| Metro systems are gradually being widely used in various cities because of their high capacity,convenience and speed.At the same time,the metro network is gradually expanding and developing,which attracts more passengers to travel by metro and makes the ridership within the metro network grow.For large cities in the sector,the network has a high number of commuters during peak hours,and when train capacity cannot meet passenger demand,a large number of passengers will gather on station platforms,thus making the subway lines appear oversaturated.To alleviate this extreme overcrowding problem,this paper proposes a synergistic optimization strategy of train schedule and capacity allocation for oversaturated metro lines,by simultaneously optimizing both the schedule and train capacity to alleviate the extreme overcrowding caused by too many passengers gathered in the oversaturated metro lines.The main studies in this paper are as follows:Firstly,the concept of an oversaturated metro line is defined in this paper.Taking the Beijing Metro Batong Line as an example,its passenger flow characteristics are analysed in terms of temporal characteristics and spatial characteristics respectively.On this basis,a novel train capacity allocation strategy is proposed in this paper.That is,by reserving and allocating carriages,train capacity is reasonably allocated to each station,thus ensuring that passengers are served fairly at all stations and that extreme congestion is alleviated.Secondly,this paper constructs a model on the train capacity allocation strategy.The non-linear constraints are linearised and a linear mixed integer programming model is successfully constructed.Based on the train capacity allocation model,a train schedule-related constraint is established and the total passenger waiting time is minimised as the objective function to construct a collaborative optimisation model of train schedule and capacity allocation.In order to improve the computational efficiency of the co-optimization model,the "LS+CPLEX" algorithm is proposed in this paper.A local search algorithm is used to obtain feasible train schedules,which are used as input data for the train capacity allocation model.The objective function of the capacity allocation model is used as an evaluation indicator so that the results of the case calculation can be continuously optimised.Finally,based on the AFC passenger flow data of the Beijing Metro Baitong Line in the downstream direction during the weekday morning peak,this paper conducts numerical experiments on each of the two models mentioned above.Experimental simulation results show that with the train capacity allocation strategy,the maximum number of passengers gathered within the line is reduced by approximately 63%,while the total waiting time for passengers across the line increases by only 0.5%.The model optimises train timetables and capacity allocations to meet passenger demand,and optimises timetables and capacity allocations to achieve a reasonable allocation of train capacity.The average waiting time for passengers in extremely congested stations has been reduced by 36% and the extreme congestion that exists on the metro lines has been effectively reduced.Passenger flows at the stations are balanced and overall operational safety is improved at line level,while the quality of passenger services is guaranteed. |
