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Inside the queue:: hypercongestion and road pricing in a continuous time-continuous place model of traffic congestion

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  • Verhoef, Erik T.

Abstract

This paper develops a continuous time - continuous place model of road traffic congestion, based on car-following theory. The model fully integrates two archetype representations of traffic congestion technology, namely "flow congestion", originating in the works of Pigou, and "vertical queuing" models, pioneered by Vickrey. Because a closed-form analytical solution of the formal model does not exist, its behaviour is explored in a numerical exercise. In a setting with endogenous departure time choice and with a bottleneck halfway the route, it is shown that "hypercongestion" can arise as a dynamic - transitional and local - equilibrium phenomenon. Also dynamic toll schedules are explored. It is found that a toll rule based on an intuitive dynamic and space-varying generalization of the standard Pigouvian tax rule can hardly be improved upon. A naïve application of a toll schedule based on Vickrey´s bottleneck model, in contrast, performs much worse and actually even reduces welfare.
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  • 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.
    • Handle: RePEc:eee:juecon:v:54:y:2003:i:3:p:531-565
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    1. Kenneth Button & Erik Verhoef (ed.), 1998. "Road Pricing, Traffic Congestion and the Environment," Books, Edward Elgar Publishing, number 940, December.
    2. 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.
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    14. Verhoef, Erik T., 2002. "Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 707-729, September.
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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. Frascaria, Dario & Olver, Neil & Verhoef, Erik, 2020. "Emergent hypercongestion in Vickrey bottleneck networks," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 523-538.
    3. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    4. Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers on Economics 3/2017, University of Southern Denmark, Department of Economics.
    5. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    6. Kaddoura, Ihab & Nagel, Kai, 2019. "Congestion pricing in a real-world oriented agent-based simulation context," Research in Transportation Economics, Elsevier, vol. 74(C), pages 40-51.
    7. O'Dea, William P., 2006. "An Economic Analysis of Construction Bottlenecks," 47th Annual Transportation Research Forum, New York, New York, March 23-25, 2006 208045, Transportation Research Forum.
    8. Antonio Russo & Martin W. Adler & Federica Liberini & Jos N. van Ommeren, 2019. "Welfare Losses of Road Congestion," CESifo Working Paper Series 7693, CESifo.
    9. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    10. Verhoef, Erik T., 2005. "Speed-flow relations and cost functions for congested traffic: Theory and empirical analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 792-812.
    11. Saenz-de-Miera, Oscar & Rosselló, Jaume, 2012. "The responsibility of tourism in traffic congestion and hyper-congestion: A case study from Mallorca, Spain," Tourism Management, Elsevier, vol. 33(2), pages 466-479.
    12. Jesper Breinbjerg & Trine Tornøe Platz & Lars Peter Østerdal, 2024. "Equilibrium arrivals to a last-come first-served preemptive-resume queue," Annals of Operations Research, Springer, vol. 336(3), pages 1551-1572, May.
    13. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.

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