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On deterministic developments of traffic stream models

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  • Nelson, Paul

Abstract

Classical deterministic (or "mechanical") developments of traffic stream models from car-following models are criticized on the following basis. The evaluation of the constant of integration for initial conditions corresponding to speed zero and headway equal to the reciprocal of jam density ignores large numbers of possibly relevant solutions of the underlying car-following model. Some undesirable consequences, particularly the restriction to temporally and spatially constant flow conditions, of viewing traffic stream models as being deterministic consequences of car-following models are also noted. It is suggested that an approach to traffic stream models via kinetic models possibly would be more appropriate and useful.

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  • Nelson, Paul, 1995. "On deterministic developments of traffic stream models," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 297-302, August.
    • Handle: RePEc:eee:transb:v:29:y:1995:i:4:p:297-302
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    References listed on IDEAS

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    1. 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.
    2. Newell, G. F., 1989. "Comments on traffic dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 23(5), pages 386-389, October.
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    4. N/A, 1989. "Comments," ILR Review, Cornell University, ILR School, vol. 43(1), pages 89-102, October.
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    6. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    7. 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.
    8. Leo, Chin Jian & Pretty, Robert L., 1992. "Numerical simulation of macroscopic continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 26(3), pages 207-220, June.
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    Cited by:

    1. Paul Nelson & Bryan Raney, 1999. "Objectives and Benchmarks for Kinetic Theories of Vehicular Traffic," Transportation Science, INFORMS, vol. 33(3), pages 298-314, August.
    2. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
    3. Nelson, Paul & Sopasakis, Alexandros, 1998. "The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 589-604, November.

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