Distributed mathematical models of undetermined "without preference" motion of traffic flow

Pages: 589 - 600, Issue Special, September 2011

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Sharif E. Guseynov - Institute of Mathematical Sciences and Information Technologies, University of Liepaja, Transport and Telecommunication Institute, 1 Lomonosov Street, Riga LV-1019, Latvia (email)
Shirmail G. Bagirov - Department of Mechanics and Mathematics, Baku State University, 23 Academician Zahid Xalilov Street, Baku AZ-1073/1, Azerbaidjan (email)

Abstract: Present work proceeds non-deterministic motion of the two-dimensional (2D) vehicular traffic flow, where the traffic flow is assumed as flow of particles in the investigated environment with allowed motion in both forward and opposite directions. Besides, it is assumed that at any fixed time interval in the 2D flow, vehicles could change its positions on the road to any arbitrary placements at the de ned probabilities, even they might be not the neighbouring ones. Such a non-deterministic motion of 2D traffic flow will be named as motion "without preference". Under the pointed assumptions, first it is constructed the non-deterministic discrete mathimatical model, and later by means f using the principle of continuous system there are applied limiting transitions to the constructed discrete model. As a result nondeterministic continuous model in the form of initial-boundary value problem for the integro-di fferential equation is elaborated. In addition probabilistic interpretations of the constructed models and the received results are given.

Keywords:  Traffic flows, non-deterministic vehicular trac motion; density of traffic flow, integro-di fferential equation, probabilistic treatment, Markov chain
Mathematics Subject Classification:  Primary: 45K05, 60J28, 82B31; Secondary: 65M75, 65N75

Received: August 2010;      Revised: April 2011;      Published: October 2011.