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Speed-Flow Relations and Cost Functions for Congested Traffic: Theory and Empirical Analysis

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Author Info
Erik T. Verhoef () (Faculty of Economic and Business Administration, Vrije Universiteit Amsterdam)

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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.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-064/3.

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Date of creation: 06 Aug 2003
Date of revision: 31 Oct 2003
Handle: RePEc:dgr:uvatin:20030064

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Traffic congestion; Road pricing; Car-following theory; Speed-flow relations; Cost functions;

Other versions of this item:

Find related papers by JEL classification:
R41 - Urban, Rural, and Regional Economics - - Transportation Systems - - - Transportation: Demand, Supply, and Congestion
R48 - Urban, Rural, and Regional Economics - - Transportation Systems - - - Government Pricing; Regulatory Policies
D62 - Microeconomics - - Welfare Economics - - - Externalities

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  5. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May. [Downloadable!] (restricted)
  6. Small, K.A. & Gomez-Ibanez, J.A., 1996. "Urban Transportation," Papers 95-96-4, California Irvine - School of Social Sciences.
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  7. Erik T. Verhoef, 2002. "Inside the Queue," Tinbergen Institute Discussion Papers 02-062/3, Tinbergen Institute, revised 27 May 2003. [Downloadable!]
  8. 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. [Downloadable!] (restricted)
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