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A Minplus Derivation of the Fundamental Car-Traffic Law

Abstract : We give deterministic models and a stochastic model of the traffic on a circular road without overtaking. The average speed is the eigenvalue of a minplus matrix describing the dynamics of the system in the first case and a Lyapounov exponentof a minplus stochastic matrix in the second one.The eigenvalue and the Lyapounov exponent are computed explicitly. From these formulae we derive the fundamental law that links the flow to the density of vehicle on the road. Numerical experiments using the maxplus toolbox of Scilab confirm the theoretical results obtained.
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https://hal.inria.fr/inria-00072263
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Submitted on : Tuesday, May 23, 2006 - 8:15:19 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
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  • HAL Id : inria-00072263, version 1

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Pablo Lotito, Elina Mancinelli, Jean-Pierre Quadrat. A Minplus Derivation of the Fundamental Car-Traffic Law. [Research Report] RR-4324, INRIA. 2001. ⟨inria-00072263⟩

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