Investigation of traffic flow dynamic processes using discrete model

Abstract

Modelling the process of traffic flow was previously studied from different points of view and different mathematical methods where used to describe the same process. All authors have an agreement on basic traffic flow parameters like, traffic flow density, traffic flow rate or the average speed of traffic flow. Besides, a lot of different investigations into the use of traffic flow models to deal with various problems of engineering are carried out. A comparison of different continuum models has drawn that a number of scientific works were based on fluid dynamic theory and gas - kinetic traffic flow theory. The kinetic traffic flow theory is used in ‘microscopic’ or “macroscopic”, traffic flow models. The kinetic traffic flow theory is used in Flötteröd G., N agel K., Ging A., Li L., Li-qun X., Prigogine I., Herman R. works where various approaches to the similar method are discussed. The ‘macroscopic’ theory of traffic flows also can be developed as the hydrodynamic theory of fluids that was first introduced by Lighthill-Whitham and Richards’s model. Plenty of traffic flow models are based on car–following theories supported by the analogues to Newton’s equation for each individual vehicle interacting in a system of vehicles on the road. Different forms of the equation of motion give different versions of car–following models. This work presents research of traffic flow dynamic processes, as nonlinear dynamic system, by using a discrete model of traffic flow (DMTF). The main variables in DMTF are traffic flow density and speed. DMTF can be used to describe various traffic flow situations in the roads. The mathematical simulation of traffic flow is made when constant value of traffic flow speed and traffic flow rate is entered. Numerical results of traffic flow dynamics are obtained.