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Generalized bathtub model of network trip flows

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  • Jin, Wen-Long

Abstract

Vickrey (1991, 2020) proposed a bathtub model for the evolution of trip flows served by privately operated vehicles inside a road network based on three premises: (i) treatment of the road network as a single bathtub; (ii) the speed-density relation at the network level, also known as the network fundamental diagram of vehicular traffic, and (iii) the time-independent negative exponential distribution of trip distances. However, the distributions of trip distances are generally time-dependent in the real world, and Vickrey’s model leads to unreasonable results for other types of trip distance distributions. Thus there is a need to develop a bathtub model with more general trip distance distribution patterns.

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  • Jin, Wen-Long, 2020. "Generalized bathtub model of network trip flows," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 138-157.
    • Handle: RePEc:eee:transb:v:136:y:2020:i:c:p:138-157
    DOI: 10.1016/j.trb.2020.04.002
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    1. Thomas, T. & Tutert, S.I.A., 2013. "An empirical model for trip distribution of commuters in The Netherlands: transferability in time and space reconsidered," Journal of Transport Geography, Elsevier, vol. 26(C), pages 158-165.
    2. Arnott, Richard & Kokoza, Anatolii & Naji, Mehdi, 2016. "Equilibrium traffic dynamics in a bathtub model: A special case," Economics of Transportation, Elsevier, vol. 7, pages 38-52.
    3. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
    4. G. F. Newell, 1988. "Traffic Flow for the Morning Commute," Transportation Science, INFORMS, vol. 22(1), pages 47-58, February.
    5. Yu Liu & Chaogui Kang & Song Gao & Yu Xiao & Yuan Tian, 2012. "Understanding intra-urban trip patterns from taxi trajectory data," Journal of Geographical Systems, Springer, vol. 14(4), pages 463-483, October.
    6. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    7. Shoup, Donald C., 2006. "Cruising for Parking," University of California Transportation Center, Working Papers qt55s7079f, University of California Transportation Center.
    8. Carson E. Agnew, 1976. "Dynamic Modeling and Control of Congestion-Prone Systems," Operations Research, INFORMS, vol. 24(3), pages 400-419, June.
    9. Lam, William H. K. & Cheung, Chung-Yu & Lam, C. F., 1999. "A study of crowding effects at the Hong Kong light rail transit stations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(5), pages 401-415, June.
    10. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    11. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    12. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    13. Arnott, Richard & Buli, Joshua, 2018. "Solving for equilibrium in the basic bathtub model," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 150-175.
    14. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    15. Shoup, Donald C., 2006. "Cruising for parking," Transport Policy, Elsevier, vol. 13(6), pages 479-486, November.
    16. Chiabaut, Nicolas, 2015. "Evaluation of a multimodal urban arterial: The passenger macroscopic fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 410-420.
    17. Hani Mahmassani & Robert Herman, 1984. "Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterials," Transportation Science, INFORMS, vol. 18(4), pages 362-384, November.
    18. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    19. Gonzales, Eric J. & Daganzo, Carlos F., 2012. "Morning commute with competing modes and distributed demand: User equilibrium, system optimum, and pricing," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1519-1534.
    20. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    21. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    22. Mariotte, Guilhem & Leclercq, Ludovic & Laval, Jorge A., 2017. "Macroscopic urban dynamics: Analytical and numerical comparisons of existing models," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 245-267.
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    Cited by:

    1. Louis Balzer & Ludovic Leclercq, 2021. "Modal equilibrium of a tradable credit scheme with a trip-based MFD and logit-based decision-making," Papers 2112.07277, arXiv.org, revised Apr 2022.
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