Traffic behavior in a mixture of different vehicles

The car following models are extended to take into account the characteristics of different vehicles. The characteristic of each car can be included in the parameter of the dimensionless delay time. The traffic behavior is investigated, analytically and numerically, under the periodic boundary condition. At a low density, all the vehicles move at a constant velocity. When the density is larger than the critical value, the traffic flow becomes unstable and the density waves appear. The jamming transition does not depend only on the mean value of the dimensionless delay time but also on the variation. With increase in the variation of dimensionless delay time, the jamming transition occurs at a higher value of the mean value. It is found that the variation of vehicles stabilizes the traffic flow and suppresses the traffic jams. The transition line obtained by the linear stability analysis is compared with the simulation result