城市轨道交通车站到达客流时间间隔分布拟合

采用7个常用分布和“通用性与解析性较好”的相位分布 （phase-type distribution，PH） 稠密子集混合埃尔朗分布 （hyper-Erlang distribution，HErD） 对多个车站的出入口到达客流时间间隔的统计分布进行拟合，得出HErD 的拟合效果最佳，并给出了各种分布的适用性. 然后抽取出HErD的拟合参数分析其变化规律，结果惊奇地发现： 该分布的参数只与变异系数有关，当变异系数小于1 时，该分布由一个指数分布 （exponential distribution，ED） 和一个4阶埃尔朗分布 （Erlang distribution，ErD） 混合而成，其中ED 的混合比例与变异系数的平方成Power函数关系： 当变异系数大于1 时，该分布由两个ED混合而成，其中一个的混合比例与变异系数的平方成S函数关系. 由此，HErD 的参数被简化成两个尺度参数. 最后给出了通过易于获取的高峰客流量和超高峰系数确定这两个参数的实用方法.

Fitting for the distribution of interval of passengers arriving at urban rail transit station

In the present paper, hyper-Erlang distribution (HErD) which is a restricted class of phase-type distribution (PH) with good versatility and analyticity and seven common distributions are used to fit the distribution of time interval between arriving passengers. From the comparison of a large number of experiments, the fitting effect of HErD is proven to be the best and the applicability of all distributions is given. Then, the fitting parameters of HErD are extracted to analyze the law of their variations, and it demonstrates that when the coefficient of variation is smaller than 1, the distribution is mixed by one exponential distribution (ED) and one 4-order Erlang distribution (ErD), in which there's a power functional relationship between the mixing ratio of ED and the square of coefficient of variation. However, when the coefficient of variation is larger than 1, the distribution is mixed by two EDs, in which there's an S functional relationship between the mixing ratio of one ED and square of coefficient of variation. As a result, the parameters of HErD are simplified into 2 scale parameters determined by the given long-term peak traffic and super-peak coefficient, and thus the PH distribution and PH queuing model can be introduced to the systemic planning and design of urban rail transit station, which will improve the rationality of the design.