随机到达车辆信号交叉路口的Markov链排队模型

Markov Chain Queuing Model for Signalized Intersections with Stochastic Vehicle Arrivals

为了克服现有交叉口排队分析模型中车流到达均服从特定规律这一假定的局限性,用嵌入马尔科夫链技术建立了定周期信号交叉口车辆随机到达的Markov链排队模型,在Excel环境下嵌入LINGO软件,编写了相应的模型程序和用于验证模型的仿真模拟程序.算例表明：本文模型计算的平均排队长度与实际调查结果很接近,与随机模拟结果的误差为0.14%;在50%~65%分位范围内,用Markov链排队模型计算的排队长度与实际样本结果和随机模拟结果相同,在其他分位最大相对误差为3.85%.

To overcome the limitation of the existing models for intersection queuing analysis in which vehicle arrivals are assumed to obey a particular distribution law,a general queuing model for signalized intersections with fixed cycle and stochastic vehicle arrivals was established using the embedded Markov chain technology.The model program and the simulation program for model verification were written using LINGO software embedded in the Excel environment.The numerical results of a case study show that,the average queue length calculated by the Markov chain queuing model is much close to the actual survey result,and has an error of 0.14% compared with the stochastic simulation result;the queue lengths obtained by the model are identical to the actual survey and stochastic simulation results at the percentiles ranging from 50% to 65%,and have a maximum relative error of 3.85% at other percentiles.