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The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations

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  • Nelson, Paul
  • Sopasakis, Alexandros

Abstract

The classical derivation of a traffic stream model (e.g. speed/concentration relation) from the equilibrium solutions of the Prigogine-Herman kinetic equation invokes the nontrivial assumption that the underlying distribution of desired speeds is nonzero for vanishingly small speeds. In this paper we investigate the situation when this assumption does not hold. It is found that the Prigogine-Herman kinetic equation has a one-parameter family of equilibrium solutions, and hence an associated traffic stream model, only for traffic concentrations below some critical value; at higher concentrations there is a two-parameter family of solutions, and hence a continuum of mean velocities for each concentration. This result holds for both constant values of the passing probability and the relaxation time, and for values that depend on concentration in the manner assumed by Prigogine and Herman. It is hypothesized that this result reflects the well-known tendency toward substantial scatter in observational data of traffic flow at high concentrations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:32:y:1998:i:8:p:589-604
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    References listed on IDEAS

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    1. Nelson, Paul, 1995. "On deterministic developments of traffic stream models," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 297-302, August.
    2. 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.
    3. Helbing, Dirk, 1995. "Theoretical foundation of macroscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 375-390.
    4. Ross, Paul, 1988. "Traffic dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 22(6), pages 421-435, December.
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    1. Siqueira, Adriano F. & Peixoto, Carlos J.T. & Wu, Chen & Qian, Wei-Liang, 2016. "Effect of stochastic transition in the fundamental diagram of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 1-13.
    2. Chiu, Yi-Chang & Zhou, Liang & Song, Houbing, 2010. "Development and calibration of the Anisotropic Mesoscopic Simulation model for uninterrupted flow facilities," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 152-174, January.
    3. Helbing, Dirk & Batic, Davide & Schönhof, Martin & Treiber, Martin, 2002. "Modelling widely scattered states in ‘synchronized’ traffic flow and possible relevance for stock market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 251-260.
    4. Qian, Wei-Liang & F. Siqueira, Adriano & F. Machado, Romuel & Lin, Kai & Grant, Ted W., 2017. "Dynamical capacity drop in a nonlinear stochastic traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 328-339.

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