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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. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part III: Multi-destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 305-313, August.
    2. Zhang, H. M., 2000. "Structural properties of solutions arising from a nonequilibrium traffic flow theory," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 583-603, September.
    3. Harold Greenberg, 1959. "An Analysis of Traffic Flow," Operations Research, INFORMS, vol. 7(1), pages 79-85, February.
    4. Cassidy, Michael J. & Bertini, Robert L., 1999. "Some traffic features at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 25-42, February.
    5. Denos C. Gazis & Robert Herman & Renfrey B. Potts, 1959. "Car-Following Theory of Steady-State Traffic Flow," Operations Research, INFORMS, vol. 7(4), pages 499-505, August.
    6. Cassidy, Michael J., 1998. "Bivariate relations in nearly stationary highway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 32(1), pages 49-59, January.
    7. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    8. Denos C. Gazis & Robert Herman & Richard W. Rothery, 1961. "Nonlinear Follow-the-Leader Models of Traffic Flow," Operations Research, INFORMS, vol. 9(4), pages 545-567, August.
    9. Leslie C. Edie, 1961. "Car-Following and Steady-State Theory for Noncongested Traffic," Operations Research, INFORMS, vol. 9(1), pages 66-76, February.
    10. Li, Michael Z. F., 2002. "The role of speed-flow relationship in congestion pricing implementation with an application to Singapore," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 731-754, September.
    11. Zhao, Yong & Kockelman, Kara Maria, 2006. "On-line marginal-cost pricing across networks: Incorporating heterogeneous users and stochastic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 424-435, June.
    12. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 373-389, October.
    13. Kara Kockelman, 2001. "Modeling traffic's flow-density relation: Accommodation of multiple flow regimes and traveler types," Transportation, Springer, vol. 28(4), pages 363-374, November.
    14. Zhang, H. M., 1998. "A theory of nonequilibrium traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 485-498, September.
    15. Kai Nagel & Peter Wagner & Richard Woesler, 2003. "Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling," Operations Research, INFORMS, vol. 51(5), pages 681-710, October.
    16. Zhang, H. M., 1999. "Analyses of the stability and wave properties of a new continuum traffic theory," Transportation Research Part B: Methodological, Elsevier, vol. 33(6), pages 399-415, August.
    17. Z.F. Li, Michael, 1999. "Estimating congestion toll by using traffic count data -- Singapore's area licensing scheme," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 35(1), pages 1-10, March.
    18. Castillo, J. M. Del & Benítez, F. G., 1995. "On the functional form of the speed-density relationship--II: Empirical investigation," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 391-406, October.
    19. Jochen Einbeck & Gerhard Tutz, 2006. "Modelling beyond regression functions: an application of multimodal regression to speed–flow data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 461-475, August.
    20. Yang, Hai & Meng, Qiang & Lee, Der-Horng, 2004. "Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 477-493, July.
    21. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    22. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    23. Jin, W. L. & Zhang, H. M., 2003. "The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 37(3), pages 207-223, March.
    24. Cassidy, M. J. & Mauch, Michael, 2001. "An observed traffic pattern in long freeway queues," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(2), pages 143-156, February.
    25. G. F. Newell, 1955. "Mathematical Models for Freely-Flowing Highway Traffic," Operations Research, INFORMS, vol. 3(2), pages 176-186, May.
    26. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
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    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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