Collaborative Optimization Of Metro Passenger Flow Control And Train Scheduling Considering Reservation Demand

With the increasing pressure of metro passenger demand,the contradiction between passenger demand and train capacity in peak hours becomes more and more prominent.Meanwhile,the problem of longer passenger travel time and crowded platform caused by passenger residence,is gradually serious.Optimization of passenger flow control and train scheduling plays an important role in alleviating the conflict of demand and service supply in metro system,which is based on the spatial and temporal distribution of passenger demand.Nowadays,the accurate passenger demand is collected in advance with Metro Reservation Mechanism(MRM).On this basis,formulating scientific passenger flow control staretgy and train scheduling is an effective way to match the service and demand of metro system,which can further reduce the passenger total travel time(TTT)under the safe operation.A metro line considering reservation is considered in this paper,and a jointly optimization model is proposed to optimize passenger flow control(for both reserved passenger and non-reserved passenger)and train scheduling.The model aims at minimizing TTT,which includes passenger waiting time outside the station(OWT),the waiting time at the platform(PWT)and on-board time(OBT).Then,case analysis is given to demonstrate the effectiveness of the collaborative optimization model.Main contents are as follow:Firstly,the MRM is clarified,and a collaborative optimization model of passenger flow control and train scheduling(PTS model)considering reservation demand is formulated.In the paper,serveral reserved stations are designed.Passengers who successfully reserved enter the station through specific passageway,while passengers fail in reserving will enter the station suffering conventional passenger flow control.Then,the optimization model is used to decide the arrive time of every reserved passenger,the proportion of local passengers allowed to enter each stations at every time interval,the train departure time at the first station and the stop pattern of trains.Secondly,a combination algorithm of Genetic Algorithm(GA)and linear programming optimization solver Gurobi is proposed,basing on the linearization of nonlinear constraints of train timetable.In particular,decision variables related to passenger flow control and stop pattern are solved by GA,and Gurobi is used to search for the optimal train timetable under the given passenger flow control strategy and train stop pattern in each iteration of GA.Then,the passenger waiting time at the platform and on-board time calculated by Gurobi will feed back to GA.Thirdly,the effectiveness of the proposed PTS model and algorithm is verified,and the application of proposed method are discussed.The results of small-scale cases show that the combined algorithm proposed in this paper can get a better solution than heuristic algorithms like GA and GASA.Compared with the cases with single station passenger flow control strategy under periodic timetable and all-stop pattern,the passenger total travel time canbe reduced by 4.11%.Comparing with other optimization models of passenger flow control or train scheduling,PTS model has the best optimization result,gaining 0.9%～3.6% shorter passenger total travel time.According to the sensitivity analysis,compared with the collaborative optimization of passenger flow control and train scheduling without reservation demand,the optimization effect of the proposed method is much better.Reduction of TTT is positively associated with the proportion of reserved passengers.Therefore,the service level can be further improved by guiding passengers to make a reservation to enter the station.In addition,PTS model can reduce passenger travel time to a greater extent by optimizing the stop pattern,which makes the method more suitable for the metro line with a larger proportion(more than 0.4)of long-distance passengers.Lastly,a real case based on Fangshan Line of Beijing Subway is used to verify the propsed model.The result shows that PTS model can get a satisfactory solution within acceptable time,and the method is applicable to the next day passenger flow control and train planning optimization.Compared with base case of Fangshan Line,PTS model catch a 9210 minutes shorter TTT,and the reduction of TTT is 2.55%.Also,the optimization of PTS model is better than other optimization models of passenger flow control or train scheduling.