Green function analytical method of solution of transport equation: modeling and simulation of the macroscopic LWR model as a distributed parameter system

Abstract

The main aim of this paper is using the obtain transfer function of the macroscopic traffic flow model, as distributed parameter system, to simulate this model (fig. 1), then based on the obtain results characteristics to make analysis and for further works to use all this simulations for the synthesis and analysis of corresponding control algorithms depending of the needed conditions in transportation problem model. Using this exact method we obtain directly the plant transfer function for the traffic flow model viewed as a distributed parameter system. The entire physical phenomenon is presenting through the partial differential equations whose show the distribution in vehicles on the high ways. All the research is devoted on the transfer function result and his control system model. In the presenting paper we shown the verification of the analytical result of the model simulation thought the time and frequency characteristics analysis.