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An analytical approximation for the macroscopic fundamental diagram of urban traffic

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  • Daganzo, Carlos F.
  • Geroliminis, Nikolas

Abstract

This paper shows that a macroscopic fundamental diagram (MFD) relating average flow and average density must exist on any street with blocks of diverse widths and lengths, but no turns, even if all or some of the intersections are controlled by arbitrarily timed traffic signals. The timing patterns are assumed to be fixed in time. Exact analytical expressions in terms of a shortest path recipe are given, both, for the street's capacity and its MFD. Approximate formulas that require little data are also given. For networks, the paper derives an upper bound for average flow conditional on average density, and then suggests conditions under which the bound should be tight; i.e., under which the bound is an approximate MFD. The MFD's produced with this method for the central business districts of San Francisco (California) and Yokohama (Japan) are compared with those obtained experimentally in earlier publications.

Suggested Citation

  • Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
    • Handle: RePEc:eee:transb:v:42:y:2008:i:9:p:771-781
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    References listed on IDEAS

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    1. Olszewski, Piotr & Fan, Henry S. L. & Tan, Yan-Weng, 1995. "Area-wide traffic speed-flow model for the Singapore CBD," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(4), pages 273-281, July.
    2. Daganzo, Carlos F., 2005. "Improving City Mobility through Gridlock Control: an Approach and Some Ideas," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt7w6232wq, Institute of Transportation Studies, UC Berkeley.
    3. Carlos F. Daganzo, 1998. "Queue Spillovers in Transportation Networks with a Route Choice," Transportation Science, INFORMS, vol. 32(1), pages 3-11, February.
    4. Daganzo, Carlos F., 2007. "Corrigendum to "Urban gridlock: Macroscopic modeling and mitigation approaches" [Transportation Research Part B 41 (2007) 49-62]," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 379-379, March.
    5. Daganzo, Carlos F., 2006. "On the Variational Theory of Traffic Flow: Well-Posedness, Duality and Applications," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt61v1r1qq, Institute of Transportation Studies, UC Berkeley.
    6. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    7. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    8. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    9. 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.
    10. Siamak Ardekani & Robert Herman, 1987. "Urban Network-Wide Traffic Variables and Their Relations," Transportation Science, INFORMS, vol. 21(1), pages 1-16, February.
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