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Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics. (English) Zbl 1141.90014
Summary: A novel traffic flow model based on stochastic microscopic dynamics is introduced and analyzed. Vehicles advance based on the energy profile of their surrounding traffic implementing the “look-ahead” rule and following an underlying asymmetric exclusion process with Arrhenius spin-exchange dynamics. Monte Carlo simulations produce numerical solutions of the microscopic traffic model. Fluctuations play an important role in profiling observationally documented but, at the simulation level, elusive traffic phenomena. Furthermore, based on scaling and limit arguments we obtain a macroscopic description of this microscopic dynamics formulation which up to leading term of the expansions takes the form of integrodifferential Burgers or higher-order dispersive partial differential equations. We outline connections and comparisons of the hierarchical models presented here (microscopic, macroscopic) with other well-known traffic flow models.

MSC:
90B20Traffic problems
60K25Queueing theory
60K30Applications of queueing theory
65C05Monte Carlo methods