CAJ | 학술논문

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（Erlangdistribution，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．
채용7개상용분포화“통용성여해석성교호”적상위분포（phase-type distribution，PH）주밀자집혼합애이랑분포（hyper-Erlang distribution，HErD）대다개차참적출입구도체객류시간간격적통계분포진행의합，득출HErD적의합효과최가，병급출료각충분포적괄용성．연후추취출HErD적의합삼수분석기변화규률，결과량기지발현해분포적삼수지여변이계수유관，당변이계수소우1시，해분포유일개지수분포（exponential distribution，ED）화일개4계애이랑분포（Erlangdistribution，ErD）혼합이성，기중ED적혼합비례여변이계수적평방성Power함수관계：당변이계수대우1시，해분포유량개ED혼합이성，기중일개적혼합비례여변이계수적평방성s함수관계．유차，HErD적삼수피간화성량개척도삼수．최후급출료통과역우획취적고봉객류량화초고봉계수학정저량개삼수적실용방법．
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 tofit the distribution of time interval between arriving passengers. From the comparison of a large numberof experiments, the fitting effect of HErD is proven to be the best and the applicability of all distributionsis given. Then, the fitting parameters of HErD are extracted to analyze the law of their variations, andit demonstrates that when the coefficient of variation is smaller than 1, the distribution is mixed byone exponential distribution （ED） and one 4-order Erlang distribution （ErD）, in which there＇s a powerfunctional 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＇san 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 canbe introduced to the systemic planning and design of urban rail transit station, which will improve therationality of the design.