Optimization On Subway Timetable Considering Train Capacity And Imbalanced Demand Of Transfer Passengers

Metro lines generally adopt regular timetables with different headways during peak hours and off-peak hours,due to the obvious peak/off-peak characteristics of passenger demand.This kind of timetable is applicable for the situation when passengers arrive at metro stations evenly.The passenger demand of metro lines connecting with intercity railway stations shows a great impulse with the arrivals of intercity trains and the passenger arrival rates are not continuously even,however.Regular timetables cannot handle the imbalanced passenger demand properly but increase passenger residence time.Especially for those oversaturated metro lines,passengers waiting on a platform are extremely likely to be left and wait for the next train because of the intensive arrivals of transfer passengers within a short time and the constraint of train capacity,which increases the risk of overcrowding on the platform greatly and to some extent influences the service level of train operating companies.This paper considers two kinds of typical transfer passenger demands(i.e.passengers transferring from intercity trains,passengers transferring between different metro lines)and describes the time-varying demand of passengers arriving at the platform of metro stations.Furthermore,train timetables are optimized based on the distribution characteristics of transfer passengers with the consideration of train capacity.The main contents and conclusions of this research are as follows.Firstly,the distribution characteristics of transfer passengers are characterized and validated.Unlike the approximately uniform inbound passenger flow at non-transfer stations,the transfer passenger flow shows a strong imbalance with the arrivals of trains.This paper formulates a mathematical model to describe the distribution of transfer passengers arriving at the platform of metro stations,via analyzing the entire transfer process of passengers and the behavioral features of passengers at different stages.The comparison with the actual passenger flow data illustrates that the passenger flow distribution obtained through the method proposed in this paper is more consistent with the reality,and the prediction accuracy can reach more than 90%.Secondly,the train departure time optimization model considering the distribution of passenger flow at large transfer stations is developed and solved.Based on the distribution of transfer passengers obtained at the former step,this paper constructs a model to optimize train departure times at the first station while taking into account the constraints of train capacity and timetable design,aiming at minimizing the passenger waiting time of the metro station with the greatest passenger demand.In view of the complexity of the model,genetic algorithm and adaptive large neighborhood search algorithm are designed respectively to solve it.Real-world case studies of Beijing Metro Line 9 demonstrate that the optimized timetable obtained by genetic algorithm and adaptive large neighborhood search algorithm can reduce the passenger waiting time of Beijing West Railway Station by 23.57%and 28.47%,respectively.Moreover,compared with the initial plan,the optimized timetable can enable more trains operate during the period when passengers arrive intensively,which can reduce the number of passengers stranded on the platform of Beijing West Railway Station effectively.Finally,the optimization of timetable based on the distribution of passenger flow on a whole metro line is carried out.In actual operation,the passenger flow at different transfer stations shows different imbalanced features.To this end,this paper builds a timetable optimization model to minimize the total passenger travel time,through adjusting train departure times at the first station,running times and dwell times of each train.The genetic algorithm and adaptive large neighborhood search algorithm are designed to solve this model respectively.The case studies of Beijing Metro Line 9 shows that the optimized timetable obtained by genetic algorithm and adaptive large neighborhood search algorithm can reduce the total travel time of passengers by 2.89%and 11.2%respectively,indicating that the adaptive large neighborhood search algorithm has great advantages in solving large-scale problems.Moreover,this model saves the travel time of passengers on the whole line(11.2%)significantly higher than the train departure time optimization model(0.61%)constructed by considering the passenger flow distribution characteristics of a single transfer station only.In addition,compared with the actual timetable,the optimized timetable can also effectively relieve the crowding of platforms and trains,which has certain significance for improving the passenger service level.