弹性需求下的网络交通流逐日动态演化

摘要

在现实交通系统中,网络的交通需求是可变的,随交通运行状态而改变.针对需求可变情形,以含两条路径的简单路网为例,建立了弹性需求下的网络交通流逐日动态演化模型,基于非线性动力学理论,证明了动态演化模型的不动点存在且唯一,并且推导出了弹性需求下网络交通流动态演化的稳定性条件.通过数值实验,分析了网络交通流演化特征.研究发现:在一定条件下流量演化会出现分岔和混沌现象,并且出行者的出行需求对费用越敏感,系统演化越可能稳定;出行者路径选择的随机性越小,系统演化越不可能稳定;出行者对前一天实际费用的依赖程度越小,系统演化越可能稳定.%Network traffic flow is an aggregated result of a huge number of travelers' route choices, which is influenced by the travelers' choice behaviors. So day-to-day traffic flow is not static, but presents a complex and tortuous day-to-day dynamic evolution process. Studying day-to-day dynamic evolution of network traffic flow, we can not only know whether the traffic network equilibrium can be reached and how the process is achieved, but also can know what phenomenon will occur in the evolution of network traffic flow if the equilibrium is not reached. In a real traffic system, taking day as scale unit, the day-to-day network traffic demand is variable and changes with everyday's traffic network state. The travelers' route choices are also influenced by the previous day's behaviors and network state. Then, will the day-to-day network traffic flow evolution be stable? If it is unstable, when will bifurcation and chaos occur? In this paper we discuss the day-to-day dynamic evolution of network traffic flow with elastic demand in a simple two-route network. The dynamic evolution model of network traffic flow with elastic demand is formulated. Based on a nonlinear dynamic theory, the existence and uniqueness of the fixed point of dynamic evolution model are proved, and an equilibrium stability condition for the dynamic evolution of network traffic flow with elastic demand is derived. Then, the evolution of network traffic flow is investigated through numerical experiments by changing the three parameters associated with travelers, which are the sensitivity of travelers' travel demand to travel cost, the randomness of travelers' route choices, and travelers' reliance on the previous day's actual cost. Our findings are as follows. Firstly, there are three kinds of final states in the evolution of network traffic flow: stability and convergence to equilibrium, periodic motion and chaos. The final state of the network traffic flow evolution is related to the above three parameters. It is found that under certain conditions the bifurcation diagram of the network traffic flow evolution reveals a complicated phenomenon of period doubling bifurcation to chaos, and then period-halving bifurcation. Meanwhile, the chaotic region is interspersed with odd periodic windows. Moreover, the more sensitive to cost the travelers' travel demand the more likely the system evolution is to be stable. The smaller the randomness of travelers' route choices, the less likely the system evolution is to be stable. The lower the degree of travelers' reliance on the previous day's actual cost, the more likely the system evolution is to be stable.