MODELS OF TRAFFIC FLOW DYNAMICS ON HIGHWAYS

Abstract

The paper is an analytical review of the currently existing methods of traffic flows modeling. The movement of vehicles on the road can be modeled in different ways. Mathematical models as tools that allow us to study complex processes in the real world, including transport infrastructure, without capital expenditures, are a popular tool for solving many problems in various spheres of the national economy. There are several approaches to mathematical modeling of traffic flows. In microscopic models, the law of motion of each car is set, depending on its current position, speed, characteristics of the movement of neighboring cars, and other factors. Microscopic models, in turn, can be divided into models that are continuous in space and time, and into models that are discrete in space and time, the so-called cellular automata. In macroscopic models, the transport flow is considered as a fluid flow with special properties. The equations of the macroscopic model establish the relationship between the flow, density, speed of movement, possibly acceleration, and so on. Macroscopic models can also be continuous or discrete. In continuous models, the change in the state of a road section without branches and intersections is usually described by partial differential equations. Modeling traffic flows is necessary because active experiments in the existing transport network are fraught with unpredictable consequences, and in many cases are not feasible at all. The work presents a description and analysis of the models, and of their advantages and disadvantages.