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A modelling platform for optimizing time-dependent transit fares in large-scale multimodal networks


  • Kamel, Islam
  • Shalaby, Amer
  • Abdulhai, Baher


With the continuous growth of urban areas around the world, overcrowding in large transit networks has become a persistent problem, with far-reaching impacts similar to those caused by congestion in large road networks. Moreover, instead of serving as a relief for large transportation systems, congested transit networks have increased delay-related traffic and transit costs. In light of these problems, cities seek cost-effective and relatively fast-to-implement strategies to mitigate transit system congestion, one of which is time-based fare structures. By implementing time-based fares, the transit demand may shift out of the congested peak periods, easing transit travel conditions. Although time-based fares are already in use in some transportation systems, their implementation is usually based on simplified what-if analyses. Such analyses of fare structures in previous studies have lacked a comprehensive evaluation of people's responses to these fares and is usually applied to simple or sometimes hypothetical transportation networks. Therefore, this paper presents a platform for analyzing and optimizing time-based transit fares in large networks, taking into consideration the effects of these fares on people's choices of mode, departure time, and route in addition to the interactions between transit vehicles and general traffic. As a case study, the largest metropolitan area in Canada, the Greater Toronto Area, is tested. The results show that the optimal time-based fares help spread the transit demand to the shoulders of the peak. However, the savings in weighted average multimodal door-to-door travel time over the whole network are slightly small compared to the large increase in peak-hour fares.

Suggested Citation

  • Kamel, Islam & Shalaby, Amer & Abdulhai, Baher, 2020. "A modelling platform for optimizing time-dependent transit fares in large-scale multimodal networks," Transport Policy, Elsevier, vol. 92(C), pages 38-54.
  • Handle: RePEc:eee:trapol:v:92:y:2020:i:c:p:38-54
    DOI: 10.1016/j.tranpol.2020.04.002

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    References listed on IDEAS

    1. Tirachini, Alejandro & Hensher, David A., 2011. "Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 828-844, June.
    2. Mohring, Herbert, 1972. "Optimization and Scale Economies in Urban Bus Transportation," American Economic Review, American Economic Association, vol. 62(4), pages 591-604, September.
    3. de Palma, André & Kilani, Moez & Proost, Stef, 2015. "Discomfort in mass transit and its implication for scheduling and pricing," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 1-18.
    4. Yang, Hai & Tang, Yili, 2018. "Managing rail transit peak-hour congestion with a fare-reward scheme," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 122-136.
    5. Roberto Cominetti & José Correa, 2001. "Common-Lines and Passenger Assignment in Congested Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 250-267, August.
    6. Deb, Kaushik & Filippini, Massimo, 2011. "Estimating welfare changes from efficient pricing in public bus transit in India," Transport Policy, Elsevier, vol. 18(1), pages 23-31, January.
    7. Finn Jørgensen & John Preston, 2007. "The Relationship Between Fare and Travel Distance," Journal of Transport Economics and Policy, University of Bath, vol. 41(3), pages 451-468, September.
    8. Shyue Koong Chang & Schonfeld, Paul M., 1991. "Multiple period optimization of bus transit systems," Transportation Research Part B: Methodological, Elsevier, vol. 25(6), pages 453-478, December.
    9. Ihab Kaddoura & Benjamin Kickhöfer & Andreas Neumann & Alejandro Tirachini, 2015. "Agent-based optimisation of public transport supply and pricing: impacts of activity scheduling decisions and simulation randomness," Transportation, Springer, vol. 42(6), pages 1039-1061, November.
    10. Huang, Di & Liu, Zhiyuan & Liu, Pan & Chen, Jun, 2016. "Optimal transit fare and service frequency of a nonlinear origin-destination based fare structure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 1-19.
    11. Mohamed Wahba & Amer Shalaby, 2011. "Large-scale application of MILATRAS: case study of the Toronto transit network," Transportation, Springer, vol. 38(6), pages 889-908, November.
    12. de Grange, Louis & González, Felipe & Muñoz, Juan Carlos & Troncoso, Rodrigo, 2013. "Aggregate estimation of the price elasticity of demand for public transport in integrated fare systems: The case of Transantiago," Transport Policy, Elsevier, vol. 29(C), pages 178-185.
    13. Sergio Jara-Díaz & Antonio Gschwender, 2003. "Towards a general microeconomic model for the operation of public transport," Transport Reviews, Taylor & Francis Journals, vol. 23(4), pages 453-469, July.
    14. Batarce, Marco & Galilea, Patricia, 2018. "Cost and fare estimation for the bus transit system of Santiago," Transport Policy, Elsevier, vol. 64(C), pages 92-101.
    15. Bing-Zheng Liu & Ying-En Ge & Kai Cao & Xi Jiang & Lingyun Meng & Ding Liu & Yunfeng Gao, 2017. "Optimizing a desirable fare structure for a bus-subway corridor," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-21, October.
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