数学建模及其应用

研究"右行左超车"规则在高速公路不同交通负荷下对通行能力及安全性的影响。引入超车欲望值及状态改变率的概念,基于交通流元胞自动机模型,建立了"右行左超车"规则下的单向双车道和三车道换道规则及相应的超车规则。选取5个评价参数,针对两车道模型,将"右行左超车"规则与无规则下的换道超车对交通效率与安全表现的影响进行对照试验。试验结果表明:在安全表现方面,低负荷状态下"右行左超车"规则较无规则情形要差,而在高负荷状态下,该规则较无规则情形好;在通行能力方面二者差别不大;试验结果还表明,无论是有规则还是无规则,提高车道的最大与最小限速不仅可以提升道路的通行能力,而且可以提升安全性。最后分析了模型的优缺点,并指出了改进的方向。

This paper discusses the performance of the"Keep-Right-Except-To-Pass Rule"(KREP)on two-lane freeway in light and heavy traffic.The focus is mainly on the traffic capacity and security.A definition of overtaking desire value,as well as the state change probability,is proposed to describe the behavior of overtaking.A two-lane and a three-lane changing rules,as well as the corresponding overtaking rules,are established based on the cellular automata model.In addition,five parameters are presented to evaluate the performance of the rule.By changing the traffic density,the traffic on two-lane freeway(two lanes per direction,four lanes in total)is simulated under the KREP rule and no-rule.The result shows that in light traffic the security of the KREP rule is poor,compared with that of no rule,while in heavy traffic,it is better than that of no-rule.However,the difference of traffic capacity between the two rules is small.In addition,under either situation,the raise of the maximum and minimum velocity of each lane will increase the capacity as well as the security.Finally,based on the simulation results,the advantages and disadvantages of the model proposed in this paper are discussed and some improvements are given.