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A Generic Characterization of Equilibrium Speed-Flow Curves

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  • Michael Z. F. Li

    (Nanyang Business School, Nanyang Technological University, Singapore 639798)

Abstract

By introducing the concept of speed elasticity of flow and density, this paper provides a generic characterization for a class of well-behaved equilibrium speed-flow curves that are differentiable and backward bending and possess monotone speed-density curves. We start with a comprehensive review on classical models, including Greenberg, Greenshields, and Underwood. A major limitation of these models is that the specification is uniquely determined by three road-specific parameters: the free-flow speed, the capacity flow, and the corresponding speed at the capacity flow, which makes the empirical application difficult due to lack of flexibility. Through a careful review of Del Castillo and Benitez [Del Castillo, J. M., F. G. Benitez. 1995. On the functional form of the speed-density relationship---I: General theory, II: Empirical investigation. Transportation Res. Part B 29 373--406], we have provided a new characterization for the Newell-Frankin model and made a connection between the family of rational generating functions and the Greenshields-type models. Based on three primitive regularity conditions, we derive a generic characterization for well-behaved macroscopic equilibrium speed-flow curves that integrate all classical models. Using the generic characterization, we show that the equilibrium speed-flow curves derived from the car-following models can be classified as a two-parameter extension of the Greenshields-type model. We have also made an attempt in proposing a plausible rectification to the speed-flow models from the Highway Capacity Manual 2000 so that they possess the backward-bending property. A formal linkage between the generic characterization of speed-flow curves and the theory of congestion pricing is also established.

Suggested Citation

  • Michael Z. F. Li, 2008. "A Generic Characterization of Equilibrium Speed-Flow Curves," Transportation Science, INFORMS, vol. 42(2), pages 220-235, May.
    • Handle: RePEc:inm:ortrsc:v:42:y:2008:i:2:p:220-235
    DOI: 10.1287/trsc.1070.0201
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    References listed on IDEAS

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    1. Power, Gabriel J. & Burris, Mark & Vadali, Sharada & Vedenov, Dmitry, 2016. "Valuation of strategic options in public–private partnerships," Transportation Research Part A: Policy and Practice, Elsevier, vol. 90(C), pages 50-68.
    2. Basso, Leonardo J. & Guevara, Cristián Angelo & Gschwender, Antonio & Fuster, Marcelo, 2011. "Congestion pricing, transit subsidies and dedicated bus lanes: Efficient and practical solutions to congestion," Transport Policy, Elsevier, vol. 18(5), pages 676-684, September.

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