一类动态交通分配中的输出流模型及其数值解法

An Outflow Model and Numerical Solution Used in Dynamic Traffic Assignment

已知路段输入流,基于Greenshields提出的速度-密度关系模型以及Jayakrishnan et.al提出的改进的Greenshields速度-密度关系模型所描述的路段交通流特征,分别给出了关于路段输出流的常微分方程模型。针对无法得到该模型的解析解,利用龙格-库塔-芬尔格算法给出初始条件下的数值解。在已知输出流的条件下,每个时刻的路段交通流的行程时间也相应给出。仿真结果表明,针对两类不同速度-密度关系所建立的输出流模型,所得到每个时刻的输出流基本相似,但路段行程时间存在明显差异。与交通流调查数据比较,基于改进的Greenshields速度-密度关系的输出流模型的行程时间更接近真实情况。

Two constant differential equation models are presented separately for given inflow pattern is based on the velocity/density relation function presented by Greenshields and the modified velocity/density relation function by Jakyakrishnan and Tsai. Considering that it is impossible to get the analytical solution of the constant differential equation, the numerical solution is obtained by Runge-Kutta-Fehlberg algorithm, as well as for the link travel time function based upon the inflow and outflow patterns.The numerical simulation indicates that the outflow patterns, which are obtained by the two outflow models respectively, are almost similar to the real traffic flow status according to the traffic survey. However, the link travel time, which comes from the outflow model and is based on modified velocity/density relation function, is more closer to the real travel time.