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• W2118049063 abstract "Exact mean field equations are derived analytically to give the fundamental diagrams, i.e., the average speed - car density relations, for the Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high speed vehicles $(v_{max}=M>1) $ with stochastic delay. Starting with the basic equation describing the time evolution of the number of empty sites in front of each car, the concepts of inter-car spacings longer and shorter than $M$ are introduced. The probabilities of having long and short spacings on the road are calculated. For high car densities $(rho geq 1/M)$, it is shown that inter-car spacings longer than $M$ will be shortened as the traffic flow evolves in time, and any initial configurations approach a steady state in which all the inter-car spacings are of the short type. Similarly for low car densities $(rho leq 1/M)$, it can be shown that traffic flow approaches an asymptotic steady state in which all the inter-car spacings are longer than $M-2$. The average traffic speed is then obtained analytically as a function of car density in the asymptotic steady state. The fundamental diagram so obtained is in excellent agreement with simulation data." @default.
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• W2118049063 date "1998-09-01" @default.
• W2118049063 modified "2023-09-23" @default.
• W2118049063 title "Analytical results for the steady state of traffic flow models with stochastic delay" @default.
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• W2118049063 doi "https://doi.org/10.1103/physreve.58.2876" @default.
• W2118049063 hasPublicationYear "1998" @default.
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