Abstract: The goal of this paper is to study the numerical simulation of multi-lane traffic flows with pantograph delay differential systems. In order to simulate dynamic road traffic flows of multi-lane, a new model is established by using differential kinetic system approach with pantograph delay differential equations, and a numerical algorithm is established. This paper gives the results of multi-lane simulation under different densities, the impacts of weight parameters and a scaling factor for the stability points are discussed, and the numerical results of Pantograph Delay Model（PDM） and Constant Delay Model （CDM） are compared. The simulation results show that PDM can better simulate the actual changes of traffic flows than CDM when the traffic density is high, and it has good reference values of the real simulation of multi-lane traffic flow.

Key words: computer simulation, multi-lane traffic flow, pantograph delay model, kinetic system

摘要： 研究基于缩放延迟微分系统的的多车道交通流量数值仿真。为了模拟多车道宏观动态变化的道路交通流量问题，采用了微分动力学系统的原理，建立了基于缩放延迟微分方程的道路交通流量模型，并给出了模型的数值求解算法。给出不同密度下多车道车辆仿真结果，讨论了缩放延迟模型权重参数和缩放因子对系统稳定点的影响;将缩放延迟模型与常延时模型的数值结果进行了对比。仿真结果表明，当车流密度处于高密度时，缩放延迟模型能更好模拟交通流量的实际变化情况，对多车道交通流量的真实模拟具有更好的参考价值。

关键词: 计算机仿真, 多车道交通流量, 缩放延迟模型, 动力系统