Heterogeneous traffic flow modeling using an extended Payne model with stochastic source term

Abstract

In this paper, we are extending Payne model with stochastic source term. The new model differs from that of Payne’s in such a way that the traffic pressure and hysteresis are formulate with driver decision. The traditional traffic pressure and hysteresis depend respectively on the traffic density and drivers decision (aggressive-timid, acceleration-deceleration). Our traffic is on an inclined road. In the context of a developing country where the traffic is very heterogeneous and there is a lack of discipline on the highway, the new traffic pressure must take care of the heterogeneity of the traffic. The road traffic hysteresis must take care of the dispersion of the vehicle on the highway. Moreover, the anticipation term is a multi-valued function depending on the vehicle class. The numerical solution of the problem was obtained using a wave analysis. The new model is a hyperbolic one in which the traffic information travels faster than the traffic and the wave propagate downstream leading to a jam formation.