A Generic Characterization of Equilibrium Speed-Flow Curves

Michael Z. F. Li ()
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Michael Z. F. Li: Nanyang Business School, Nanyang Technological University, Singapore 639798

Transportation Science, 2008, vol. 42, issue 2, 220-235

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.

Keywords: vehicular traffic flow; speed-flow relations; speed-density relations; highway capacity (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:42:y:2008:i:2:p:220-235

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