Density waves in traffic flow of two kinds of vehicles

Through the car-following model, the traffic flow of two types of vehicles (cars and trucks) on a single-lane flow is studied, in which drivers on different vehicles have different sensitivities and the safety distance is assumed to be the same for all vehicles. The linear analysis is carried out to determine the condition of critical stability. With the nonlinear analysis, it proves that the small fluctuation of the vehicle density near the critical stable state satisfies the Korteweg-deVries equation and different sensitivities affect only the soliton evolution. When the headway in the critical state is more than the safety distance, the density around the soliton peak exceeds the density of the critical stable state, which can be explained as the formation of traffic jam. Contrarily, when the headway state is less than the safety distance, drivers will increase the headway to avoid the jam. The direct approach of the soliton perturbation shows that drivers' sensitivity will increase the soliton's amplitude continuously. Moreover, the increase of the number of trucks in the traffic flow will slow down the evolution of the amplitude.