随机计及相对速度的交通流跟驰模型

从研究微观个体车辆行为出发，考虑车辆加速过程的不确定性，提出了随机计及相对速度的 交通流跟驰模型(SR-OV模型).对随机相对速度的跟驰模型的动力学方程进行稳定性分析，得 到与Bando跟驰模型不同的稳定性判据，其稳定性优于Bando模型.运用摄动理论分析交通过 程中密度波的变化，结果表明，在发生交通阻塞相变时，交通密度波以mKdV方程描述的扭结 -反扭结波演化.对随机相对速度跟驰模型进行数值模拟和分析，结果发现车流速度的变化小 于Bando模型的速度变化，而且与随机概率有关，当随机考虑相对速度的概率增大时，初始 的小扰动不会放大对车流产生影响，甚至长时间就消失，这与Bando模型完全不同.数值模拟 所得到的相图与解析解相符合,而且交通流稳定区域大于Bando模型.从车间距-速度演化图上 ，随着随机概率的增大，SR-OV模型在初始时存在的滞后现象，随着时间的增长，趋于稳定 状态后，滞后曲线收敛于一小区域，滞后效应被削弱.这完全不同于Bando模型，在Bando模 型中，滞后曲线由一点向外扩散，滞后曲线区域越来越大，车流趋于不稳定状态. 关键词： 交通流 跟驰模型 稳定性判据 相对速度

A car-following model with stochastically considering the relative velocity in a traffic flow

In this paper, the car-following model with stochastically considering the relative velocity in a traffic flow is presented through investigating the vehicle a cceleration process with uncertainty. The stability criterion superior to the Ba ndo's model is derived by the linear stability analysis. The density wave is inv estigated analytically with the perturbation method. The results show that the o ccurrence of traffic jamming transitions can be described by the kink solution o f the modified Korteweg-de Vries equation. The effects of stochastic relative ve locity on the traffic flow are simulated and analyzed. It is shown that the chan ge rate of velocity in the new model is smaller than that of the Bando's model u nder the same condition and depends on the probability p. As the probability p i ncreases, a small initial disturbance does not magnify and influence on the traf fic 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 hyst eresis in the new model will approach to a small region with the increase of tim e in the headway-velocity plot, which is exactly different from that in the Band o's model.In contrast,the hysteresis region in Bando's model will be continuousl y extended to cause traffic flow instability.