit Assignment DTA 2.1.5.1. Equilibrium:

As mentioned previously, there are two types of transit assignment models. The Static STA and Dynamic transit assignment models DTA. Both share some similar general concepts which are the travelers want to reach their destination at the shortest time and minimum cost, the travelers want to minimize their travel times, by common sense, using shorter routes which will provide shorter travel time. Imagine a pair of O-D that connected with a set of routes, each with different travel times. Intuitively, all users tend to use the shorter route. The short route could be a single path or a set of multiple routes, each with a probability describing the usage by passengers. As all the

6 passengers started to use this shortest path, this will lead to a reduction of the traveler time on the other routes (less crowded), and an increment of the travel time on this shorter route (crowded); this process will continue until all the routes between these O-D reach the same minimal travel time, this procedure called equilibrium.

Caculate route travel time

Adjust route Find shortest choice toward path equilibruim

Figure 4: equilibrium procedure

2.1.5.2. Static transit assignment STA

The static transit assignment used for strategic planning and policy-making due to its simplicity, efficiency and the ability to manage vast scale network and require less computational power [19] [20], however, the static models overall fail to capture the effect of time-dependent phenomena. There are several static models with different procedures; however, the one that is used widely and mainly at Traffic administration (SL) is the ''user equilibrium transit assignment model,'' which uses the equilibrium process that previously elaborated in2.1.5.1 An iterative process involving three main steps Figure 4 explains the procedure in solving STA. This application seeks to capture the impact of different traveler departure times on network conditions; the constant origin-destination (OD) demands matrix is input. It remains constant between iterations in addition to the network, which is also a constant component, it mentioned that the headway is constant as well throughout the assignment procedure.

2.1.5.3. Dynamic transit assignment DTA

The dynamic assignment based on transit timetables or schedules; the idea is to capture time- dependent trends such as the peak periods demand instead of giving an average measure of the network performance values (only travel time and cost) as in static. Unlike the static assignment, the network is time-varying and expected to be more realistic. In this model, the demand, which is the time-dependent origin-destination matrix (OD), is the input for the model, the supply is the network, both considered as time-dependent attributes, in this method the goal is to observe the effect of different commuter’s departure times on network conditions. This application required high computational power and sufficient detailed data [20].

2.1.6. Assignment procedures for Base and Crowding scenarios:

In addition to the different types of assignment models, there are different types of assignment procedure as well that common share concept in using the equilibrium method but vary in the required input data, the accuracy of results, and computing time [19]. The assignment procedure categorized into three different procedures: The Transport System-Based suitable for a simple network as a draft to identify the ‘’ideal line network’’ which is unrealistic, commuter picks the fastest route without any restriction of a timetable in this assignment method, Number of transfers, transfer wait time, and service frequency cannot be calculated or considered. [19] The Headway-Based Procedure (also referred to as frequency-based models) is when no timetable provided for the network; this procedure does not require a detailed public transport timetable as an input; only averaged headway is sufficient. The headway procedure is used mainly for strategic planning for future investment, where the data of the timetable is not available. SL adopted this procedure for analyzing future transport projects as it is the most suitable for strategic development The Timetable-Based Procedure: when a detailed timetable provided as an input. 3. Data Sources

The first source provided from ‘’Fackta om SL och länet 2014’’ [6], the data are the boarding and alighting counts for all the stations and modes in the transit network; however, only the inner buses stations were considered in this study, the extracted information is during the morning rush period (6:00–9:00 am) on working day during wintertime. The methodology used to collect this data are Automated Passenger Count (APC) in Buses and the on-board load scale in the metro cars. The Automated Passenger Count (APC) is data acquisition system that can automatically count passengers via a sensor installed in vehicles register the number of legs boarding and alighting at each stop/station, a tenth of the vehicles mainly used in all mode of transport equipped by APC except the metro cars. The other method is the onboard load scale data, basically, on the metro, the number of passengers in each car is estimated based on an average weight of 78 kg per passenger, the device installed on each pair in all cars, it obtained by dividing the total passenger load at each link by the average passenger weight 75 kg. The second source is the national travel survey RVU 2015 per_resa 160601 [21] which represents travel diaries collected form passengers traveling from the origin zone till destination zone, this source used for calibration purposes.

4. Modelling approach: The scope can shortly be described as to implement the crowding multipliers, evaluate the performance of the model outputs, validate the model's outputs with the observed data from [6], and last calibrate the model output with the data obtained from the travel survey of the year 2015. The software that used to apply the assignment method is the PTV Visum 18. The main objective is to capture how crowding would affect the passenger's route assignment; the crowding multipliers are added only on the 4th step of the traditional four steps models, this action will only affect how people choose their route exclusively, thus remaining a fixed value for the demand in the transit system. Some studies add the crowding in the 3rd step of modeling; the mode choice step, however, this method will result in changing the O-D matrix values and thus changing the route assignment values. In this study, the O-D matrix (demand) and the supply (the network) are fixed components in the transit network as it is a static assignment model.

4.1. PTV Visum:

VISUM is macroscopic transport planning and analysis software designed for simulation of planning-level networks. VISUM is the leading software used at SL for forecasting and measuring the effect of plans regarding transport infrastructure investment. At SL, the 4th step (route assignment) usually carried out on PTV Visum along with the calculations of the LOS travel time matrix, which is the input for Sampers software. the 1st step (generate the O-D matrix), the 2nd (Trip Distribution), and the third (Modal Split) step carried on Samper software. [19].

4.2. Sampers:

VISUM is macroscopic transport planning and analysis software designed for simulation of planning-level networks. VISUM is the leading software used at SL for forecasting and measuring the effect of plans regarding transport infrastructure investment. At SL, the 4th step (route assignment) carried out on PTV Visum along with the calculations of the LOS travel time matrix, which is the input for Sampers software. The 1st step (generate the O-D matrix), the 2nd (Trip Distribution), and 3rd (Modal Split) step carried on Samper software.

4.3. Stockholm public transport assignment model:

Stockholm’s public transport assignment model is established by Storstockholms lokaltrafik (SL). The model is a headway based and implemented in PTV Visum version 18. Consists of 1394 zones, 4018 nodes, 11204 links, and 942 public transport lines covering Stockholm region urbanized parts and all transit modes. The model only captures the public transit system; the private vehicles are excluded, covering the trips between 6:00 to 9:00 am during a wintertime and weekday trips as well. For each pair of origin and destination, the travelers are assigned to the different routes and transit lines. The output of the model is the weighted average travel times known as Perceived journey time (PJT), route volumes, and line flows [22].

5. Implementing Crowding:

This study is built on the output of Ilaf Hashim’s thesis [5] in which she calculated the crowding multiplier values and applied the result in a cost-benefit analysis CBA. Ilaf concluded the advantages of using weighted crowding (WCM) over the average crowding (ACM). The values of ACM replicate the values of the average on-boarding crowding (average passenger load of all the observation), this means the variation of highly values observation and low values will eventually compensate each other and thus the crowding neglect the load differences between different departures which lead to less or more severe crowding condition.

∑푛 푝푎푠푠푒푛푔푒푟 푙표푎푑 2 ( 푚=1 푖,푚) 푛 퐴퐶푀 = 0.85 + 0,35 × ( ) 푆푒푎푡 푐푎푝푎푐𝑖푡푦푖

Equation 1: average crowding (ACM).

∑푛 푝푎푠푠푒푛푔푒푟 푙표푎푑 2 ( 푚=1 푖,푚) 푛 푛 ∑푚=1 푃푎푠푠푒푛푔푒푟 푙표푎푑푖,푚 × ( 0.85 + 0,35 × ( ) ) 푆푒푎푡 푐푎푝푎푐𝑖푡푦푖

푊퐶푀푖 = 푛 ∑푚=1 푃푎푠푠푒푛푔푒푟 푙표푎푑푖,푚

Equation 2: weighted crowding (WCM ) Basically (HASHIM, 2017) created a simple linear regression equation to link between the ACM and the WCM for each mode and concluded the following Table 1, The table below gives the values that should be used in order to convert the ACM into a WCM where (X) is the average crowding in Equation 2

Mode Approximation Slope Intercept Inner city trunk lines Y = 2.05LN(X)+1.28 2.05 1.28 Double decker lines Y=1.04LN(X)+1.03 1.04 1.03 All other bus lines Y=1.45 LN(X)+1.10 1.45 1.10 Light rail Y=1.54 LN(X)+1.11 1.54 1.11 Commuter trains Y=2.08 LN(X)+1.10 2.08 1.10 Metro Y=1.43 LN(X)+1.10 1.43 1.10 Table 1: Crowding Multipliers

5.1. Perceived journey time PJT

The term ‘’generalized cost’’ in Visum is expressed as Perceived journey time (PJT) or Impedance. The generalized cost includes a linear combination of seven weighted attributes, as shown in Equation 3 and Table 2. The PJT value is higher than the actual time of the journey mainly because PJT includes costs that refer to time spent carrying out the journey, such as waiting time and transfer time. The generalized cost is used both in modeling the choice of stops and in the route and line choice.

푃퐽푇 = 퐼푛푣푒ℎ𝑖푐푙푒 푡𝑖푚푒 ∙ 푊 푖푛푣 + 퐴푐푐푒푠푠 푡𝑖푚푒 ∙ 푊푎푐푐 + 퐸푔푟푒푠푠 푡𝑖푚푒 ∙ 푊 푒푔푟 + 푂푟𝑖푔𝑖푛 푤푎𝑖푡 푡𝑖푚푒 ∙ 푊 푂푊푇 + 푇푟푎푛푠푓푒푟 푤푎푙푘 푡𝑖푚푒 ∙ 푊 푊푎푙푘 + 푇푟푎푛푠푓푒푟 푤푎𝑖푡 푡𝑖푚푒 ∙ 푊 푊푎푖푡 + 푁푢푚푏푒푟 표푓 푡푟푎푛푠푓푒푟푠 ∙ 푊푁표푇

Equation 3: The generalized travel time

Variable Description Default Time multipliers (min) In-vehicle time [Inv] Time spent in a vehicle 1.00 Access time [Acc] Time spent on a connector from an origin 2.00 Egress time [Egr] Time spent on a connector to a destination 2.00 Origin wait time [OWT] Wait time at the first stop, determine by a headway of a line 2.00 Transfer walk time [Walk] Time spent walking to a transfer 2.00 Transfer wait time [Wait] Time spent waiting for a connecting line determined by a headway of the connecting line 2.00 Number of transfers [Not] The numbers of transfer an individual make 5.00

Table 2: The generalized travel time weights

5.2. Modeling steps (technical application on Visum PTV): 5.2.1. 1st step: Calculate the Travel time component and OD matrix:

The first step is to calculate the level of serves (LOS) in a format of travel time matrix, also known as skim-matrix, which represents the input to Sampers software for the public transport network. The travel time component is equal to the sum of generalized cost, the Perceived journey time (PJT), or impedance. The skim is the process used to measure time, costs and distances between a pair of zones, skim is calculated for each of attributes of impedance (in-vehicle time, waiting time, walking time, Egress time, Transfer time, Origin waiting time, Numbers of transfer and other attributes such as journey time, etc.) [23]. Paths are assessed by their generalized costs, respectively, using the equilibrium method. For the base scenario (no-crowding), the LOS value is the input for Sampers, form the public transport attributes along with other inputs form Emme, which is LOS for cars, bikes, and walk. Sampers gives the results of the Trip generation, Trip distribution and mode choice these values that represent the ‘’Demand matrix for transit network (OD)’’ the resultant (O-D) is the new input for Visum to calculate the route assignment model for the different scenarios, see Figure 5 below. 5.2.2. 2nd step: In this step, the crowding multipliers are implemented in the crowding a scenario in the assignment model. The crowding multipliers values ( 푊 퐶푟표푤푑푖푛푔 ) in Table 1 were added as a weighted parameter on the In-vehicle time attribute, as shown in Equation 4 below: 푃퐽푇 = 퐼푛푣푒ℎ𝑖푐푙푒 푡𝑖푚푒 ∙ 푊 푖푛푣 . 푊 퐶푟표푤푑푖푛푔 + 퐴푐푐푒푠푠 푡𝑖푚푒 ∙ 푊푎푐푐 + 퐸푔푟푒푠푠 푡𝑖푚푒 ∙ 푊 푒푔푟 + 푂푟𝑖푔𝑖푛 푤푎𝑖푡 푡𝑖푚푒 ∙ 푊 푂푊푇 + 푇푟푎푛푠푓푒푟 푤푎푙푘 푡𝑖푚푒 ∙ 푊 푊푎푙푘 + 푇푟푎푛푠푓푒푟 푤푎𝑖푡 푡𝑖푚푒 ∙ 푊 푊푎푖푡 + 푁푢푚푏푒푟 표푓 푡푟푎푛푠푓푒푟푠 ∙ 푊푁표푇 Equation 4: Crowding perceived time journey

Figure 5: route assignment model Procedure 12

The crowding multipliers for each mode has represented as a linear equation that has a slope and intersects. In Visum, these values were added in user-defined attributes, both the slope and intersect values as an attribute of ‘’Vehicle combination’’. The reason behind that it is affected mainly by the capacity of the vehicle; how many persons in this vehicle compared to the number of seats, however, since the crowding is a time-varying event that might occur at any time during the peak hour span (7-8 am), the crowding equation treated as a ’’time profile item’’ attribute. After adding the crowding multipliers as impedance, the procedure requires identifying import assignment characteristics for the route, the assignment known as the Choice Model for Boarding Decision. It can be explained as a choice between several boarding stops; when the passenger decided to board into a specific line/path or other based on different observations such as the level of information provided, the cost of the line, which line will provide the least remaining cost this step is discussed in detailed in the following section .

5.3. Choice models for boarding decisions:

There are in total of five different models when it comes to boarding decisions, each with different principles that vary in the procedures that commuters were adopting when they decided to board. The five models are varying between each other on the level of information given to the passenger, basically different assumption in each model regarding the passenger’s level of information is set in order to decide which next line should be taken based on arriving vehicle information, i.e., does the passenger knows the information about the arrival of next vehicles or the headways. In the headway-based assignment, it assumed that the passengers are aware of certain information such as headways and times [19]. The five models are: [19] • None (optimal strategies) The commuter has no more info. The headways distributed exponentially (No information and exponentially distributed headways). • None (constant headways) The passenger has no further information. The headways are constant (No information and constant headways). • Elapsed wait time, the passenger uses information on the elapsed wait time. The headways are constant (Information on the elapsed wait time). • Departures from stop area at the stop (Information on the next departure times of the lines from the stop). In this model, the headway is constant; the model tries to mimic that a traveler has information on upcoming departures at the stops, and the following assumption is made: o The passenger knows the departure time information of the lines (i.e., provided on a dynamic passenger information system). o Information about lines serving stops nearby is also presented at the stops o And information on departure times from the next stop is provided in the vehicle for passengers who intend to alight at the next stop o information on departure times from the next stop is provided in the vehicle for passengers who intend to alight at the next stop • Complete information Already in the origin zone, the passenger knows the departure times in detail. Know precisely the departure time. Time and headways of lines. The headways are

constant. This model attempts to simulate that the traveler knows the timetable of the public transports [19]

SL assigned their base model (no-crowding) with the ‘’Complete Information’’ method. In this method, the model attempts to simulate the passengers assuming they know in detailed information such as the departure times of all the routes from the Origin Stop, and the headways. Based on this information, the passenger decided to board into the line that gives the least cost in terms of money and time (in this method, the waiting time assumed to be the least). The focus of this thesis is to Departure from the stop area and complete information methods.

5.4. Methodology:

A total of 3 scenarios were tested and compared against each other and with the result by SL statistic (Lokaltrafik, 2014); the models are: • The ''base model'' for the year 2014 (no crowding scenario). • Crowding scenario-1 using Complete Information methods in assignment procedure. • Crowding scenario-2 using Departure from Stop Area method in assignment procedure.

The assignment procedure used in the two crowding scenarios is almost identical; the only change is on the Choice model method see Figure 5. The Complete information method is tested against the Departure from The Stop Area. By testing both methods, a significant change occurred at the outputs values of boarding and alighting in addition to the volume of links, more explanation for the methods and result is carried out in the following parts. .

Figure 6; The complete information and departure from stop area choice model in Visum window

6. Evaluating the outputs of the crowding scenarios: 6.1. Comparison Between the Complete Information and the Departure from stop area model choice:

Table 3 and Table 4 below provide the outputs of the crowding assignment procedure using the two crowding scenarios illustrated in 5.4. A total of 5 iterations were carried out to reach the equilibrium, [5] has found that more than five iterations would not provide any significant difference at the averages assignment outputs (the values for all the routes and links volume at the network). Table 3 gives the result for both scenario-2 and scenario-3, Departure from the stop area, and complete information, respectively, in addition to SL observations. Table 4 gives the same values in terms of percentages.

Mode Crowding -Complete Crowding-Departures from stop area SL observations Information

Boarding Alighting Boarding Alighting Boarding Alighting Tunnelbana 85,276.00 85,276.00 103,930.00 103,930.00 131,350.00 146,900.00 Pendeltåg 27,622.00 31,082.00 32,182.00 35,545.00 40,350.00 40,350.00 Light Rail 16,587.00 18,734.00 18,316.00 19,716.00 20,507.50 20,337.50 Bus Inner city 85,621.00 97,732.00 87,183.00 94,435.00 47,982.50 74,800.00 Total 215,106.00 232,824.00 241,611.00 253,626.00 240,190.00 282,387.50 Total / SL values 89.5% 82.4% 100.6% 90%

Table 3: The 2 scenarios boarding and alighting values for different modes in addition to SL values

Mode Crowding -Complete Information to SL Crowding-Departures from stop area to SL Boarding Alighting Boarding Alighting Tunnelbana 65% 58% 79% 71% Pendeltåg 68% 77% 80% 88% Light Rail 81% 92% 89% 97% Bus Inner city 178% 131% 182% 126%

Table 4: The 2 scenarios boarding and alighting percentages to SL From Table 3, by implementing crowding in the model, a noticeable increase in the bus’s boarding value using the CI method equal to (+78%) and (+82%) using the DFSA method in comparison to the SL observations. Another observation is the overall decrease in the boarding and alighting values of the metro (Tunnelbana) equal to (-35% in boarding and -42% in alighting using CI and - 21% in boarding and -29% in alighting using DFSA), the commuter train (Pendeltåg) equal to (in boarding -32% and -23% in alighting using CI and -20% in boarding and -12% in alighting using DFSA), and the light rail equal to (in boarding -19% and -8% in alighting using CI and -11% in boarding and -3% in alighting using DFSA). However, as previously mentioned, bus boarding and alighting passenger value have significantly increased, which creates a balance with the decrease in the other mode in the system, in which a decrease in the other modes faced by an increase in Bus modes as shown in Table 3 and Table 4. From the results and the previous discussion, it can be concluded that the crowding scenario using Departure from stop area (DFSA) overall, gave a better presentation and result than the

15 crowding using Complete information (CI) when comparing the result to SL observations, the variance between DFSA (scenario-2) to SL observations in the boarding and alighting values is less than CI (scenario-3). Overall, assignment outputs using DFSA are within ±30% error range except the boarding of the bus, which exceeded +82%.

TOTAL (BOARDING+ALIGHTING)

35,664.50

-27,340.50

-74,647.50

C R O W D I N G - C O M P L E T E CROWDING - DEPARTURES FROM BASE MODEL (NO - CROWDING) INFORMATION S T O P A R E A

Figure 7: SL (boarding + alighting) – each scenario (Boarding+alighting)

Figure 7 represents the differences between SL observation (the sum of boarding + alighting) and each scenario (sum of boarding + alighting), the Departure From Stop Area gave better result and fewer variances in comparison to SL observations (-27,340.50 persons) than the Complete Information method ( -74,647.50 persons) and the Base model (+35,664.50) persons.

7. Crowding analysis:

After determining the Departure from Stop Area (DFSA) as the ‘’choice mode for boarding model’’ in the assignment procedure in this study, evaluation and validation of the result are carried out in this section.

7.1. RTW Spårfaktor:

In this section, a comparison between the crowding scenario to no crowding is carried out. In the calculation of the base scenario assignment model, a factor called RTW (Spårfaktor) was added to the assignment procedure in the ’’ transport system’’ attribute in Visum PTV18, this factor is only dedicated toward the bus mode with a value equal to (1.3) multiplied by the in- vehicle time of the bus mode only. The factor is introduced to the SL assignment model as a calibrating factor to make the bus mode less attractive.

Mode Base with RTW Base without RTW SL observations Boarding Alighting Boarding Alighting Boarding Alighting Bus BI 34,156.00 35,342.00 42,674.00 45,253.00 47,982.50 74,800.00 Light Rail 23,172.00 24,501.00 20,086.00 21,622.00 20,507.50 20,337.50 Pendeltåg 44,761.00 48,263.00 40,580.00 44,055.00 40,350.00 40,350.00 Tunnelbana 138,359.00 138,359.00 126,303.00 126,303.00 131,350.00 146,900.00 total 240,448.00 246,465.00 229,643.00 237,233.00 240,190.00 282,387.50

100.1% 87.3% -95.6% 84%

Table 5: Base scenario with and without RTW value (boarding and alighting values for different modes in addition to SL values)

Mode Base with RTW Base without RTW Boarding Alighting Boarding Alighting Bus BI -29% -53% -11% -40% Light Rail 13% 20% -2% 6%

Pendeltåg 11% 20% 1% 9%

Tunnelbana 5% -6% -4% -14%

Table 6: Base model with RTW and without in percentages value to SL A base model without RWT gave a total of (229,643) passengers (see Table 5), which is lesser than the SL observation (240,190) by 4% (see Table 6). However, after adding the RTW, the total sum of boarding passengers jumped to (240,448 passengers), which is similar to the total of the SL observations (240,190)

Adding the RTW to the base model has made better results in the total sum of boarding and alighting passengers at the network. However, separately, the metro, commuter train, and the light rail have faced adverse effects by adding the RTW factor. Table 6 provides the percent of the differences between the base model scenario (with RTW and Without RTW) to SL

observation. The Base model without RTW gave fewer variance results than the base model with RTW values; i.e., in light rail, the variance between the base model concerning the SL observations in boarding and alighting values Without RTW are ( -2% and +6%) respectively, and with RTW to the SL observations are (+13% and +20). In Pendeltåg Without RTW (1% and 9% ) and with RTW (+11% and +20%), in BI Bus (Without RTW (-11 and -40%) compare to (-29% and - 53%) with RTW and in the metro the variance between the base model Without RTW to SL observations are (-4% and -14%) and with RTW (+5% and -6%). From the above, we can indicate that the result of adding the ‘’RTW’’ factor to the model has increased the variance between each mode (boarding and alighting passengers) to SL observations in comparison to ‘’Without adding RTW factor’’.

METRO STATION BASEMODEL COMPARISON

With RTW/ SL Without RTW / SL

162%

152%

147%

140%

139%

137%

127%

117% 117%

114%

113%

112%

111%

110%

109%

108%

106%

104%

102%

100%

98%

96%

95%

93%

84%

82%

81%

80%

79%

77%

75%

73%

72%

71%

70%

66%

62%

60%

55%

16%

15%

2% 2%

Figure 8: the boarding percentage of base model to the SL observation in random station from the tunnelbana

Figure 8 gives the percentage of boarding passengers for the base model with two scenarios (Without RTW and with RTW) concerning SL observation for random metro stations. The main point of this is to test whether adding RTW factor has made an impact on the passenger distribution among the stations or not, in other words, does adding RTW makes the boarding in stations more realistic than not adding it? The result from Figure 7 indicates that adding the RTW factor has not made the boarding values more realistic compare to not adding it; in fact, it harms each mode.

7.2. Crowding Vs, No Crowding:

From Figure 9, Implementing crowding increased the numbers of boarding and alighting by 14% (51,796) from no crowding scenario. In total, the demand at origin and destination nodes reminded the same, (only 0.6% variance), which considers insignificant error for a total of 1394 zones that cover the urbanized area of Stockholm. The same number of people started their journey from an origin zone, and these commuters board into different routes based on different characteristics and priorities, i.e. ( the least remaining cost), the same number of people reached their desired destination regardless of the mode or route used. However, the numbers of the boarding and alighting have increased in crowding scenario; the most convenient explanation is that people started to use multiple routes/lines in order to get to their destination which has been seen at the resultant number of transfers which has increased by 26% (74,381) from no crowding scenario.

Boarding at stop level Departure from stop point

Crowding scenario No Crowding (Base) Differences Series1 425,499.00 373,703.00 51,796.00

Figure 9: Differences between crowding to no crowding scenarios

7.2.1. Result from implementing crowding at the network:

This part is studying the effect of crowding multipliers in a detailed approach by taking into consideration each mode and some representative stations at the network to capture the difference between crowding to no crowding. Looking at Figure 10 , which represent the differences between the Crowding – no crowding, the green color represents an increase of the volume; the red color represents a decrease of the volume: 퐶푟표푤푑𝑖푛푔 푆푐푒푛푎푟𝑖표 − 푁표 푐푟표푤푑𝑖푛푔 푆푐푒푛푎푟𝑖표 = (+푝표푠푡𝑖푣푒) 퐼푛푐푟푒푎푠푒 표푓 푡ℎ푒 푝푎푠푠푒푛푔푒푟푠 표푟 𝑖푛 푣표푙푢푚푒 퐶푟표푤푑𝑖푛푔 푆푐푒푛푎푟𝑖표 − 푁표 푐푟표푤푑𝑖푛푔 푆푐푒푛푎푟𝑖표 = (− 푝표푠푡𝑖푣푒) 퐷푒푐푟푒푠푒푠 표푓 푡ℎ푒 푝푎푠푠푒푛푔푒푟푠 표푟 𝑖푛 푣표푙푢푚푒

The network overall (see Figure 10) gives the perception that the crowding increased the volume in all lines and routes except some lines i.e., blue metro line and some Pendeltåg lines. The values support this claim from results in Figure 9 and Table 7 as the total of the Boarding and alighting has increased by 14%. All modes tested individually to observe the passenger’s assignment changes after implementing crowding.

Figure 10: the difference between crowding to no crowding in Stockholm’s network

Mode Base model (No-crowding) Crowding-Departures from stop area SL observations

Boarding Alighting Boarding Alighting Boarding Alighting T.bana 138,359 138,359.00 103,930.00 103,930.00 131,350.00 146,900.00 Pendeltåg 44,761 48,263 32,182.00 35,545.00 40,350.00 40,350.00 Light Rail 23,172 24,501 18,316.00 19,716.00 20,507.50 20,337.50 BI 34,156 35,342 87,183.00 94,435.00 47,982.50 74,800.00 Total 240,448.00 246,465.00 241,611.00 253,626.00 253,626.00 253,626.00

Table 7: assignment output for crowding and no crowding scenarios

7.2.2. Tunnelbana:

The result is based on the comparison between the volume (the numbers of passengers at a line) of crowding scenario to no crowding scenario. SL observations for volume data is not available. Therefore, the changes in volumes are tested only within the Visum software estimations and predictions for each scenario; Figure 11 below represents the difference between crowding to no crowding (No crowding scenario (Base) – crowding scenario).

Figure 11: crowding - no crowding volume in metro network

From Figure 11, an increase in the metro network’s volume is observed; this might be contrary to the decrease in the number of boarding and alighting as described (-34,429 persons) in Table 7. Table 8 shows the values of the boarding and alighting passengers for the metro, the decreasing stations added separately, and the increasing stations are added as well, the network was subjected to a decrease equal to ( -45,793) in the boarding, an increase equal to (+11,360 persons) in boarding (crowding – no crowding), almost similar values at the alighting too. The next section explains the reason behind the volume increases despite the decreases in the number of boarding. Crowding - no crowding Boarding - Boarding + Alighting - Alighting + -45,793.00 +11,360.00 -47,096.00 +12,671.00

Table 8: decreasing and increasing in boarding and alighting in metro (crowding - no crowding)

Figure 12, Figure 13, and Figure 14 provide the differences between the crowding to no crowding for only boarding values for random stations.

Figure 12: crowding -no crowding in boarding values and percentage for stations between Hässelby strand and Ängbyoplan

Looking at Figure 12 and by tracking the red arrow, the numbers of boarding at Hässelby strand station (terminal station) has decreased by (-39 persons) (-5%) which lead to a decrease at the volume at the line equal to (-5%), the following station Hässelby gård decreased by 5% (-40 persons) in boarding which lead to a decrease of the volume equal to 5% . Same decreasing in boarding the Johannelund station lead to a decrease at the volume by -5%. However, when reaching Vällingby station, an increase equal to almost 46% has occurred at the number of boarding which lead to increase the volume at the line by 24% from the no crowding, this sudden increasing is followed by a steady decrease at the following stations as the numbers of boarding continue to decrease, Råcksta -14% in boarding which effected the line volume yet still larger than the volume in this section with no crowding..

Figure 13: crowding -no crowding boarding values and percentages for terminal stations

Figure 13 shows the 3 terminal stations of the green line, Hagsätra, Farsta strand, and Skarpnäck. The values in blue and red columns in each station are the boarding values and percentages, similar as Figure 12, after implementing crowding factors, the terminal stations subjected to an increase in the number of the boarding passengers compare to no crowding which led to an increase at the volume of the line. In some parts, such as the line from Rågsved station (positioning at far right, right after Hagsätra station in Figure 13) the boarding increased by 2% (+17 passengers board more than no crowding). However, the volume decreased (from 76% at Hagsätra to 30% in Rågsved ), the reason is that the numbers of alighting at Rågsved have increased after implementing crowding to (131%) which is significantly larger than the increased at boarding (2%) therefore, a decrease in the volume has occurred from (76 % to 30%).

Figure 14: crowding -no crowding boarding values and percentages for terminal station at red line, Figure 14, indicates a decrease in the volume of the line due to a decrease at the boarding values started from the terminal stations Ropsten (-14% -386 persons) a volume decreased by -14% and continue throughout the red line as the boarding values continue to decrease throughout the stations in the red line.

TERMINAL STATION BOARDING (CROWDING - NO CROWDING )

Borading (Crowding -no crowding) Boarding precentage

1077

467

166

165

128

82%

43%

12% 10% 2% 17% 37%

5% 8%

40 40

- -

16% 13%

44% 39%

- -

160 160

173

- -

387

FRUÄT

ALVIKT

ROPSTT ÅKESHT

HAGSÄT

MÖRBYT

FARSTRT

AKALLAT

HÄSSTRT

SKARPNT

NORSBOT HJULSTAT KUNGSTRT Figure 15: crowding to no crowding values and percentages at terminal stations

7.2.2.1. Conclusion about volume increasement in metro: To summarize the reasons behind the increase of the volume at the metro lines despite the decrease in the total numbers of boarding and alighting when comparing crowding to no crowding and by looking at Figure 12, Figure 13, Figure 14 and Figure 15above, a conclusion can be drawn based on the previously explained observations. Overall, when a terminal station is subjected to an increase in the number of boarding, the rest of the line will be accompanied by this increase, as shown in Figure 12and Figure 13and vice versa. In order for a change in volume to happen (in the form of an increase at the volume after a decrease and vice versa), this required a significant decrease or an increase in boarding values or alighting to make a change in the volume of passenger i.e., Rågsved station in Figure 13. From Figure 15, the majority of terminal stations in the metro network subjected to an increase in boarding, which leads to an increase in the volume. Looking at Figure 13, the terminal stations with negative boarding values subjected to a decrease in the volume i.e., Akalla, Hjulsta, Ropsten. On the other hand, the stations that gave subjected to an increase at the boarding i.e., Åkeshov, Hagsätra, Farsta strand, Skarpnäck accompanied by an increase of the volume values throughout the line. 7.2.2.2. The effect of crowding in boarding and alighting: This part is explaining the distribution of passengers among the routes after implementing crowding. Random stations are taken as an example to explain the commuter’s new route choices. It can be noticed that the route choices are enormously influenced by crowding. i. Ropsten station: From Figure 16, , the crowding decreased the boarding at Ropsten metro station by (-386 persons, -14%), the passengers load has transferred from the metro station to the adjacent bus line station (serving Bus #4) where the boarding has increased by (+810 person), the volume has switched from the metro station to the bus stations (+662% till Ropsten and 107% RopsenB). Additionally, the boarding at Roslasbanan has also decreased by (-124 person, -23%) in favor of the bus line that crosses the bridge till to Lidingö island (RopstenB bus station) a volume equal to (+619 %) transferred to the bus station from the Roslasbanan station.

Figure 16: Ropsten station (crowding to no crowding)

7.3. Pendeltåg: Figure 17 and Figure 18 represent the differences between the crowding to no crowding at Pendeltåg. Figure 17 represents the boarding passengers at the Pendeltåg station represented in the red and blue columns, an apparent decrease (indicated by red column) at the numbers of boarding over the network. Figure 18 shows the volume change over the Pendeltåg lines. A total decrease at the numbers of boarding and alighting at the Pendeltåg equal to (-12,579 persons, - 28%) in boarding and (-12,718 persons, -26%) in alighting has occurred after implementing crowding.

Figure 17: Pendeltåg boarding values (crowding - no crowding)

Figure 18: Pendeltåg volume (crowding - no crowding)

7.4. Buses: Unlike the other modes, the Bus’s network subjected to an increase in volume and also the numbers of boarding and alighting after implementing crowding Table 9. The inner-city buses network (BI bus) added a total of (+53,027, +55%) passengers compare to no crowding; the rest of the network bus values are added in Figure 19.

Mode Boarding increasement of Boarding Alighting increasement of Alighting crowding to no crowding (crowding - no crowding) crowding to no crowding (crowding - no crowding) SBY 45% 16,780.00 42% 19,161.00 SBL 86% 5,882.00 79% 7,095.00 SBI 214% 47,389.00 216% 50,440.00 DB 28% 644.00 45% 1,128.00 BI 155% 53,027.00 167% 59,093.00 BY 46% 61,107.00 44% 57,339.00

Table 9: boarding and alighting values and percentages (crowding - no crowding)

Figure 19: different Buses types increasement after implementing crowding

7.5. Light rail: The light rail network consists of (Tvärbanan, Lidingöbanan, Nockebybanan)) Figure 21 and Spårvagn City Figure 21. Overall, the network has subjected to a decrease in volumes after implementing crowding, as shown in the figures below. Also, the numbers of boarding and alighting passengers at stations, as illustrated in Table 10 , i.e., the Roslasbanan at Ropsten till island Lidingö, faced a decrease in the volume after crowding, the passengers choose the Bus line that goes toward the Lidingö instead of the light rail.

mode Boarding Boarding increasement of Alighting Alighting increasement of crowding - no crowding crowding to no crowding crowding - no crowding crowding to no crowding Lokal -2,487 -30% -2,481 -30% Spårvagn -2,369 -16% -2,304 -14% Table 10: boarding and alighting values and percentages (crowding - no crowding)

Figure 20: Tvärbanan, Lidingöbanan, Nockebybanan volumes crowding to no crowding

Figure 21: Spårvagn volume (crowding -no crowding)

8. Statistical validation of the model outputs:

The point of this part is to validate the goodness of the crowding model outputs statistically (boarding and alighting passengers) in comparison to the SL observations and the base model; the review is carried out by statistical analysis and correlation analysis. In statistics, the reason behind this step is to confirm that the outputs of the crowding model are acceptable in their values concerning the SL observations. It is vital to trust the newly developed method used in the crowding model and the criteria used in order to ensure the validity of the model outputs. Accordingly, it is essential to know whether the new model can be trusted and accepted as it is or rejected and modified it in order to make it suitable for the intended use. Each one of the modes is taken into consideration separately. Only boarding data considered at this part; the reason behind this is to simplify this part and to avoid excessive data representing it.

8.1. Tunnelbana: The section below describes the boarding statistical descriptive analysis and correlations to the three metro lines and also compare between the base model and the crowding model concerning SL observation.

8.1.1. Blue line:

BLUELINE: BOARDING

crowding /SL Base / SL

157%

146%

129%

127%

122%

121%

114%

113%

110%

105%

99%

96%

95%

88%

82%

81%

80%

79%

77%

76%

73%

72%

66%

55%

52%

49%

48%

44%

39%

31%

28%

27%

KISTA

HUSBY

RISSNE

AKALLA

TENSTA

D U V B O

RINKEBY

HJULSTA

RÅDHUSET

HUVUDSTA

NÄCKROSEN

STADSHAGEN

HALLONBERGEN

VÄSTRA SKOGEN

SOLNA CENTRUM KUNGSTRÄGÅRDEN

SUNDBYBERGS CENTRUM

Figure 22: a comparison between the Crowding and base model to SL, Blue line Boarding percentage

Figure 22 above illustrates an indication of the variance concerning the SL observations between the base model (no crowding) boarding values and the crowding model values at randomly picked stations of the blue line. Overall, it can be concluded from this graph that the base model gives a better representation of the SL observations than the crowding model does. By looking at the descriptive analysis in Table 11, the mean value of the boarding of the Base model is (854 persons) which is identical to SL observation (853 persons, in the other hand the crowding has a lower value equal (524 persons) which indicates less boarding to the blue line after implementing crowding. The summation of SL observations is (14,500 persons) the base model (14,512 persons), the crowding model (8,906 persons). The coefficient of variation CV gives evidence that the dispersion of observations in SL values (38%) is lower when compared to both base model and crowding; however, its value still closer to the base model (45%) than the crowding model (68%). The correlation between the SL observations and base model (85%), the correlation between SL and the crowding is (50%) Table 12. All this indicates that the base model gives more acceptable values of the boarding and alighting passengers at stations when compare it to the crowding model values concerning SL observations.

8.1.1.1. Descriptive analysis of blue metro line:

Crowding SL statistic base Model Mean 524 853 854 Median 419 850 852 Standard Deviation 356 322 380 Coefficient of variation 68% 38% 45% Minimum 150 300 216 Maximum 1,601 1,350 1,522 Sum 8,906 14,500 14,512 Count 17 17 17

Table 11: Descriptive analysis of blue line for different scenarios

8.1.1.2. Correlation: SL statistic

Crowding data 0.50 Base data 0.85

Table 12: correlation between the base model and crowding with respect to SL (blue line)

8.1.2. Greenline: GREENLINE

Crowding/SL Base/SL

263%

213%

195%

162%

158%

151%

140%

117%

115%

112%

111%

110%

107%

104%

103%

102%

99%

95%

94%

92% 92%

91%

88%

87%

84%

82%

80%

73%

70%

69%

48%

38%

24%

23%

21%

19%

15%

VÄLT

GLOBT

BÅSUTT

BJÖRKHT

SKARPNT

ODENPLT

MEDBPLT

HÖTORGT

THORIPLT

RÅDMSGT

SKANSTUT

JOHALUNT

GULLMPLT

SANDSBOT

SKÄRMBRT

F R I D H P L T 3

BAGARMOT

STERIKSPLT

KRISTINEBT

KÄRRTORPT HAMMBYHÖT

Figure 23: a comparison between the Crowding and base model to SL, Green line Boarding percentage

Figure 23 delivers a similar indication as to the blue line in Figure 22; the base model gave an overall less variance output when compare the outputs to the crowding model outputs concerning the SL observations. The mean values of the boarding passengers are (994 persons), (1063 persons), and (995 persons) for the Crowding model, SL observations, and base model respectively; both crowding and base have similar average values and slightly less than SL average. Overall, the statistical indicators (average, median, coefficient of variation, standard deviation). Table 13 shown that the crowding model and base model have almost similar values; however, the crowding has slightly better values compared to the base. Table 14 indicates that the base model is 97% correlated to the SL observation in comparison to 84% of crowding. 8.1.2.1. Descriptive analysis of Green metro line: Crowding SL statistic base Mean 994 1063 995 Median 145 144 156 Standard Deviation 987 979 1060 Coefficient of variation 99% 92% 107% Minimum 29 150 22 Maximum 5,524.00 5,900.00 6,596.00 Sum 45,737.00 48,900.00 45,750.00 Count 46.00 46.00 46.00 Table 13: Descriptive analysis of green line for different scenarios

8.1.2.2. Correlation: SL statistic Crowding data 0.84 Base data 0.97 Table 14: correlation between the base model and crowding with respect to SL (green line)

8.1.3. Redline:

REDLINE: BOARDING

Crowding/SL Base/SL

371%

174%

152%

148%

136%

127%

117%

115%

113%

105%

104%

95%

94%

87%

86%

82% 82%

80%

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72%

70%

69%

66%

65%

63%

59%

51%

49%

48%

43%

24%

23%

UNIVT

FRUÄT

TFNPLT

ROPSTT LILJEHT

BREDÄT

ASPUDT

ÖRNSBT

AXELSBT

ZINKDAT

VÄSTTOT

GÄRDETT

MÄLARHT

KARLAPLT

STADIONT

HÄGERSTT

MARIATOT

HORNSTUT

TEKHÖGSKT MIDSOMKRT ÖSTMALMTOT

Figure 24: a comparison between the Crowding and base model to SL, Red line Boarding percentage Similar to the blue line and the green line, in the red line, the statistical indicators (average, median, coefficient of variation, standard deviation …) proved that the base model outputs are less variance to the SL observation than the crowding model outputs. The correlation between the two models and SL observations are almost equal (77% Crowding and 78% base) Table 16.

8.1.3.1. Descriptive analysis of the red metro line:

Crowding SL statistic base Mean 913 1112 1097 Median 710 850 705 Standard Deviation 906 801 821 Coefficient of variation 99% 72% 75% Minimum 108 250 245 Maximum 4,124 3,650 3,266 Sum 31,046 37,800 37,308 Count 34 34 34

Table 15:) A comparison between the Crowding and base model to SL, Red line Boarding percentage

8.1.3.2. Correlation:

Correlation SL statistic Crowding 0.77

Base 0.79

Table 16: correlation between the base model and crowding with respect to SL (red line

8.2. Pendeltåg: BOARDING PENDELTÅG

Crowding/SL Base/SL

275%

166%

152%

149%

146%

138%

136%

128%

124%

120%

118%

114%

107%

104%

99%

98%

93% 93%

92%

90%

88%

87%

86%

83%

78%

75%

74%

73%

71%

66%

65%

60%

48%

47%

45%

43%

40%

38%

33%

31%

29%

24%

23%

22% 11%

Figure 25: A comparison between the Crowding and base model to SL, Pendeltåg Boarding percentage

Figure 25 above provides the percentages of the Base model and the Crowding model boarding values to SL observations for random stations of Pendeltåg (commuter train). Overall, the base model gave less variance representation to the SL observations than the crowding. Looking at the descriptive analysis, the average value of the Base model (829 persons), SL observation (803), the crowding has a lower value (596). Overall, average, median, coefficient of variation, standard deviation proved that the base model outputs are less variance to the SL observation than the crowding model outputs the base model. The correlation between the SL observations and base model (82%), the SL, and the crowding (63%). All this indicates that the base model gives more closer values if compared to the crowding concerning SL observations. 8.2.1. Descriptive analysis for Pendeltåg network:

Boarding Crowding Boarding Base Boarding SL Mean 596 829 803 Median 319 618 750 Standard Deviation 887 989 721 Minimum 13 38 10 Maximum 4579 6144 4450 Sum 32184 44762 43380 Count 54 54 54 Coefficient of Variation 1.49 1.19 0.90 Table 17: A comparison between the Crowding and base model to SL, Pendeltåg Boarding percentage

8.2.2. Correlation SL Boarding Crowding 0.63 Boarding Base 0.82 Table 18: correlation between the base model and crowding with respect to SL (Pendeltåg)

8.3. Light rail

BOARDING SPÅRVAGN REPRESENTATIVE STATIONS

Crowding/SL Base/SL

235%

219%

206%

170%

152%

135%

114%

112%

106%

101%

98%

94%

93%

86%

84%

82%

77%

75%

74%

70%

67%

66%

64%

63%

62%

58%

55%

49%

47%

42%

38%

34%

31%

30%

25%

22%

18%

16% 15%

Figure 26: A comparison between the Crowding and base model to SL, Spårvagn Boarding percentage

BOARDING LOKAL

Crowding/SL Base/SL

675%

377%

302%

238%

218%

195%

165%

155%

150%

136%

132%

131%

127%

115%

114%

110%

107%

103%

102%

101%

99%

98%

95%

91%

90%

87%

86%

83%

82%

77%

76%

74%

69%

68%

67%

66%

65%

37%

36%

33%

31%

30%

26%

18%

14%

13%

2% 2% 1%

Figure 27: A comparison between the Crowding and base model to SL, lokal Boarding percentage

Figure 26 and Figure 27 provide the percentages of the Base model and the Crowding model outputs to SL observations for random stations of a Light rail (Spårvagn and lokalbana). Similar to the other modes, the base model provided more appropriate values (less variance) in comparison to crowding outputs. Again, the base model gave better representation to the SL observations than the crowding. When looking at the descriptive analysis Table 19, Table 20 the average value of the Base model (164 persons), SL observation (154 persons ), the crowding has a lower value (115) in lokalbana mode and crowding (263), Base (300) and SL observation (292) in Spårvagn. This supports the claim that the base model gives a better representation than the crowding also, the rest of the analysis in Table 19 and Table 20 indicate that the base model outputs are less variance to SL data than the crowding outputs. The correlation between the SL observations and base model in Lokalbana and Spårvagn, respectively are (89%) (68%), the SL, and the crowding (39%) (51%).

8.3.1. Descriptive analysis for Lokalbana + Spårvagn:

Lokal Crowding Lokal Base Lokal SL Mean 115 164 154 Median 51.5 96.5 100 Minimum 0 2 5 Maximum 1350 925 700 Sum 5738 8223 7715 Count 50 50 50 Coefficient of Variation (%) 1.93 1.18 1.08

Table 19: A comparison between the Crowding and base model to SL, lokalbana Boarding percentage

Spårvagn Crowding Spårvagn Base Spårvagn SL Mean 263 300 292 Median 175 188 150 Minimum 7 1 3 Maximum 1271 1409 2300

Sum 12355 14083 13743 Count 47 47 47 Coefficient of Variation (%) 1.14 1.04 1.47

Table 20: A comparison between the Crowding and base model to SL, Spårvagn Boarding percentage

8.3.2. Correlation:

Spårvag SL Lokal SL

Boarding Base 0.68 0.89 Boarding Crowding 0.51 0.39

Table 21: correlation between the base model and crowding with respect to SL (light rail) 35

8.4. Conclusion about the Validation:

To conclude, the crowding scenario impact on the network against the base scenario using the RTW factor and also SL observations. A breakdown for each scenario outputs (Boarding+ alighting passengers at stations and the volume of the lines) is needed.

8.4.1. Boarding and alighting passengers at the stations:

The RTW is added on the base scenario to the in-vehicle time for only bus mode to decrease the attractiveness of the buses. The value of the RTW is 1.3 multiplied by all the buses type (inner- city, Double decker, outer city buses); however, the crowding multipliers for the buses are varies based as shown in Table 22 below:

Mode Approximation Slope Intercept Inner city trunk lines Y = 2.05LN(X)+1.28 2.05 1.28 Double decker lines Y=1.04LN(X)+1.03 1.04 1.03 All other bus lines Y=1.45 LN(X)+1.10 1.45 1.10

Table 22: Bus crowding multipliers

Results in Table 5 in section 7.1 proved that Without adding the RTW factor to the base mode model, the base model gave outputs that are significantly similar in amount and less variance to SL observations in comparison to adding the RTW factor. The results indicate a decrease in the boarding passenger at Tunnelbana (-5%), Pendeltåg (-11%), and Light rail (-13%) and an increase in the inner-city bus by (+29%) as shown in Table 23.

Result = (SL Observations - Base model) Mode Boarding increase/decrease = Boarding: percent of Alighting increase/decrease: Alighting: percent of SL Observations - Crowding model increase/decrease SL Observations - Crowding model increase/decrease Bus BI +13,826.50 +29% +39458 +53% Light Rail -2,664.50 -13% -4163.5 -20% Pendeltåg -4,411.00 -11% -7913 -20% Tunnelbana -7,009.00 -5% +8541 +6%

Table 23: the differences between the SL observation to the crowding model boarding and alighting percentages and values On the other hand, the crowding multipliers are added to the in-vehicle time of the perceived journey time PJT for all transit modes, as shown in Equation 4 in section 5.1. After implementing the crowding, the passengers shifted from (Metro, Light rail, and commuter train) toward the bus mode. The number of boarding passengers at the inner-city bus has increased by (+82%), unlike the other modes where a drop in the number of boarding has occurred, as shown in Table 23. The mode that has affected the most is the metro lines, which decreased by 27,420 (-21%) from the SL observations followed by Pendeltåg (-20) and then Light rail (-11).

Result= (SL Observations - Crowding model) Mode Boarding increase/decrease = Boarding: percent of Alighting increase/decrease: Alighting: percent of SL Observations - Crowding model increase/decrease SL Observations - Crowding model increase/decrease Bus BI +39,200.50 +82% +19,635.00 +26% Light Rail -2,191.50 -11% -621.50 -3% Pendeltåg -8,168.00 -20% -4,805.00 -12% Tunnelbana -27,420.00 -21% -42,970.00 -29%

Table 24: the differences between the SL observation to the crowding model boarding and alighting percentages and values

From Table 23 and Table 24, we can conclude the variation of the values of boarding and alighting passengers when compare to SL observation are less extreme in the base model scenario than the Crowding model concerning the SL observation.

8.4.2. Volumes of the lines: As discussed on7.2.2.1, the volumes of the lines have increased after implementing crowding; this can be due to the increase at the total number of boarding and alighting passengers at the network after implementing crowding. Overall, after crowding, the total of boarding and alighting has increased by 14% in comparison to SL observations.

8.4.3. Stations level: When observing the models in station level and by looking into each station in the transit system. The base scenario gave more similar results than the crowding scenario concerning the SL observation. After implementing crowding Some stations were subjected to an overestimating i.e., the Danderyds sjukhus station, the base scenario (2,700 passengers), SL observation (2,703 passengers), the crowding (4,124 passengers), Välingby the base model (1,750 passengers), SL observation (1,816), the crowding (2,646). Other stations the crowding scenario gave an underestimated calculation in the numbers of passengers i.e., Hägersta base (709 passengers ), SL observation (1,200 passengers), the crowding (292 passengers), Sundbybergs centrum base (1,420 passengers ), SL observation (1,350 passengers), the crowding (419 passengers). Overall, the base model gave more balanced values than crowding model outputs.

Statistically, as shown in 8, the base scenario gave a better representation at the average numbers of passenger’s values in all the modes, the statistical indicators (Mean, coefficient of variation, sum, … etc.) which indicated the extent of variability between the different modes are also in favor of the base scenario. Additionally, the base scenario outputs obtained a higher correlation than the crowding concerning the SL observations.

To sum up, the passenger’s travel behaviors and route choices are greatly influenced by implementing crowding, in particular, the Buses mode (BI, BY, SBY, SBI). Implementing crowding has helped to make the network less crowded in all transit modes expect the bus mode; however, crowding has increased the numbers of transfer and exchanges between the routes.

9. Model Calibration:

For calibration, a simple regression model used in this section, regression is known as a standard method to solve calibration problems by comparing the model’s outputs to the observed, collected data to calculate the calibrating parameters. There is no transparent methodology on how to carry the calibration application for the public transport network; the reason behind that is due to the lack of the collected observational data that are similar to the model’s outputs most of the time. The outputs of the transit assignment model are the numbers of boarding and alighting passengers at each station and stop, in addition to the volume of the lines and different time components. In order to carry out calibration, the model outputs have to be of the same type as the observations. In our case, the available observed data are the boarding and alighting passengers [6] and the journey dairies that contain the journey time from zone to another for the year 2015 [21].

The linear regression is a standard statistical method in calibration [24] , a mathematical function used to express the relation between one or more variables; ‘’y’’ the dependent variable (the observations) and ‘’x’’ the independent variables, in this tool, calibration of a dependent variable (in our case the journey time diaries) is related to known independent variables (crowding Journey times) basically by establishing the relations between the two reference values.

The first attempt to calibrate the model outputs is by calculating new parameter values using the assignment model outputs (boarding/alighting passengers) as dependent variables and the observational data (collected by SL [6]) as an independent variable. A simple reverse linear regression used as shown in Equation 5 to calculate the calibration parameter 훽0,푚표푑푒 values for each mode separately, the resultant calculated parameters 훽0,푚표푑푒, has been compensated in Equation 5 to calculate the new calibrated boarding and alighting passengers values for crowding. The new calibrated boarding and alighting values led to a change in the numbers of the total passengers at the O-D zones, i.e., (increasing the numbers of travelers at some zones and decreasing it in other zones). The results have two main problems; firstly, it is not applicable to validate the passengers at each zone in our case due to the lack of the collected observational data about the numbers of travelers. Secondly, the primary assumption in this assignment method (static assignment procedure see section 2.1.5 ) is that the demand matrix is constant, i.e., the number of passengers at each zone fixed. Furthermore, in this calibration method, each mode has its calibrating parameters for boarding and alighting separately, and with a total of five modes of transportation (Buses, Metro, Light rail, Pendeltåg, and long-distance trains), a total of 10 calibration parameters required. In practice, this is not practical, using ten different calibrating factors without knowing how they affect each other and how they affect the network collectively.

퐵표푎푟푑𝑖푛푔푠푙_푂푏푠푒푟푣푎푡푖표푛푠,푚표푑푒 = 훽0,푚표푑푒 × 퐵표푎푟푑𝑖푛푔푐푟표푤푑푖푛푔_푚표푑푒푙_표푢푡푝푢푡,푚표푑푒 퐴푙𝑖푔ℎ푡𝑖푛푔푠푙_푂푏푠푒푟푣푎푡푖표푛푠,푚표푑푒 = 훽0,푚표푑푒 × 퐴푙𝑖푔ℎ푡𝑖푛푔푐푟표푤푑푖푛푔_푚표푑푒푙 표푢푡푝푢푡,푚표푑푒

Equation 5: Regression equation used to calibrate the boarding and alighting

As seen from the previous paragraph, the calibration for boarding and alighting is not suitable in our case, now what left from the route assignment outputs are the volumes of the lines data and different time components. Observational data about the volume of the lines are not available or collected by the authorities; however, the Swedish national survey [25] provided information about ‘’Journey Time’’. The route assignment has different time components as outputs; these components are the total Perceived journey time, the Journey time, the riding time, in-vehicle time, the waiting time, the access time, the Egress time, Origin waiting time, Transfer walking time, Transfer time in addition to other attributes that have a different unit but time which is the number of transfers. The ‘’Journey time’’ observations are collected by random travelers traveling from the origin zone to the destination zone, the corresponding time from the route assignment procedure is equal to the summation of the in-vehicle time (IVT), Access time (ACT), Transfer waiting time (TWT), Walking time (WKT), Egress time (EGT) see Equation 6 [19] .

퐽표푢푟푛푒푦 푡𝑖푚푒푐푟표푤푑푖푛푔 = 훽0 퐴퐶푇푐 + 훽1 푂푊푇푐 + 훽2 ∑ 푇푊푇푐 + 훽3 ∑ 푊퐾푇푐 + 훽4 ∑ 퐼푉푇푐 + 훽5 퐸퐺푇푐

Equation 6: Crowding Journey time

퐽표푢푟푛푒푦 푡𝑖푚푒 표푏푠푒푟푣푎푡𝑖표푛 = 훽0 ∗ 퐽표푢푟푛푒푦 푡𝑖푚푒 푐푟표푤푑𝑖푛푔

Equation 7: Journey time Linear regression

The idea is to calibrate the model output (crowding journey time) using the collected journey time from the observational data by calculating the calibrating parameters 훽0, 훽1 훽2 훽3훽4 훽5 as in Equation 6 using inverse linear regression as in Equation 7. The goal is to find suitable values for the parameters; for the sake of simplicity, the intercept value considered equal to zero in this calculation. These new calibrated parameters are pre-compensated in the route assignment model in Visum algorithm in order to obtain the new calibrated values of boarding and alighting passengers, these calibrated results are evaluated concerning SL observations. The ultimate goal for the model is to be able to produce fewer variance values between the attributes of concern, which are the boarding and alighting of crowding and the SL observations.

9.1. Methodology:

A total of 618 journeys extracted from the travel dairies, the travel diaries document contains the starting time of a journey from the zone (i) to arriving time till zone (j) for all the 3000 zones, the document in total has 21,793 journeys during a winter day for various days between (8-25 October 2015). From these 21,793, only 618 used due to the limitation of time and resources. Visum route assignment model contains ‘’6’’ attributes values, as shown in Equation 6 and Table 25. One-third of the 618 journeys (200 journeys) were separated for validation purposes. Table 25 below represents an example of the data that used; the times are in the minute unit.

Journey diaries FROM_ZONE FROM_ TO_ZONE TO_ ACT_C OWT_C IVT_C WKT_C EGG_C JOURNEYTIME_ ZONE_ ZONE_ Crowding Code Code 85.00 UppsalaKn 50410 Observatorielunden 721125 8 7 58 5 3 83 45.00 UppsalaKn 50410 Norra Vasalund 718426 8 8 56 1 7 83 95.00 UppsalaKn 50410 Grönlandsgången 710298 8 8 54 1 6 80 90.00 UppsalaKn 50410 Frescati 720136 8 7 69 4 4 95 15.00 Håbo-Tibble 713912 Bolinder Strand 712337 6 23 34 2 7 84 glesbygd 5.00 Håbo-Tibble 713912 Håbo-Tibble kyrkby 713909 6 23 5 0 7 44 glesbygd 30.00 Håbo-Tibble 713912 UppsalaKn 50410 6 20 116 1 8 172 glesbygd 570.00 Åby 711502 Sorunda östra 719213 3 3 163 4 8 200 glesbygd 60.00 Åby 711502 Norra Station 2 725186 3 3 71 3 3 86 55.00 Åby 711502 Kungssten 720126 3 3 63 3 4 80

Table 25: data used for model calibration that’s contained Journey time from the observation to the crowding journey time attributes 9.1.1. Data filtering:

The obtained data from [21] has subjected to different data filtering procedures to determine and exclude "extreme outlier data" from the analysis. The procedures used are:

• Method 1: Interquartile Range (IQR) Method; the IQR method a commonly used in dedicating outliers using the range between 75th Quartile and 25th quartile values.

• Method 2: A percentage values with a range between (30% < data point < 130%), if the differences between the real journey time value and the crowding journey time value in percentage is larger than 30% or less than 30% the data treated as an outlier.

• Method 3: new procedure (1 hr. max procedure), if the differences between the collected journey time value and the crowding journey time value are 60 mins more or less, this data point treated as an outlier.

Three different models with different weights have been calculated; each of the data filtering procedures has applied to the models, as shown in Figure 28.

IQR method 1 hr. max method

Model-1 Model-2 Model-3 Model-1 Model-2

Statistical analysis in order to determine which scenarios are closer to the observations values

The selected models are added as a new scenario in Visum PTV for route assignment purposes

Outputs are the Boarding and alighting

values in addition to the network’s

volumes for the different scenarios

Validating the results with the SL observations to determine which model is most appropriate and representative

Figure 28: Calibration procedures

9.2. Model analysis: 9.2.1. Model-1: In the first model, the ‘’Crowding Journey time’’ is calibrated using ‘’the observational journey time’’ from [21], the data used is similar as data in

Table 26 Table 26, using Equation 7. From the Regression Analysis in Table 27 the 훽0 value found to be equal to 0.7 using 1 hr: Max method and 0.6 using IQR method Table 29.

퐽표푢푟푛푒푦 푡𝑖푚푒 표푏푠푒푟푣푎푡𝑖표푛 = 훽0 ∗ 퐽표푢푟푛푒푦 푡𝑖푚푒 푐푟표푤푑𝑖푛푔

Equation 8: Model-1, simplified linear regression model for calibration purposes

Journey diaries Observations Journey Time Crowding

85 83 45 83 95 80 90 95

Table 26: example of the data that used in the simplified linear regression model

9.2.1.1. Model-1 outputs: i. Using the 1 hr. max method: A. Regression Statistics Multiple R 0.93 R Square 0.86 Adjusted R Square 0.86 Standard Error 16.87 Observations 384 B.

df SS MS F Significance F

Regression 1 702619.3 702619.3 2469.002 8.2E-169 Residual 383 108992.7 284.5762 Total 384 811612

C. Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 훽 0.70 0.014 49.69 4.6E-169 0.669 0.725

Table 27: Regression output using 1hr data filtering for model-1

1) Descriptive analysis for model 1, 1 hr. max method:

Observations Journey time Crowding JOURNEY TIME Predicted Observations after (Survey) before Calibration calibration Mean 38 54 38 Median 30 48 33 Mode 30 37 26 Standard Deviation 26 29 20 Coefficient of Variation 68% 53.7% 52,6% Minimum 3 8 6 Maximum 180 163 114 Sum 14,456 20,740 14,457 Count 384 384 384

2) Correlation for model 1, 1 hr. max method:

Observations Journey time Crowding journey time before calibration 0.77 Predicted Observations after calibrating 0.77

Table 28: 1&2 Descriptive analysis + correlation for model-1 1 hr method Result Observations using 1 Hr. max method:

From the results in Table 27: Regression output using 1hr data filtering for model-1above, the variables that within our concern are the parameters of the explanatory variable (β) (Table 27 - C) , Standard Deviation, T-statists and P-value, the average passenger numbers, the sum of the passengers in addition to the Coefficient of Variation (CV) and correlation (Table 27 1&2). The β is the only explanatory variable in this method. (c) shows a significant value of T-statistics and small p-value, which indicates the statistical significance of this variable. From Table 28 (1) the average value of passengers is (38 passengers) for both ‘’observation Journey time’’ and ‘’the predicted values’’, ‘’the crowding journey time’’ average number of passengers is (54 passengers). An Identical value of the sum of the passengers for both ‘’Observations’’ and ‘’the predicted values’’ after calibration (14,456persons) and crowding journey time (20,740 persons). From Table 28 (2) The correlation between ‘’the observation’’ and ‘’crowding journey time’’ before and after the calibration has not changed and equal to 77%.

ii. IQR method: a)

SUMMARY OUTPUT Regression Statistics Multiple R 0.900 R Square 0.810 Adjusted R Square 0.81 Standard Error 19.7 Observations 428

df SS MS F Significance F Regression 1 704925 704925 1824.26 4.7E-156 Residual 427 165000 386.4169 Total 428 869925

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

훽 0.60 0.014 42.71 3.1E-156 0.56 0.62 Table 29: Regression output using IQR data filtering for model-1

The statistical analysis of the IQR method is provided in the appendix (Descriptive analysis for model-1 IQR method: and Correlation for model-1 IQR method:). Both methods gave almost similar results in the attributes of our concern; however, the 1-hr has performed better in ‘’CV’’ values and correlation when comparing to IQR, according, this method will be the one to implement on Visum.

9.2.2. 2nd model:

The second model is using the concept provided by [19], according to PTV Visum. According to PTV Visum, the Journey time is equal to the sum of time attributes that are (ACT, OWT, TWT, WKT, IVT, and EGT) Equation 9 . The idea is to calibrate the different time attributes using the observational Journey time from [25] by replacing the crowding journey time by the observational Journey time. (Equation 10) average crowding (ACM)., similar to the previous model, linear regression is used to determine the values of the new parameters.

퐶푟표푤푑𝑖푛푔 퐽표푢푟푛푒푦 푡𝑖푚푒 𝑖푛 푉𝑖푠푢푚 = 2 퐴퐶푇 + 2 푂푊푇 + 2 ∑ 푇푊푇 + 2 ∑ 푊퐾푇 + 2 ∑ 퐼푉푇 + 2 퐸퐺푇

Equation 9: Journey time in Visum

푁푒푤 퐽표푢푟푛푒푦 푡𝑖푚푒 = 훽1 퐴퐶푇 + 훽2 푂푊푇 + 훽3 ∑ 푇푊푇 + 훽4 ∑ 푊퐾푇 + 훽5 ∑ 퐼푉푇 + 훽6 퐸퐺푇 Equation 10: Model-2 equations with attributes

9.2.2.1. Model-2 outputs: i. 1 hr. max outputs: a)

SUMMARY OUTPUT Regression Statistics Multiple R 0.93 R Square 0.87 Adjusted R Square 0.86 Standard Error 16.8 Observations 384 b)

df SS MS

Residual 378 106754.3631 282.4189

Total 384 811612

c) Coefficients Standard t Stat P-value Lower Upper Error 95% 95% 훽1 (ACT) 0.54 0.291374332 1.853811 0.064545 -0.03276 1.11307 훽2 (OWT) 1.12 0.205495666 5.448744 9.16E-08 0.715635 1.523751

훽5(IVT) 0.75 0.050309877 14.86188 1.14E-39 0.648777 0.846622 훽4(WKT) 1.36 0.39646698 3.435068 0.000658 0.582334 2.141448 훽6(EGG) 0.49 0.507033688 0.963396 0.335965 -0.50849 1.485434 훽3(TWT) -0.03 0.043840431 -0.67698 0.498831 -0.11588 0.056522

Table 30: Regression output using 1hr data filtering for model-2

ii. IQR : a)

SUMMARY OUTPUT Regression Statistics Multiple R 0.90868654 R Square 0.82571123 Adjusted R Square 0.82127653 Standard Error 18.9548076 Observations 428

df SS MS F Significance F

Regression 6 718306.8 119717.8 333.2115 2E-156

Residual 422 151618.2 359.2847 Total 428 869925 c) Coefficients Standard t Stat P-value Lower Upper Error 95% 95% 훽 (ACT) 0.27 0.235655 1.14 0.254292 -0.194 0.732 1 훽2 (OWT) 1.42 0.216027 6.59 1.29E-10 1.000 1.849

훽5(IVT) 0.63 0.049902 12.65 2.46E-31 0.533 0.730 훽4(WKT) 1.79 0.397657 4.51 8.27E-06 1.013 2.577 훽6(EGG) 0.22 0.512539 0.42 0.671258 -0.790 1.225

훽3(TWT) -0.06 0.042572 -1.32 0.185857 -0.140 0.027

Table 31: Regression output using IQR data filtering for model-2

Model 2 results: The statistical analysis of both 1hr max and IQR provided in 12.2. Model-2 From the results in Tables above (Table 27 - Table 28), the variables that within our concern are the parameters of the explanatory variable (β), Standard Deviation, T-statists and P-value, the average passenger numbers, the sum of the passengers in addition to the Coefficient of Variation (CV) and correlation. Results from both methods in Table 30 (c), (c) for OWT, IVT, and WKT has shown a significant value of T-statistics and small p-values, which indicates these attributes are statistically significant. Low p-values mean statistically more significant correlation between the independent and dependent variables also a small p-value (<0.05) indicates strong evidence against the null hypothesis (null hypothesis is that the parameters in the model are equal to zero). However, ACT, EGT, and TWT in both methods gave high p-values and low t-statistics. A trail has made by using the (Log) and square root to the ACT, EGT and TWT in Equation 10, nevertheless, the values still statistically insignificant. Accordingly, these calculations will not be implemented on Visum as they require different calibration methods but the simple linear regression method, which is our main focus in this part.

9.2.3. Model-3:

The 3rd model is using a different procedure than model-1 and model-2, instead of using the journey diaries observation data for the year 2015 [21], in this section the base model data is used to calibrate the crowding model outputs instead of the observational data. According to Visum and as it is shown in section ’’Perceived journey time PJT’’, the PJT consists of different time components, as shown in Equation 4: Crowding perceived time journey component. The base model has a better representation of the network as discussed in detail in section ‘’Result from implementing crowding at the 7.2.1’’ and gave fewer variance results to SL observation [6]. Furthermore, the original data used in building the base model is the same journey diaries data for the year 2014. Accordingly, the data of the base model is used in this model. The idea is to calibrate the ‘’crowding time attributes’’ using ‘’Perceived journey time PJT of the base model’’ using a linear regression model as in Equation 11 to determine the values of the new weights. An example of the data used in this method is as in Table 32: example of the data that used in linear regression for model-3

푃퐽푇 푏푎푠푒 푚표푑푒푙 = 퐼푛푣푒ℎ𝑖푐푙푒 푡𝑖푚푒 푐 ∙ 푊 푖푛푣,푐 + 퐴푐푐푒푠푠 푡𝑖푚푒푐 ∙ 푊푎푐푐,푐 + 퐸푔푟푒푠푠 푡𝑖푚푒푐 ∙ 푊 푒푔푟,푐 + 푂푟𝑖푔𝑖푛 푤푎𝑖푡 푡𝑖푚푒 푐 ∙ 푊 푂푊푇,푐 + 푇푟푎푛푠푓푒푟 푤푎푙푘 푡𝑖푚푒푐 ∙ 푊 푊푎푙푘,푐 + 푇푟푎푛푠푓푒푟 푤푎𝑖푡 푡𝑖푚푒푐 ∙ 푊 푊푎푖푡,푐 + 푁푢푚푏푒푟 표푓 푡푟푎푛푠푓푒푟푠푐 ∙ 푊푁표푇,푐 Equation 11: Model-3 equations with attributes

ODPAIR\FROMZONE\ ODPAIR\TOZONE\NAME PJT Crowding IVT OWT TWT WKT ACT EGT NTR PJT base NAME UppsalaKn KnivstaKn 27.18 13.47 8.15 1.96 0.17 8.4 8.4 0.1 59 UppsalaKn EnköpingKn 40.14 85.79 6.1 14.03 2.04 8.4 8.4 1.18 160 UppsalaKn TierpMflKn 29.73 43.49 11.98 0.82 0.06 8.4 8.4 0.08 96 Table 32: example of the data that used in linear regression for model-3 9.2.3.1. Model-3 outputs: a) Regression Statistics Multiple R 0.900182 R Square 0.810328 Adjusted R Square 0.807987 Standard Error 19.65749 Observations 428

b) df SS MS F Significance F Regression 7 61025015 8717859.3 37776.2652 0 Residual 3322 766638.2 230.7761

Total 3329 61791653

Coefficients Standard t Stat P-value Lower Upper Error 95% 95%

IVT (훽1) 0.66 0.014472 45.819831 0 0.634739 0.69149

OWT(훽2) 3.04 0.13081 23.272414 4.139E-111 2.787778 3.300729 TWT(훽3) 1.48 0.054235 27.333979 1.474E-148 1.376111 1.588784 WKT(훽4) 2.37 0.156787 15.140395 3.978E-50 2.066403 2.68122

ACT(훽5) 1.77 0.207454 8.5280033 2.2281E-17 1.362418 2.175919 EGT(훽6) 2.50 0.068828 36.372559 3.989E-244 2.368491 2.638389 NTR (훽7) 2.10 0.431271 4.8660045 1.1918E-06 1.252984 2.944153

Table 33: Regression output using IQR data filtering for model-3

1) Descriptive analysis for model 3:

PJT base model Predicted PJT after PJT crowding value (before calibration calibration) Mean 131 131 35 Median 126 129 34 Mode 121 131 37 Standard Deviation 37 33 10 Sample Variance 1365 1095 91 Range 350 437 230 Minimum 33 36 13 Maximum 383 473 243 Sum 436,555 437,059. 116,021 Count 3329 3329 3329

2) Correlation by model-3 output:

PJT base Predicted PJT base 0.91 PJT crowding 0.81

Table 34: Descriptive analysis + correlation for model-3

Result Observations from model 3:

From the results in Table 27 and Table 28 above, the variables that within our concern are the parameters of the explanatory variables (β), Standard Deviation, T-statists and P-value, the average passenger numbers, the sum of the passengers in addition to the Coefficient of Variation (CV) and correlation. From Table 33all parameters have large values of T-statistics and small p-values, which indicates these attributes are statistically significant with strong evidence against the null hypothesis (null hypothesis is that the parameters in the model are equal to zero). From Table 28 (1) the average value of passengers is (131 passengers) for both the ‘’PJT base model’’ and ‘’Predicted PJT after calibration’’, for ‘’the crowding journey time’’ the average numbers of passengers is (35 passengers). It demonstrated that the new calibrated weights had improved the outputs significantly. Similar values for the ‘’PJT base model’’ and ‘’Predicted PJT after calibration’’ after calibration for the ‘’sum’’ of the passengers at the network (436,555 and 437,059 persons respectively), a smaller value for crowding journey time (116,021 persons) The Coefficient of Variation CV values indicate the dispersion has an equal value in both the ‘’PJT base model’’ and ‘’Predicted PJT after calibration’’ values (25.2 %) compare to ‘’PJT crowding value (before calibration)’’ (28.5 %). From Table 34 (2) The correlation between the ‘’PJT base model’’ and ‘’PJT crowding journey time’’ after the calibration is equal to 91% before calibration 81%; after calibration, the correlation has increased by 10% (high correlation value).

9.3. Result from Visum Implementations:

Model-1 using 1 hr. Method and model-3 values implemented in Visum route assignment model by creating a different scenario for each method; the results are illustrated in Table 35:

mode Model-1 (after calibration) Model-3 (after calibration) SL observations

Boarding Alighting Boarding Alighting Boarding Alighting BI 93,625.81 106,136.94 123,082.00 142,701.00 47,982.50 74,800.00 Pendeltåg 28,436.85 31,855.84 26,010.00 29,370.00 40,350.00 40,350.00 Light rail 33,493.20 36,937.17 18,564.00 21,574.00 20,507.50 20,337.50 T.bana 89,586.61 89,586.61 87,778.00 87,778.00 131,350.00 146,900.00 Total 245,142.47 264,516.56 255,434.00 281,423.00 240,190.00 282,387.50

Table 35: Result from implementing Model-1 and Model-3

9.4. Discussion and Conclusion:

Figure 29: Comparison between the outputs of Model-1, Model-3, Crowding before calibration and SL observations for Boarding values

Figure 30: Comparison between the outputs of Model-1, Model-3, Crowding before calibration and SL observations for Alighting values

Mode Model-1 percent to SL Observation Model-3 percent to SL Crowding-Departures from stop area before calibration

Boarding Alighting Boarding Alighting Boarding Alighting BI 195% 142% 257% 191% 182% 126% Pendeltåg 70% 79% 64% 73% 80% 88% Light rail 163% 182% 91% 106% 89% 97% T.bana 68% 61% 67% 60% 79% 71%

Table 36: Comparison between the outputs of Model-1, Model-3, to SL observations for Alighting values Looking at data in Table 36, Overall, when comparing the boarding and alighting passengers to the SL observations, model-1 performed better than model-3 in (Bus, Pendeltåg, and T.bana) modes the only exception is the light rail where Model-3 gave a better result. However, when comparing the crowding outputs after calibration to the outputs before calibration, results from Table 35, Table 36, Figure 29 and Figure 30 indicated an increase at the variance in each mode after calibration rather than making it less concerning SL values. Besides the three different models tested in this section, an additional five different scenarios analyzed separately, and the results reported in the appendix (Table 40, Table 41, Table 42 and Table 43). The main reason behind these scenarios is to be able to create a model with a calibrated parameters that give fewer variant outputs to SL observations when implementing crowding, the average computational time for a single scenario ( including crowding multipliers and calibration parameters) is around (3-4) hrs. It indicates the expensive computational cost required. One of the five trials to calibrate the crowding model was made by adding the RTW value (1.3) to the bus mode in addition to the crowding multipliers to make the bus" less attractive" yet the method did not deliver the expected outputs after implementing it in Visum as shown in Table 40, Table 41 and Table 42. Overall, when implementing crowding as a scenario, the model increased the weight of in-vehicle time for all transit modes at the network, this led to an increase at travel times, accordingly, the cost of traveling. Crowding has decreased the passenger's ridership in the metro, light rail and commuter train, however, the bus ridership has increased although all the modes have subjected to crowding multipliers including the bus mode, yet, the bus faced an increase in the readership when comparing it to the base model and SL observation. Route assignment model with crowding multiplier outputs are within ±30% margin compare to SL observation (see Table 9) , which is acceptable margin according to the traffic analysis at trafikförvaltningen (Ilaf Hashim and Gerasimos Loutos), expect for bus values which exceeded the threshold percentage as shown in Table 9. According to (Gerasimos Loutos, a traffic analyst at trafikförvaltningen) the base model of Stockholm rote assignment model for the year 2014 has a tendency to give the buses a higher proportion of passengers compared to other modes and required calibration and the RTW was one of the trails to calibrate the model.

10. Recommendations:

The recommendations based on the outputs of this thesis and overall observations for the next person who wants to continue the work

• From results in section (RTW Spårfaktor:7.1), the RTW calibration factor has not improved the base model; it has increased the variance between the model’s boarding and alighting outputs concerning the SL observations, it can be said the base model is better without RTW. • The crowding output validation has shown a consistent result as discussed in section 9.4 in shifting the passengers from crowded modes to others; it is vital to carry out a cost-benefit analysis that uses these results to measure the economic effect of adding crowding in the assignment model. The route assignment model is only a simulation scenario that imitates what could happen if crowding implemented, the cost of crowding calculated in a time form; therefore, it is essential to estimate the cost of crowding in the money i.e., how many a person is willing to buy to avoid crowding and how much. • In the upcoming studies, while implementing crowding into Visum PTV, personally would highly recommend using the ‘’ discrete choice model’’ as shown in Figure 31 and use the default values as it is. This method gives more reliable result; the discrete model should favor over the (0/1 decision in favor of the best alternative) method that has used in this thesis, the reason behind that is the advantages the discrete model has over the (0/1) method, the method used in this thesis reduced the expected reminding costs and did not reflect the fuzziness of the passenger’s behavior [19]. The reason why it was not possible to carry this work using the discrete choice model option is due to the high computational power required to assign the model, two trials using this method took up to +18 hr. to curry the assignment procedure.

Figure 31: discrete choice model in Visum PTV 52

11. Bibliography

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12. Appendix

Figure 32: Future expanstion for stockholm's metro lines Model-1

12.1. Model-1: 2) Descriptive analysis for model-1 IQR method:

Journey time (observations) Journey time Crowding Predicted Observations Mean 37 59 36 Median 30 54 32 Mode 30 37 22 Standard Deviation 26 33 20 Sample Variance 70% 56% 55% Minimum 3 8 5 Maximum 180 178 107 Sum 15,741 25,217 15,148 Count 426 426 426

3) Correlation for model-1 IQR method:

Observations JOURNEYTIME_C 0.66 Predicted Observations 0.66

Table 37: Descriptive analysis + correlation for model-1 IQR Result Observations using IQR method:

From the results in Table 27 and Table 28 above, the variables that within our concern are the parameters of the explanatory variable (β), Standard Deviation, T-statists and P-value, the average passenger numbers, the sum of the passengers in addition to the Coefficient of Variation (CV) and correlation. The β is the only explanatory variable in this method. Table 27 (c) shows a large value of T-statistics and small p-value which indicates the statistically significant of this variable. From Table 28 (1) the average value of passengers is (36 passengers) for both ‘’observation Journey time’’ and ‘’the predicted values’’ for ‘’the crowding journey time’’ the average numbers of passengers is (59 passengers). Similar values for the ‘’Observations’’ and ‘’the predicted values’’ after calibration for the sum of the passenger at the network (15,741 and 15,148 persons respectively), a larger value for crowding journey time (25,217 persons) Similar as The Coefficient of Variation CV values indicate the dispersion has a lower value in both ‘’crowding’’ and ‘’the predicted crowding’’ values compare to ‘’the observation data’’. From Table 28 (2) The correlation between ‘’the observation’’ and ‘’crowding journey time’’ before and after the calibration is equal in values (high correlation value 66%)

12.2. Model-2 d) Descriptive analysis for model-2 1 hr method:

JOURNEYTIME_C Observations Predicted Observations Mean 54.01 37.65 37.52 Median 48.00 30.00 33.59 Mode 37.00 30.00 70.33 Standard Deviation 29.17 26.42 20.70 CV 54% 70% 55% Minimum 8.00 3.00 5.53 Maximum 163.00 180.00 113.13 Sum 20740.00 14456.00 14409.04 Count 384 384 384

Table 38: Descriptive analysis + correlation for model-2 1hr method

e) Descriptive analysis for model-2 1 IQR method:

JOURNEYTIME_C Observations Predicted Observations Mean 60 37 36 Median 55 30 33 Mode 37 30 73 Standard Deviation 33 26 20 Coefficient of Variation 55% 70% 55% Minimum 8 3 4.220223 Maximum 178 180 106 Sum 25509 15845 15352 Count 428 428 428 f) Correlation for model-1 IQR method

Observations JOURNEYTIME_C 0.66 Predicted Observations 0.69

Table 39: Descriptive analysis + correlation for model-2 IQR

Mode Crowding weight 0.73 + RWT Boarding Alighting Bus BI 58,156.00 64,997.00 Light Rail 17,332.00 17,871.00 Pendeltåg 33,953.00 37,341.00 Tunnelbana 96,230.00 96,230.00 total 205,671.00 216,439.00

Table 40: Calibration using weight 0.73 + RWT

Mode Crowding weight 1 + RWT Boarding Alighting Bus BI 65,044.00 72,289.00 Light Rail 17,374.00 17,913.00 Pendeltåg 32,960.00 36,341.00 Tunnelbana 98,612.00 98,612.00 total 213,990.00 225,155.00

Table 41: Calibration using weights equal to 1 + RTW value (1.3)

Mode crowding 1.4+RWT Boarding Alighting Bus BI 74,576.00 81,842.00 Light Rail 17,730.00 18,575.00 Pendeltåg 32,314.00 35,690.00 Tunnelbana 101,478.00 101,478.00 total 226,098.00 237,585.00

Table 42: Calibration using weights equal to 1.4 + RTW value (1.3)

Mode crowding with 2 weight Boarding Alighting Bus BI 87,183.00 94,435.00 Light Rail 18,316.00 19,716.00 Pendeltåg 32,182.00 35,545.00 Tunnelbana 103,930.00 103,930.00 total 241,611.00 253,626.00

Table 43: Calibration using weights equal to 2