Kinetic model of network traffic

We present the first results on the application of the Prigogine–Herman kinetic approach (Kinetic Theory of Vehicular Traffic, American Elsevier Publishing Company, Inc., New York, 1971) to the network traffic. We discuss the solution of the kinetic equation for homogeneous time-independent situations and for the desired speed distribution function, obtained from traffic measurements analysis. For the log-normal desired speed distribution function the solution clearly shows two modes corresponding to individual flow patterns (low-concentration mode) and to collective flow patterns (traffic jam mode). For low-concentration situations we found almost linear dependence of the information flow versus the concentration and that the higher the average speed the lower the concentration at which the optimum flow takes place. When approaching the critical concentration there are no essential differences in the flow for different desired average speeds, whereas for the individual flow regions there are dramatic differences