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A Bathtub Model of Traffic Congestion

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  • Arnott, Richard

Abstract

In the standard economic models of traffic congestion, traffic flow does not fall under heavily congested conditions. But this is counter to experience, especially in thedowntown areas of most major cities during rush hour. This paper presents a bathtub model of traffic congestion. The height of water in the bathtub corresponds totraffic density, velocity is negatively related to density, and outflow is the product of density and velocity. Above a critical density, outflow falls as density increases. The model indicates that, when demand is high relative to capacity, applying an optimal time-varying congestion tolls generates benefits that are considerably larger than those obtained from the standard models and exceed the toll revenue collected.

Suggested Citation

  • Arnott, Richard, 2011. "A Bathtub Model of Traffic Congestion," University of California Transportation Center, Working Papers qt9zx130zz, University of California Transportation Center.
    • Handle: RePEc:cdl:uctcwp:qt9zx130zz
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    References listed on IDEAS

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    1. Henderson, J. Vernon, 1981. "The economics of staggered work hours," Journal of Urban Economics, Elsevier, vol. 9(3), pages 349-364, May.
    2. Richard Arnott & Tilmann Rave & Ronnie Schöb, 2005. "Alleviating Urban Traffic Congestion," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012197, December.
    3. 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.
    4. Arnott, Richard & Inci, Eren, 2006. "An integrated model of downtown parking and traffic congestion," Journal of Urban Economics, Elsevier, vol. 60(3), pages 418-442, November.
    5. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    6. Small, Kenneth A., 1992. "Using the Revenues from Congestion Pricing," University of California Transportation Center, Working Papers qt32p9m3mm, University of California Transportation Center.
    7. Ian W. H. Parry & Kenneth A. Small, 2005. "Does Britain or the United States Have the Right Gasoline Tax?," American Economic Review, American Economic Association, vol. 95(4), pages 1276-1289, September.
    8. Daganzo, Carlos F. & Gayah, Vikash V. & Gonzales, Eric J., 2011. "Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 278-288, January.
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    10. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
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    Cited by:

    1. Fosgerau, Mogens & Small, Kenneth A., 2013. "Hypercongestion in downtown metropolis," Journal of Urban Economics, Elsevier, vol. 76(C), pages 122-134.

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