Simulation of Vehicular Traffic using Macro- and Microscopic Models

Abstract

To effectively regulate traffic on highways and networks of modern megacities, it is necessary to introduce Intelligent Transport Systems, which include many innovative solutions, in particular, mathematical models for describing the dynamics of traffic flows.The article is devoted to a brief description of the current state in this area in its development — from the simplest macroscopic and microscopic models that have become classic to modern developments.Special attention is paid to the original multilane models developed by the authors of the article within both approaches.The macroscopic model is based on the quasigasdynamic approach, while the microscopic one uses the ideology of cellular automata and constitutes a generalization of the Nagel-Schreckenberg model for the multilane case.The difference in the representation method and the mathematical apparatus for the mac-roscopic and microscopic description of traffic flows is briefly described, followed by the review of the main models at different stages of their development, presented by foreign and Russian authors.Special attention is paid to the three-phase theory of Boris Kerner and models built in the framework of this theory.Examples of modern software for traffic modeling are given.The original quasigasdynamic model of traffic flows, which uses the continuum approximation and is constructed by analogy with the well-known model of gas dynamics, is briefly described. Due to the introduction of the lateral speed, the model is generalized to the multilane case.An original microscopic model based on the cellular automata theory and representing a generalization of Nagel- Schreckenberg model for the multilane case is described. The model has been further developed by taking into account various driving strategies and behavioral aspects.The article presents a brief overview of the state of the art in the field of mathematical modeling of traffic flows, as well as original macroscopic and microscopic models developed by the authors for the case of multilane traffic.