城市道路隧道入口车头时距的幂律分布研究∗

摘要

车头时距是交通流与随机过程中的重要参数。为了清晰地描述城市道路隧道入口的交通流特性，采集了广州市内的官洲隧道和 CBD 隧道入口不同车道、不同时段的车头时距数据。通过数据分析发现车头时距的随机过程具有偏离负指数分布的非泊松特性，提出了一种适用于描述车头时距分布的特殊形式的幂律分布，并通过理论推导建立了幂律分布函数。利用极大似然法和遗传算法优化对幂律分布进行了参数估计，并通过卡方检验对各组实测数据进行了拟合优度检验。结果表明，实测的车头时距分布曲线呈现先递增后递减的性质，实测的车头时距数据均不服从负指数分布，具有偏离负指数分布的非泊松特性，而9组实测数据中有8组服从幂律分布，幂律分布拟合效果较好。幂律分布可为城市道路隧道入口车头时距分布的刻画提供一种新的统计建模方法，但车头时距的随机过程中所蕴含的非泊松过程产生机制和动力学效应则需要进一步研究。%Headway is one of the most important parameters in traffic flow and random process.In order to study the statistical characteristics of traffic flow at tunnel entrance,this study investigates headway data on different lanes and different periods in Guanzhou tunnel and CBD tunnel in Guangzhou.The results show that the random process of vehicle headway deviates from the negative exponential distribution,and presents non-Poisson characteristics.A new power-law distribution function is therefore proposed to fit the headway distribution.Furthermore,the unknown parameters for the proposed power-law distribution are estimated by maximum likelihood estimation and genetic algorithm.The goodness-of-fit of model is verified through a Chi-square test against 9 sets of observed data.The results show that the empirical head-way distributions present the feature that the headways firstly increase and then decrease.The results also illustrate that the exponential distribution does not fit the observed data and is rejected by the Chi-square test.The non-Poisson charac-teristic of headway distribution is clear.On the other hand,the power-law distribution fits the observed datasets well with the fact that 8 out of 9 data sets passed the Chi-square test.In conclusion,the power-law distribution can fit the headway distribution well,especially when non-Poisson characteristics are dominant.The mechanism and dynamic effect behind the non-Poisson characteristics requires further study.