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Equilibrium Flows on Urban Freeways

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  • V. F. Hurdle

    (University of Toronto, Toronto, Ontario)

Abstract

The equilibrium between supply and demand for travel on a roadway is reexamined without the usual assumption that the system is in a steady state. The demand for travel is treated as a function not only of the perceived cost of travel, but also of the time of day, with strong morning and evening peaks. In order to model typical urban freeway congestion, it is presumed that the peak demand will be sufficient to bring about capacity flow on some critical section of the roadway. Two different situations are studied, an afternoon case in which the travelers are on their way home from work and a morning case. It is shown that the duration of a trip made at a given time during the peak periods is not ordinarily a function of the flow at that particular time, but of the flows that existed prior to that time. Because of this, the equilibrium flows for the afternoon peak cannot be determined by finding the intersection of predetermined supply and demand functions, but only by solving an integral or differential equation. The results for the morning peak come closer to being a straightforward generalization of the usual steady state analysis.

Suggested Citation

  • V. F. Hurdle, 1981. "Equilibrium Flows on Urban Freeways," Transportation Science, INFORMS, vol. 15(3), pages 255-293, August.
    • Handle: RePEc:inm:ortrsc:v:15:y:1981:i:3:p:255-293
    DOI: 10.1287/trsc.15.3.255
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    Cited by:

    1. 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.
    2. Richard Arnott, 1986. "Information and Time-Of-Use Decisions in Stochastically Congestable Facilities," Discussion Papers 788, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Kuwahara, Masao, 2007. "A theory and implications on dynamic marginal cost," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(7), pages 627-643, August.
    4. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun & Zhang, H. Michael, 2005. "Integrated scheduling of daily work activities and morning-evening commutes with bottleneck congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(1), pages 41-60, January.
    5. Coria, Jessica & Zhang, Xiao-Bing, 2017. "Optimal environmental road pricing and daily commuting patterns," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 297-314.
    6. Coria, Jessica & Zhang, Xiao-Bing, 2016. "Optimal Environmental Road Pricing and Integrated Daily Commuting Patterns," Working Papers in Economics 682, University of Gothenburg, Department of Economics.
    7. Richard Arnott, 1992. "Information and Usage of Congestible Facilities Under Free Access," Discussion Papers 974, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Zhang, Xiaoning & Huang, Hai-Jun & Zhang, H.M., 2008. "Integrated daily commuting patterns and optimal road tolls and parking fees in a linear city," Transportation Research Part B: Methodological, Elsevier, vol. 42(1), pages 38-56, January.
    9. Li, Chuan-Yao & Xu, Guang-Ming & Tang, Tie-Qiao, 2018. "Social optimum for evening commute in a single-entry traffic corridor with no early departures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 236-247.

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