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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 Teodoor

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.

Suggested Citation

  • Verhoef, Erik Teodoor, 2002. "Inside the queue: hypercongestion and road pricing in a continuous time - continuous place model of traffic congestion," ERSA conference papers ersa02p068, European Regional Science Association.
    • Handle: RePEc:wiw:wiwrsa:ersa02p068
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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    7. 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).
    8. 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.
    9. 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.
    10. 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.
    11. Ravner, Liron, 2014. "Equilibrium arrival times to a queue with order penalties," European Journal of Operational Research, Elsevier, vol. 239(2), pages 456-468.
    12. 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.
    13. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    14. Yu, Xiaojuan & van den Berg, Vincent A.C. & Verhoef, Erik T., 2025. "Preference heterogeneity in a dynamic flow congestion model," Transportation Research Part B: Methodological, Elsevier, vol. 195(C).
    15. 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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