Mathematical modeling and managing of traffic flow with two time scales

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Authors: Soloviev V. A., Fayzullin R. T.

Annotation: Microscopic mathematical model of traffic flow, in which moving of vehicles is determined by the leader of the flow, is proposed. The model describes single-lane traffic which takes into account the narrowing of roads and traffic lights. Model equations and series of optimization problems, which are supposed to be solved by using the proposed model, are described. Analogy between the optimization problem and the problem of «Multiprocessor scheduling» is shown.

Keywords: mathematical modeling, traffic flow, optimization problem