科研之友
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摘要
In this paper, the car-following model with stochastically considering the relative velocity in a traffic flow is presented through investigating the vehicle acceleration process with uncertainty. The stability criterion superior to the Bando's model is derived by the linear stability analysis. The density wave is investigated analytically with the perturbation method. The results show that the occurrence of traffic jamming transitions can be described by the kink solution of the modified Korteweg-de Vries equation. The effects of stochastic relative velocity on the traffic flow are simulated and analyzed. It is shown that the change rate of velocity in the new model is smaller than that of the Bando's model under the same condition and depends on the probability p. As the probability p increases, a small initial disturbance does not magnify and influence on the traffic flow, but fades away for a long time. The stable region in the new model is larger than in the Bando's model in the phase diagram. The existent initial hysteresis in the new model will approach to a small region with the increase of time in the headway-velocity plot, which is exactly different from that in the Bando's model. In contrast, the hysteresis region in Bando's model Will be continuously extended to cause traffic flow instability.
