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A mathematical theory of traffic hysteresis

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  • Zhang, H. M.

Abstract

This paper presents a mathematical theory for modeling the hysteresis phenomenon observed in traffic flow. It proposes that acceleration, deceleration and equilibrium flow should be distinguished in obtaining speed-concentration and/or occupancy relationships, such that the phase transitions from one phase to another can be correctly identified. The analysis shows that the speed-concentration curves obtained following this approach are hysteresis loops, as predicted by the theory. The paper also gives a discussion of the general properties of the proposed modeling equations and examines the relationship between traffic hysteresis and stop-start waves observed in traffic flow.

Suggested Citation

  • Zhang, H. M., 1999. "A mathematical theory of traffic hysteresis," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 1-23, February.
    • Handle: RePEc:eee:transb:v:33:y:1999:i:1:p:1-23
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    References listed on IDEAS

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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. Acha-Daza, Jorge A. & Hall, Fred L., 1994. "Application of catastrophe theory to traffic flow variables," Transportation Research Part B: Methodological, Elsevier, vol. 28(3), pages 235-250, June.
    3. Harold Greenberg, 1959. "An Analysis of Traffic Flow," Operations Research, INFORMS, vol. 7(1), pages 79-85, February.
    4. Leslie C. Edie & Robert Herman & Tenny N. Lam, 1980. "Observed Multilane Speed Distribution and the Kinetic Theory of Vehicular Traffic," Transportation Science, INFORMS, vol. 14(1), pages 55-76, February.
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