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The two-mode problem with bottleneck queuing and transit crowding: How should congestion be priced using tolls and fares?

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  • Li, Zhi-Chun
  • Zhang, Liping

Abstract

This paper proposes a bi-modal bottleneck model with time-varying scheduling preferences for investigating the two-mode problem with bottleneck queuing and transit crowding. In the proposed model, the activity scheduling utilities of commuters at home and at work vary by the time of day, and two kinds of congestion externalities (i.e., traffic congestion among vehicles at the bottleneck and in-bus passenger crowding discomfort) are considered. Commuters choose their travel modes and departure times from home to work during the morning commute to minimize their own generalized travel cost. The properties of the proposed bi-modal bottleneck model are analytically explored. Particularly, the relationship between the departure intervals of auto and bus commuters is revealed. The time-varying charging schemes and step charging schemes for reducing the congestion externalities are also investigated. A critical condition for passenger shift from one mode to the other mode with congestion charging schemes is identified, and the effects of congestion charging schemes with and without internalizing the bus-related congestion externalities (including the bottleneck congestion externality induced by auto and bus interaction and the in-bus passenger crowding externality) on the bottleneck system are compared.

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  • Li, Zhi-Chun & Zhang, Liping, 2020. "The two-mode problem with bottleneck queuing and transit crowding: How should congestion be priced using tolls and fares?," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 46-76.
    • Handle: RePEc:eee:transb:v:138:y:2020:i:c:p:46-76
    DOI: 10.1016/j.trb.2020.05.008
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    as
    1. Kenneth Button & Erik Verhoef (ed.), 1998. "Road Pricing, Traffic Congestion and the Environment," Books, Edward Elgar Publishing, number 940.
    2. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    3. Knockaert, Jasper & Verhoef, Erik T. & Rouwendal, Jan, 2016. "Bottleneck congestion: Differentiating the coarse charge," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 59-73.
    4. Fosgerau, Mogens & de Palma, André, 2012. "Congestion in a city with a central bottleneck," Journal of Urban Economics, Elsevier, vol. 71(3), pages 269-277.
    5. Huang, Hai-Jun, 2002. "Pricing and logit-based mode choice models of a transit and highway system with elastic demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 562-570, August.
    6. Ling-Ling Xiao & Hai-Jun Huang & Ronghui Liu, 2015. "Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity," Transportation Science, INFORMS, vol. 49(1), pages 46-65, February.
    7. Liu, Tian-Liang & Huang, Hai-Jun & Yang, Hai & Zhang, Xiaoning, 2009. "Continuum modeling of park-and-ride services in a linear monocentric city with deterministic mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 692-707, July.
    8. Fosgerau, Mogens & Kim, Jinwon & Ranjan, Abhishek, 2018. "Vickrey meets Alonso: Commute scheduling and congestion in a monocentric city," Journal of Urban Economics, Elsevier, vol. 105(C), pages 40-53.
    9. Mun, Se-il & Konishi, Ko-ji & Yoshikawa, Kazuhiro, 2005. "Optimal cordon pricing in a non-monocentric city," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 723-736.
    10. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C., 2014. "Bottleneck model revisited: An activity-based perspective," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 262-287.
    11. Jia, Zehui & Wang, David Z.W. & Cai, Xingju, 2016. "Traffic managements for household travels in congested morning commute," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 91(C), pages 173-189.
    12. Kijung Ahn, 2009. "Road Pricing and Bus Service Policies," Journal of Transport Economics and Policy, University of Bath, vol. 43(1), pages 25-53, January.
    13. Engelson, Leonid & Fosgerau, Mogens, 2011. "Additive measures of travel time variability," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1560-1571.
    14. Feng Xiao & H. M. Zhang, 2014. "Pareto-Improving and Self-Sustainable Pricing for the Morning Commute with Nonidentical Commuters," Transportation Science, INFORMS, vol. 48(2), pages 159-169, May.
    15. Laih, Chen-Hsiu, 1994. "Queueing at a bottleneck with single- and multi-step tolls," Transportation Research Part A: Policy and Practice, Elsevier, vol. 28(3), pages 197-208, May.
    16. Richard Arnott & An Yan, 2000. "The Two-Mode Problem: Second-Best Pricing and Capacity," Boston College Working Papers in Economics 474, Boston College Department of Economics.
    17. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    18. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.
    19. de Palma, André & Lindsey, Robin & Monchambert, Guillaume, 2017. "The economics of crowding in rail transit," Journal of Urban Economics, Elsevier, vol. 101(C), pages 106-122.
    20. Fosgerau, Mogens & Engelson, Leonid, 2011. "The value of travel time variance," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 1-8, January.
    21. Wen-Xiang Wu & Hai-Jun Huang, 2014. "Equilibrium and Modal Split in a Competitive Highway/Transit System Under Different Road-use Pricing Strategies," Journal of Transport Economics and Policy, University of Bath, vol. 48(1), pages 153-169, January.
    22. Eric Pels & Erik T Verhoef, 2007. "Infrastructure Pricing and Competition between Modes in Urban Transport," Environment and Planning A, , vol. 39(9), pages 2119-2138, September.
    23. Huang, Hai-Jun, 2000. "Fares and tolls in a competitive system with transit and highway: the case with two groups of commuters," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 36(4), pages 267-284, December.
    24. Richard Arnott & An Yan, 2000. "The Two†Mode Problem: Second†Best Pricing and Capacity," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 12(3), pages 170-199, November.
    25. Li, Zhi-Chun & Wang, Ya-Dong, 2018. "Analysis of multimodal two-dimensional urban system equilibrium for cordon toll pricing and bus service design," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 244-265.
    26. Mark Wardman & Gerard Whelan, 2011. "Twenty Years of Rail Crowding Valuation Studies: Evidence and Lessons from British Experience," Transport Reviews, Taylor & Francis Journals, vol. 31(3), pages 379-398.
    27. Tseng, Yin-Yen & Verhoef, Erik T., 2008. "Value of time by time of day: A stated-preference study," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 607-618, August.
    28. Robin Lindsey, C. & van den Berg, Vincent A.C. & Verhoef, Erik T., 2012. "Step tolling with bottleneck queuing congestion," Journal of Urban Economics, Elsevier, vol. 72(1), pages 46-59.
    29. Kraus, Marvin, 2003. "A new look at the two-mode problem," Journal of Urban Economics, Elsevier, vol. 54(3), pages 511-530, November.
    30. Huang, Hai-Jun & Tian, Qiong & Yang, Hai & Gao, Zi-You, 2007. "Modal split and commuting pattern on a bottleneck-constrained highway," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 578-590, September.
    31. Liu, Henry X. & He, Xiaozheng & Recker, Will, 2007. "Estimation of the time-dependency of values of travel time and its reliability from loop detector data," Transportation Research Part B: Methodological, Elsevier, vol. 41(4), pages 448-461, May.
    32. Tabuchi Takatoshi, 1993. "Bottleneck Congestion and Modal Split," Journal of Urban Economics, Elsevier, vol. 34(3), pages 414-431, November.
    33. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C., 2017. "Step tolling in an activity-based bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 306-334.
    34. Danielis, Romeo & Marcucci, Edoardo, 2002. "Bottleneck road congestion pricing with a competing railroad service," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 38(5), pages 379-388, September.
    35. Fosgerau, Mogens & Lindsey, Robin, 2013. "Trip-timing decisions with traffic incidents," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 764-782.
    36. Jenelius, Erik & Mattsson, Lars-Göran & Levinson, David, 2011. "Traveler delay costs and value of time with trip chains, flexible activity scheduling and information," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 789-807, June.
    37. Börjesson, Maria & Eliasson, Jonas & Franklin, Joel, 2012. "Valuations of travel time variability in scheduling versus mean-variance models," Working papers in Transport Economics 2012:2, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
    38. Xu, Shu-Xian & Liu, Ronghui & Liu, Tian-Liang & Huang, Hai-Jun, 2018. "Pareto-improving policies for an idealized two-zone city served by two congestible modes," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 876-891.
    39. Small, Kenneth A., 2015. "The bottleneck model: An assessment and interpretation," Economics of Transportation, Elsevier, vol. 4(1), pages 110-117.
    40. Zhang, Fangni & Liu, Wei & Wang, Xiaolei & Yang, Hai, 2017. "A new look at the morning commute with household shared-ride: How does school location play a role?," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 198-217.
    41. Kraus, Marvin & Yoshida, Yuichiro, 2002. "The Commuter's Time-of-Use Decision and Optimal Pricing and Service in Urban Mass Transit," Journal of Urban Economics, Elsevier, vol. 51(1), pages 170-195, January.
    42. Hjorth, Katrine & Börjesson, Maria & Engelson, Leonid & Fosgerau, Mogens, 2015. "Estimating exponential scheduling preferences," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 230-251.
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