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Speed-Flow Relations and Cost Functions for Congested Traffic: Theory and Empirical Analysis

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  • Erik T. Verhoef

    (Faculty of Economic and Business Administration, Vrije Universiteit Amsterdam)

Abstract

A dynamic 'car-following' extension of the conventional economic model of traffic congestion is presented, which predicts the average cost function for trips in stationary states to be significantly different from the conventional average cost function derived from the speed-flow function. When applied to a homogeneous road, the model reproduces the same stationary state equilibria as the conventional model, including the hypercongested ones. However, stability analysis shows that the latter are dynamically unstable. The average cost function for stationary state traffic coincides with the conventional function for non-hypercongested traffic, but rises vertically at the road's capacity due to queuing, instead of bending backwards. When extending the model to include an upstream road segment, it predicts that such queuing will occur under hypercongested conditions, while the general shape of the average cost function for full trips does not change, implying that hypercongestion will not occur on the downstream road segment. These qualitative predictions are verified empirically using traffic data from a Dutch bottleneck.

Suggested Citation

  • Erik T. Verhoef, 2003. "Speed-Flow Relations and Cost Functions for Congested Traffic: Theory and Empirical Analysis," Tinbergen Institute Discussion Papers 03-064/3, Tinbergen Institute, revised 31 Oct 2003.
    • Handle: RePEc:tin:wpaper:20030064
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    References listed on IDEAS

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    9. Verhoef, Erik T., 2001. "An Integrated Dynamic Model of Road Traffic Congestion Based on Simple Car-Following Theory: Exploring Hypercongestion," Journal of Urban Economics, Elsevier, vol. 49(3), pages 505-542, May.
    10. Erik T. Verhoef, 2002. "Inside the Queue," Tinbergen Institute Discussion Papers 02-062/3, Tinbergen Institute, revised 27 May 2003.
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    12. Verhoef, Erik T., 2003. "Inside the queue:: hypercongestion and road pricing in a continuous time-continuous place model of traffic congestion," Journal of Urban Economics, Elsevier, vol. 54(3), pages 531-565, November.
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    Cited by:

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    3. Button, Kenneth, 2004. "1. The Rationale For Road Pricing: Standard Theory And Latest Advances," Research in Transportation Economics, Elsevier, vol. 9(1), pages 3-25, January.
    4. Hall, Jonathan D., 2018. "Pareto improvements from Lexus Lanes: The effects of pricing a portion of the lanes on congested highways," Journal of Public Economics, Elsevier, vol. 158(C), pages 113-125.
    5. Antonio Russo & Martin W. Adler & Federica Liberini & Jos N. van Ommeren, 2019. "Welfare Losses of Road Congestion," CESifo Working Paper Series 7693, CESifo.
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    7. Lehe, Lewis J. & Pandey, Ayush, 2020. "Hyperdemand: A static traffic model with backward-bending demand curves," Economics of Transportation, Elsevier, vol. 24(C).
    8. Holgui­n-Veras, Jose & Cetin, Mecit & Xia, Shuwen, 2006. "A comparative analysis of US toll policy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(10), pages 852-871, December.
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    More about this item

    Keywords

    Traffic congestion; Road pricing; Car-following theory; Speed-flow relations; Cost functions;
    All these keywords.

    JEL classification:

    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise
    • R48 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Government Pricing and Policy
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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