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Speed-flow relations and cost functions for congested traffic: Theory and empirical analysis

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  • Verhoef, Erik T.

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. Finally, it is shown that reduced-form average cost functions, that relate the sum of average travel cost and average schedule delay costs to the number of users in a dynamic equilibrium, certainly need not have the intuitive convex shape, but may very well be concave - despite the fact that the underlying speed-flow function may be convex.

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Bibliographic Info

Article provided by Elsevier in its journal Transportation Research Part A: Policy and Practice.

Volume (Year): 39 (2005)
Issue (Month): 7-9 ()
Pages: 792-812

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Handle: RePEc:eee:transa:v:39:y:2005:i:7-9:p:792-812

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References

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  1. Erik T. Verhoef, 2002. "Inside the Queue," Tinbergen Institute Discussion Papers 02-062/3, Tinbergen Institute, revised 27 May 2003.
  2. Small, K.A. & Gomez-Ibanez, J.A., 1996. "Urban Transportation," Papers 95-96-4, California Irvine - School of Social Sciences.
  3. 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.
  4. 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.
  5. De Meza, David & Gould, J R, 1987. "Free Access versus Private Property in a Resource: Income Distributions Compared," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1317-25, December.
  6. Smith, W. Spencer & Hall, Fred L. & Montgomery, Frank O., 1996. "Comparing the speed-flow relationship for motorways with new data from the M6," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(2), pages 89-101, March.
  7. Evans, Alan W, 1992. "Road Congestion: The Diagrammatic Analysis: Comment," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 211-17, February.
  8. Mun, Se-il, 1999. "Peak-Load Pricing of a Bottleneck with Traffic Jam," Journal of Urban Economics, Elsevier, vol. 46(3), pages 323-349, November.
  9. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  10. Chu Xuehao, 1995. "Endogenous Trip Scheduling: The Henderson Approach Reformulated and Compared with the Vickrey Approach," Journal of Urban Economics, Elsevier, vol. 37(3), pages 324-343, May.
  11. Hiroshi Ohta, 2001. "Probing A Traffic Congestion Controversy: Density and Flow Scrutinized," Journal of Regional Science, Wiley Blackwell, vol. 41(4), pages 659-680.
  12. Erik T. Verhoef, 2001. "Probing A Traffic Congestion Controversy: A Comment," Journal of Regional Science, Wiley Blackwell, vol. 41(4), pages 681-694.
  13. Hiroshi Ohta, 2001. "Probing a Traffic Congestion Controversy: Response to Comment," Journal of Regional Science, Wiley Blackwell, vol. 41(4), pages 695-699.
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Cited by:
  1. 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.
  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. 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.
  4. 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.
  5. Tsekeris, Theodore & Geroliminis, Nikolas, 2013. "City size, network structure and traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 1-14.

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