Inter-arrival time distribution of passengers at service facilities in underground subway stations: A case study of the metropolitan city of Chengdu in China

Document Type

Journal Article

Publication Date


Subject Area

place - asia, place - urban, mode - subway/metro, operations - capacity, operations - performance, planning - methods


Inter-arrival time distribution of passengers, Hyper-Erlang distribution, Parameter estimation model, Service facility, Underground subway station


Inter-arrival time distribution of passengers plays an important role in the capacity design of service facilities such as, fare gate, ticket vending machine, and passageways, in an underground subway station. An inaccurate inter-arrival time distribution likely causes traffic congestion or resource wastage at service facilities. In this study, to obtain accurate inter-arrival time distribution, we collected an inter-arrival time of passengers at existing service facilities in three underground subway stations of a metropolitan city, Chengdu, China. We fitted eight types of distributions, including Hyper-Erlang distribution (HErD), which is firstly introduced in the capacity design of service facilities in an underground subway station, to the observed data set based on maximum likelihood estimation. Results showed that the HErD works the best in terms of fitting quality and flexibility. We also fitted eight types of distribution to the observed inter-arrival time data at service facilities of seventy-seven underground subway stations of another metropolitan city—Shenzhen, China—to confirm our findings. Results also showed the HErD still performs the best. Simulation is also conducted to examine the effect of inter-arrival distributions on the performance of service facilities. To estimate future inter-arrival time based on HErD for the capacity design of service facilities to be constructed in the planning period, we developed a basic parameter estimation model according to two given design parameters namely, long-term peak-hour volume and peak-hour factor. However, the proposed model did not work well because the HErD has many free parameters to be estimated. Thus, we derived a method to reduce the number of free parameters, and then we proposed an improved parameter estimation model of HErD to describe future inter-arrival time distribution based on given long-term peak-hour volume and peak-hour factor.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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