Green- function for the highway vehicular traffic flow modeling and analysis

In the present article we offer a method for the highway traffic flow modeling, based on the Green function as a transformation tool. This approach is suitable for distributed parameter systems in order to reformulate their partial differential equation description as sets of transfer functions. The model used in our work is the macroscopic continuous Lighthill-Whitham-Richards representation. The physical phenomena characteristic for the vehicular flow on a highway section are analyzed over some important length. This implies the description of the traffic as a distributed parameter plant. We present the Green function transformation's general case and after we apply it to the considered traffic flow model in order to obtain its transfer function form. The sets of expressions obtained can be specified using concrete fundamental diagrams and data, and also can be implemented in the design of control strategies.