Optimisation method for chainmail-type Buslaev nets on a torus under topology variations

The paper is devoted to the study and optimization of Buslaev contour networks of the chainmail type on a torus, which represent discrete dynamical systems with a complex topological structure. These networks explicitly consider conflicts in the shared nodes of contours, making them particularly suitable for modelling traffic flows on complex urban road networks where intersections and overlapping traffic streams play a critical role in determining the overall system capacity and stability. The study presents a comprehensive combinatorial analysis of the network topology, including the determination of the number of diagonals, the distribution of contours across diagonals, and the derivation of the spectrum of average particle velocities. Analytical formulas are developed for estimating the number of allowed states and admissible velocity configurations, taking into account the spatial and topological constraints inherent in the system. A simulation-based investigation is performed for chainmail networks, demonstrating clear correlations between directional movement configurations and the resulting average velocities of particles. A topology optimization method is proposed, enabling the identification of optimal directional patterns that maximize average system velocity while mitigating local conflicts. The obtained results confirm theoretical predictions regarding the minimum achievable velocities and reveal structurally stable optimal configurations that significantly enhance system throughput. Practical recommendations are formulated for applying the developed models to optimize traffic flows in real-world urban street and road networks, offering potential for improving transport efficiency under complex topological and operational constraints.