Research On Passenger Service Interval Distribution Law And Queueing Modle Of Fare Collection System In Subway Station

Along with our country large-scale planning and constructing of urban rail transit in response to the problem of traffic congestion in major cities, the station as a service window for passengers into the rail transit network, its construction of economy, service of safety and convenience is the focus problem at planning design phase. The station facility system service passengers to purchase tickets, in and out of the station, of which ticket purchasing and checking links are easy to gather a large number of passengers to wait at line, meanwhile slow down the speed and affect the safety of passengers in and out of the station. Therefore, the rationality of fare collection system configuration is the decisive factors of the station’s efficient and safe operation.This paper take Automatic Gate Machine, Ticket Vending Machine, Artificial Ticket Window in fare collection system as research focus. As the phase type distribution is suitable for describing variables with multi-level and complex parameters, and have good generality and analyticity, so this paper introduce it to fit the passenger service interval probability distribution in fare collection system. With the purpose of exploring the real probability distribution of passenger sevice interval in the fare collecthion facility system and facilitating comparative analysis of PH distribution fitting effect, eight kinds of probability distribution is selected to fit passenger service intervals, including two kinds of special forms in the phase type distribution class (PH dense subset mixed Erlang distribution and a simplified PH distribution) and six kinds of commonly used probability distribution (Uniform distribution, Normal distribution, Lognormal distribution, Weibull distribution and the Gamma distribution). By comparing the fitting accuracy, HErD has been verified the best fitting result.As the parameter number of HErD probability function fitting well is more than other commonly used probability distributions, for improving the availability of HErD in the fare collection facility system, this paper explore the correlation of passenger service intervals’ HErD probability function parameters in each kind of facility and find the regression equation which can successfully simplify the method of solving parameters of HErD probability function to fit the service interval probability distribution. And finally service interval probability distribution functions of excellent fitting result can be calculate which just need mean and coefficient of variation of service intervals in each kind of facility.On the basis, in order to configure the number of facility with the service interval probability distribution model of HErD in fare collection system which have general applicability, a PH/PH/C1/C queuing model has been established. Using the Ticket Vending Machine for example to compare the facility configuration results of queuing model and the traditional method which rely on Metro Design or facility average service capacity of the actual surveys, the result shows the superiority of the queuing model method.