A min-plus derivation of the fundamental car-traffic law

Author

Lotito, Pablo A. ; Mancinelli, Elina M. ; Quadrat, Jean-Pierre

Author_Institution

GRETIA-INRETS, Arccueil, France

Volume

50

Issue

5

fYear

2005

fDate

5/1/2005 12:00:00 AM

Firstpage

699

Lastpage

705

Abstract

We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing the dynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulas, we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the MAXPLUS toolbox of SCILAB confirm the theoretical results obtained.

Keywords

Lyapunov methods; algebra; automobiles; eigenvalues and eigenfunctions; road traffic; stochastic systems; Lyapunov exponent; car traffic law; deterministic model; eigenvalue; minplus algebra; stochastic matrix; stochastic model; Algorithm design and analysis; Art; Automatic control; Discrete event systems; Dynamic programming; Optimal control; Parameter estimation; Sensitivity analysis; Stochastic processes; Terminology; Cellular automata; Lyapunov exponent; fundamental diagram; max-plus algebra;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.848336

Filename

1431054