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A Model of Rush-Hour Traffic Dynamics in an Isotropic Downtown Area

Author

Listed:
  • Richard Arnott

    (Department of Economics, University of California Riverside)

  • Anatolii Kokoza

    (Department of Economics, University of Arizona)

  • Mehdi Naji

    (Department of Money and Foreign Currencies, Money and Banking Research Institute)

Abstract
For a quarter century, a top priority in transportation economic theory has been to develop models of rush-hour traffic dynamics that incorporate hypercongestion – situations of heavy congestion where throughput decreases as traffic density increases. Unfortunately, even the simplest models along these lines appear to be analytically intractable, and none of the models that have made approximations in order to achieve tractability has gained widespread acceptance. This paper takes a different tack focusing on a special case – the isotropic model with identical commuters and the α − β − γ cost function – for which an analytical solution is possible. A complete, closed-form solution is presented for the no-toll equilibrium in which departures and arrivals occur in masses, and the solution for the social optimum is fully characterized.

Suggested Citation

  • Richard Arnott & Anatolii Kokoza & Mehdi Naji, 2016. "A Model of Rush-Hour Traffic Dynamics in an Isotropic Downtown Area," Working Papers 201612, University of California at Riverside, Department of Economics.
    • Handle: RePEc:ucr:wpaper:201612
    as

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    File URL: https://economics.ucr.edu/repec/ucr/wpaper/201612.pdf
    File Function: First version, 2016
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    References listed on IDEAS

    as
    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. Carson E. Agnew, 1976. "Dynamic Modeling and Control of Congestion-Prone Systems," Operations Research, INFORMS, vol. 24(3), pages 400-419, June.
    3. Small, Kenneth A., 2015. "The bottleneck model: An assessment and interpretation," Economics of Transportation, Elsevier, vol. 4(1), pages 110-117.
    4. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    5. 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.
    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    7. Nikolas Geroliminis & David M. Levinson, 2009. "Cordon Pricing Consistent with the Physics of Overcrowding," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 219-240, Springer.
    8. Fosgerau, Mogens & Small, Kenneth A., 2013. "Hypercongestion in downtown metropolis," Journal of Urban Economics, Elsevier, vol. 76(C), pages 122-134.
    9. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    10. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    equilibrium; rush hour; traffic congestion;
    All these keywords.

    JEL classification:

    • L91 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Transportation: General
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

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