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

Author

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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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    Cited by:

    1. Arnott, Richard & Inci, Eren, 2010. "The stability of downtown parking and traffic congestion," Journal of Urban Economics, Elsevier, vol. 68(3), pages 260-276, November.
    2. Holgun-Veras, Jos & Cetin, Mecit, 2009. "Optimal tolls for multi-class traffic: Analytical formulations and policy implications," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(4), pages 445-467, May.
    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. Antonio Russo & Martin W. Adler & Federica Liberini & Jos N. van Ommeren, 2019. "Welfare Losses of Road Congestion," CESifo Working Paper Series 7693, CESifo.
    5. Pandey, Ayush & Lehe, Lewis J. & Gayah, Vikash V., 2024. "Local stability of traffic equilibria in an isotropic network," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    6. 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.
    7. Holguín-Veras, José, 2011. "Urban delivery industry response to cordon pricing, time-distance pricing, and carrier-receiver policies in competitive markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(8), pages 802-824, October.
    8. Lehe, Lewis J. & Pandey, Ayush, 2020. "Hyperdemand: A static traffic model with backward-bending demand curves," Economics of Transportation, Elsevier, vol. 24(C).
    9. Lehe, Lewis J. & Pandey, Ayush, 2024. "A bathtub model of transit congestion," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    10. 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.
    11. Tsekeris, Theodore & Geroliminis, Nikolas, 2013. "City size, network structure and traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 1-14.
    12. 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.
    13. Kathrin Goldmann & Gernot Sieg, 2020. "Quantifying the phantom jam externality: The case of an Autobahn section in Germany," Working Papers 30, Institute of Transport Economics, University of Muenster.

    More about this item

    Keywords

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    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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