Analysis of flow dynamics on Buslaev contour networks

Traffic flow models on networks are relevant because of exponential growth of road transport in megalopolises worldwide. But there are not enough adequate approaches to describe such processes. Buslaev A.P. with co-authors had introduced networks of contours with common nodes, local particles movement on each contour in given direction and competition resolution rules in common nodes. The problem is to study limit system behavior in dependence on initial conditions. In mathematical models of communication systems and computer networks, particles correspond to messages or information blocks (message packages). Behavior of particles on a contour chain with two cells on each contour is similar to behavior of Ising model used in quantum mechanics. In particular, Ising model is used for modeling of behavior of experimental computers based on principles of quantum mechanics. Contour network models can be used for study of spectral quantization. We study a behavior contour networks of Buslaev type for regular cases depending on rules of competition resolutions in common nodes. Exact results were obtained for closed chain with opposite and odd-even resolution rules, and stochastic version of left-priority rule with non-zero probability of indecisive movement.