Optimization Method Of Parking Line Layout In Urban Rail Transit

Train fault is one of the main faults in urban rail transit,which may lead to train delay and even operation interruption of some sections,affecting the safe operation of urban rail transit.To cope with the sudden occurrence of train fault,the Code for design of metro stipulates that a specific assistant line for parking faulty train temporarily,which is named as parking line,shall be set every 5 to 6 stations or 8 to 10 km on the main line,so that the total time of taking the faulty train off the main line can be controlled within 30 min as far as possible wherever the faulty train is.However,in the actual operation,only when the train loses its travelling ability and needs rescue,the nearby parking line will be considered as one of the temporary parking places.In this case,whether it is worth building parking lines for faulty train rescue or how many parking lines need to be built has drawn the attention of the urban rail transit industry.Therefore,this paper jumps out of the restriction of the parking line spacing stipulated in the Code for design of metro and proposes an optimization method of parking line layout aiming at minimizing the total social cost.This method can comprehensively consider the use frequency of parking line,the impact of faulty train rescue on passengers and the faulty train rescue time from the perspective of cost and utility to determine a reasonable parking line layout.The main contents are summarized as the following four aspects:(1)A prediction model of train fault probability is established.Train formation,cumulative running kilometer and un-wheeling repair or overhaul experience are determined as the main influencing factors of train fault probability through qualitative analysis.After obtaining the basic data,a discrete data set of fault occurrence number for a single train in a certain running kilometer period is generated with 120,000 km as the observation range.According to the data distribution characteristics,Poisson distribution and zero-inflated Poisson distribution are used to build three alternative models with possible function forms.After comparison and selection,the prediction model of train fault probability based on Poisson distribution is established.Study results show that the train fault probability increases with the train formation,and decreases first and then increases with the cumulative running kilometer which will be reset after un-wheeling repair or overhaul.(2)Based on the assumption that passengers won’t change their origin-destination stations and can’t know the accurate train delay time,a prediction model of passenger travel behavior under abnormal operation is established.The travel behavior options of this model are as follows: Ⅰ)travelling according to the original route;Ⅱ)detouring in the network;Ⅲ)waiting at the platform;Ⅳ)leaving the station and choosing other transportation modes.To establish this model,a judgment method of affected passengers based on origin-destination and travel path is proposed first.Then a survey in combination with revealed preference and stated preference is designed to obtain the basic data.Subsequently,a prediction model of passenger detour intention under abnormal operation is established by using nonlinear regression,which correlates the passenger detour intention with the travel time of the detour path,the buffer time of the whole trip and the travel time of the original path.Finally,a prediction model of passenger waiting time under abnormal operation based on the survival analysis theory is established,which adopts the parameter model and Weibull distribution according to the characteristics of passenger waiting time.(3)A calculation model of passenger travel delay time caused by faulty train rescue is established according to the logical relations among faulty train,parking line,affected station and affected passenger.To establish this model,a calculation model of faulty train rescue time for different temporary parking places is established according to the principle of “giving priority to rescuing along the forward direction and restoring operation as soon as possible”.Then several temporary adjustment strategies for train operation organization are proposed to determine the temporary parking place of the faulty train,the operation of temporary train routing,and the running time of the detained trains under different conditions.On these bases,a calculation method of the affected time of each station is proposed.After that,an improved Dijkstra algorithm suitable for the urban rail network under abnormal operation is proposed.By combining this algorithm and the prediction model of passenger travel behavior under abnormal operation,an aggregation model of affected passengers’ travel delay time is established.(4)Modeling and its solution to parking line layout optimization problem is studied.Firstly,an optimization model of parking line layout with the minimum social cost as the objective function is established.The social cost is composed of the additional passenger travel time cost and the construction and maintenance cost related to the parking line,and then a calculation model of the social cost in the evaluation period is established.On this basis,an improved genetic algorithm with a memory unit and elite retention strategy is proposed to solve the optimization model.Then a program for the optimization of parking line layout is developed using Python3.Finally,the feasibilities of the optimization model and the improved genetic algorithm are verified through a case study.