Non-Uniform Loading Control on an Asymmetrical Two-Contours Network

In this paper we study a dynamical system belonging to the class of Buslaev's contour networks. The system consists of two closed discrete contours and two common points called nodes. Each contour contains a cluster of different length with particles moving in a given direction every time t. The delays in the movement of clusters are due to the fact that two clusters cannot pass through the node at the same time. Situations when two clusters claim to be a node at the same time are called conflicts and are resolved according to deterministic rules for resolving conflicts. The main characteristic is the average cluster velocity, considering the delays. In view of the determinism, the system goes into a periodic mode of motion from a certain moment. The behavior of this system depends on the initial state and the choice of the conflict resolution rule. In this study, the rule is derived according to which the set of initial states is divided into subsets with different modes of motion.