On properties of closed/open two-dimensional network-chainmail with different rules of particle movement

With the increase in the number of vehicles and the dimension of road networks, the problem of developing adequate and effective mathematical models to traffic simulation arises. The paper represents the traffic studies based on deterministic two-dimensional network of contours called chainmail introduced by A.P. Buslaev et al. Each contour consists of four cells and one particle moving around it. The open and closed versions of chainmail models with one-directional and co-directional particle movement are considered. The average velocity and other characteristics of chainmail are studied. Four theorems and hypotheses formulated in 2013, 2018 describing the dependence of average velocities of one-directional/co-directional particle movement on initial states of closed/open chainmail are tested and extended with the simulation modeling.