时滞车辆跟驰模型及其分岔现象

交通流车辆跟驰理论中, 由于生理因素, 造成司机在处理前方车辆变化信息和采取应对措施之间存在时间滞后. 即使是在自动巡航控制系统中, 设备在感知信息、计算所需操作并最终作动车辆这一过程中时滞也不可避免. 因此交通流跟驰理论的数学模型本质上应包含时滞. 时滞的存在对各种交通模式的出现及其相互演化产生怎样的影响? 这是值得我们关注的问题. 本文首先综述了各类时间和空间连续的时滞车辆跟驰模型.其次探究这类模型中存在的分岔现象的研究进展, 并指出目前研究中存在的不足. 最后提出作者的一些看法,运用时滞动力系统理论来深入挖掘富含参数的交通流时滞跟驰模型中隐藏的各种的非线性动力学现象, 这样既可以更好解释真实交通中的各种堵塞模式的形成及其演化机制, 又可以结合交通流参数平面内动力学行为从同步观点给出交通堵塞一种分类. 为交通管理部门的交通控制策略制定提供一定的参考依据, 减缓由于司机反应时滞等因素造成的交通堵塞的发生.

REVIEW OF TIME-DELAYED CAR FOLLOWING MODELS AND BIFURCATION PHENOMENA

In car following theory of traffic dynamics, human drivers need a finite period of time to process stimuli of preceding vehicles and make a decision, which is attributed to human physiological factors. Since mechanical devices also need time for sensing, computing and actuating, time delay seems unavoidable even in autonomous cruise control systems. As a result time delays should be considered as an inherent factor in car following theories of traffic dynamics. One of the key problems in need of study is how time delays affect the traffic flow patterns and their evolutions. In this paper, time-delayed car following models which are continuous in both time and space are firstly surveyed. Then the progress in the dynamic behaviors based on bifurcation theory is reviewed. Defects of these models and the corresponding bifurcation research are pointed out in this summary. Finally we conclude that research on dynamic behaviors of time-delayed car following models with traffic flow parameters based on bifurcation theory are of great significance and necessity. By means of such research, the underlying mechanisms of traffic jam formation and evolution can be better understood. Traffic jam patterns can be categorized from a synchronization perspective through classifying dynamic behaviors in parameter plane, and hence, different traffic control strategies can be put forward by traffic management department based on the above jam patterns.