PH fitting of the arrival interval distribution of the passenger flow on urban rail transit stations

•The arrival interval of input stream of subway station is fitted by HErD.•Some parameters of HErD are simplified by regression analysis.•The simplified HErD are determined by the parameters in design of subway station.

The urban railway transit station is a type of stochastic service system. The accurate description for the arrival interval distribution of the passenger flow with strong randomness is the basis of the planning, design and operation of the urban rail transit stations; however, the existing fitting distributions are not accurate enough to satisfy the demand in practice. Although the famous phase-type distribution (PH) has been proven to have the merits of high accuracy, universality and analyticity, it has too many parameters needed to be calibrated. In this paper, seven common distributions and hyper-Erlang distribution (HErD) which is a dense subset of PH were applied to fit arrival interval distribution of the passenger flow of entrances and platforms on subway stations. The comparative results indicated that HErD achieves the highest accuracy. On this basis, the fitting parameters of HErD were analysed, finding that this distribution is required to determine two parameters, and only related with variation coefficient, possessing good practicability. Finally, this paper puts forward a practical method to determine the two parameters of HErD through the easy-captured peak passenger flow volume and super-peak coefficient during station planning and design stage. This research provides a new alternative PH distribution for fitting passenger flow arrival interval distribution on urban rail transit stations.