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On the fundamental diagram and supply curves for congested urban networks


  • Liu, Ronghui
  • May, Tony
  • Shepherd, Simon


Macroscopic fundamental diagrams (MFD) of traffic for some networks have been shown to have similar shape to those for single links. They have erroneously been used to help estimate the level of travel in congested networks. We argue that supply curves, which track vehicles in their passage through congested networks, are needed for this purpose, and that they differ from the performance curves generated from MFD. We use a microsimulation model, DRACULA and two networks, one synthesizing the network for Cambridge, England, and one of the city of York, England, to explore the nature of performance curves and supply curves under differing patterns of demand. We show that supply curves differ from performance curves once the onset of congestion is reached, and that the incorrect use of performance curves to estimate demand can thus seriously underestimate traffic levels, the costs of congestion, and the value of congestion relief measures. We also show that network aggregated supply curves are sensitive to the temporal distribution of demand and, potentially, to the spatial distribution of demand. The shape of the supply curve also differs between origin-destination movements within a given network. We argue that supply curves for higher levels of demand cannot be observed in normal traffic conditions, and specify ways in which they can be determined from microsimulation and, potentially, by extrapolating observed data. We discuss the implications of these findings for conventional modelling of network management policies, and for these policies themselves.

Suggested Citation

  • Liu, Ronghui & May, Tony & Shepherd, Simon, 2011. "On the fundamental diagram and supply curves for congested urban networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 951-965, November.
  • Handle: RePEc:eee:transa:v:45:y:2011:i:9:p:951-965

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    References listed on IDEAS

    1. Hiroshi Ohta, 2001. "Probing A Traffic Congestion Controversy: Density and Flow Scrutinized," Journal of Regional Science, Wiley Blackwell, vol. 41(4), pages 659-680.
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    3. Verhoef, Erik T., 1999. "Time, speeds, flows and densities in static models of road traffic congestion and congestion pricing," Regional Science and Urban Economics, Elsevier, vol. 29(3), pages 341-369, May.
    4. 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.
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    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 Levinson, 2008. "Cordon pricing consistent with the physics of overcrowding," Working Papers 000038, University of Minnesota: Nexus Research Group.
    8. Evans, Alan W, 1992. "Road Congestion: The Diagrammatic Analysis: Comment," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 211-217, February.
    9. Newbery, David M, 1990. "Pricing and Congestion: Economic Principles Relevant to Pricing Roads," Oxford Review of Economic Policy, Oxford University Press, vol. 6(2), pages 22-38, Summer.
    10. Liu, Ronghui & Van Vliet, Dirck & Watling, David, 2006. "Microsimulation models incorporating both demand and supply dynamics," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(2), pages 125-150, February.
    11. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
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    Cited by:

    1. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.


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