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Theoretical foundation of macroscopic traffic models

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  • Helbing, Dirk

Abstract

On the basis of the elementary laws of individual driver behavior concerning the acceleration and interaction of vehicles a gas-kinetic traffic model is constructed. This yields theoretical relations for the fundamental diagram and the equilibrium variance-density relation, but above all it allows the derivation of macroscopic traffic equations. These build a hierarchy of non-closed equations which can be closed by different zeroth-order approximations. In this way one obtains the traffic equations of Lighthill and Whitham or those of Phillips. Alternatively one can derive Euler-like traffic equations which are proposed here since they include additional dynamical equations for the velocity variance. The new variance equation is able to describe the empirically observed increase of variance directly before a traffic jam develops.

Suggested Citation

  • Helbing, Dirk, 1995. "Theoretical foundation of macroscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 375-390.
    • Handle: RePEc:eee:phsmap:v:219:y:1995:i:3:p:375-390
    DOI: 10.1016/0378-4371(95)00174-6
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    References listed on IDEAS

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    1. Robert E. Chandler & Robert Herman & Elliott W. Montroll, 1958. "Traffic Dynamics: Studies in Car Following," Operations Research, INFORMS, vol. 6(2), pages 165-184, April.
    2. 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.
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    5. Robert Herman & Elliott W. Montroll & Renfrey B. Potts & Richard W. Rothery, 1959. "Traffic Dynamics: Analysis of Stability in Car Following," Operations Research, INFORMS, vol. 7(1), pages 86-106, February.
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    Cited by:

    1. 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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