Macro model of transport flow at the crossroads

Currently, one of the important problems of the megalopolis is traffic management, and in connection with the problem of the formation of predatory and congestion situations in settlements, respectively, these studies are relevant. There are several approaches to mathematical modelling of the behaviour of vehicle traffic. The most common ones: microscopic, macroscopic, based on the theory of cellular automata. The third approach is macroscopic, with its help analog models are built, and the traffic flow is considered as a hydrodynamic, or gas-dynamic flow. Using this approach, you can find the time or traffic intensity, average speed, and the level of network load. One of the creators of this approach, which simulates the traffic flow by the Navier–Stokes system, which describes the flow of a viscous incompressible fluid, is A.B. Kurzhansky. A distinctive feature of this article is that the traffic flow model is built on the basis of the Oskolkov system of equations, which generalize the Navier–Stokes system. Here, in addition to the viscosity and incompressibility of the flow, elasticity is taken into account, due to which the retardation effect inherent in viscoelastic incompressible fluids appears.