Timetable Optimization On Metro Lines Connecting Mainline Railway Stations

The metro with high carrying capacity and reliability plays an important role in passenger collection and distribution at intercity railway station.The connection quality in timetable between metro system and the intercity railway system directly affects the waiting time of passengers and the number of passengers gathered in the station,which has an important impact on the level of transport services.As for the metro lines connecting intercity railway stations,where a large number of passengers may enter the metro system in short time after the arrival of intercity trains.The timetable with a regular train headway is unable to adapt to this kind of pulsing passenger demand,which can prolong passenger waiting time at the station and even increase the risk of platform overload.To this end,this paper design a framework that is able to optimize timetable of metro line connecting intercity railway stations,taking into account passenger demand at intercity railway stations specially.The aims of the present work are as follows:First,deduction and verification of inbound flow of metro system at intercity railway station is conducted.Different from the normal stations with uniform arrival passengers,the passenger distribution in intercity railway station often shows a strong imbalance(pulsing)in time.This is closely related to the arrival of the trains from intercity railway.This paper systematically analyzes the transfer process from intercity railway to metro system to build a mathematical model which can deduce dynamic demand based on intercity railway arriving trains information(arrival time,train capacity,load ratio,transfer distance etc.).Compared with the statistical passenger flow,the results show that the prediction accuracy of the above model reached more than 90%,which can well describe the distribution of inbound passenger flow.Second,timetable optimization model based on deduced passenger demand is established.On the basis of deduced passenger demand from last part and the assumption of even arrival at other stations,a metro timetable optimization model is proposed to find the best departure time of metro trains at each station in order to minimizing passengers' waiting time.In addition,in order to improve the efficiency of the nonlinear model in this paper,part of the timetable optimization model is linearized.Correspondingly,a bi-level genetic algorithm combined with Interior-Point algorithm is developed to solve the proposed model.Taking Beijing Metro Line 7 as an example,the validity of the model is verified.The case results show that the optimization effect of passengers waiting time reaches 7.34%in off-peak hour and 3.62%in peak hour.Moreover,the metro platform maximum gathered passenger number also dropped significantly,the decline rate was 29.1%in off-peak and 15.1%in peak hour.Third,the fluctuation of arrival time of intercity railway train is considered.The intercity railway train always arrives earlier or later than scheduled time in reality.Therefore,based on the previous research,the probability distribution of train arrival time is used to replace the scheduled arrival time.The minimum expected value of passenger waiting time is taken as the goal to generate the optimal timetable which can meet most situations.The case of Beijing Metro Line 7 shows that the optimized timetable considering the railway station arrival time fluctuation in the metro peak-hour period,the effect is better.Compared with the current timetable and the optimized timetable based on the scheduled arrival time,the average passenger waiting time at Beijing West Railway Station was reduced by 23.3%and 6.9%,the whole line average passenger waiting time was reduced by 6.4%and 1.5%,which is effective in daily operation.