Research On Optimization Of Urban Rail Rapid Transit Fast-slow Train Operation Cosidering Intercity Train Cross-line Operation

Airports and railway stations are the key nodes of urban rail transit network services.These urban external transport hubs are generally located in different directions of the city,and the distance between them is usually far.So urban rail rapid transit is planned and constructed to meet the passenger demands.Currently,the intercity train passengers must transfer to the subway or regional express line in order to reach the airport or other railway stations after arriving at the terminal station.As a result,the passengers’ travel time is long and the convenience is poor.This part of the passengers urgently need intercity train direct service.In addition,the regional express lines are usually commuter lines.Through reasonable operation organization,the line capacity can also be excavated.Therefore,using regional express surplus capacity to organize inter-city train cross-line operation has become a choice to improve passenger travel accessibility and build high-quality cities or urban agglomerations on track.Among them,whether to organize the intercity train cross-line operation and how to organize the intercity train cross-line operation are the key problems to be solved in the process of scientific cross-line operation organization.Based on the operation organization of intercity trains crossing the Shanghai Airport Liaison Line,this paper studies the influence of intercity trains crossing the line on the capacity of regional express lines,the passenger flow condition and the capacity condition of regional express lines for cross-line operation.And the optimization model of regional express train operation organization considering inter-city train cross-line operation is further constructed.The main contents and results are as follows :(1)Analyzed the influence of inter-city train cross-line operation on the capacity of regional expressway.In this paper,several continuous departure trains are regarded as a combination,and the total departure interval changes of the train combination after crossing the line are described by the empty time.A method for calculating the line capacity by using the empty time and the train combination is proposed.The relationship between the maximum number of intercity trains and the number of regional express trains of three different cross-line operation model of intercity trains is analyzed.Based on this,the influence of intercity train running interval on the capacity of the regional express is explored,and the calculation method of the empty time of different intercity train stop schemes is proposed.(2)Proposed the cross-line passenger flow condition of intercity trains cross-line operation and the capacity conditions of regional express line.In this paper,the comprehensive benefits of intercity train cross-line operation are introduced,and the factors such as the travel time of cross-line passengers,the maintenance cost of regional expressway reconstruction and the ticket income of operation enterprises are comprehensively considered.Taking the non-negative comprehensive benefits as the precondition,the calculation method of cross-line passenger flow scale necessary for cross-line operation organization is proposed.Based on the different cross-line modes of intercity trains(‘ substitution mode ’ and ‘ non-substitution mode ’),taking the total travel demand of passengers as the precondition,and considering the maximum line capacity constraint and the maximum congestion tolerance constraint of passengers,the urban expressway capacity conditions for organizing the cross-line operation of intercity trains are obtained.(3)Constructed the optimization model and solution algorithm for the operation organization of fast-slow trains on the urban expressway considering the cross-line operation of intercity trains.The train running process is equivalent to the sequential occupation of line facilities and equipment by the train.The 0 – 1 cumulative flow variable is introduced to describe the change of the occupation of line resources by the train.Taking the shortest total train running time and the shortest train departure delay time as the optimization objectives,the cumulative flow variable is used to describe the train interval operation constraint,the station stop time constraint,and the train tracking interval constraint.The 0 – 1 integer programming model for the optimization and adjustment of the operation organization of the urban fast-slow trains considering the inter-city train cross-line operation is constructed,and the Lagrange relaxation algorithm is designed to solve the model.The correctness of the algorithm is verified by Python programming.(4)Taking the inter-city train crossing the Shanghai airport contact line as an example,the operation organization scheme of fast-slow trains on the Shanghai airport contact line is optimized.The intercity train only stops at stations 4,7 and 9 of Shanghai Airport Liaison Line,and the crossing time is 38 min.The proportion of fast and slow trains running on Shanghai Airport Liaison Line is 3 : 1.The slow train stops at every station,and the fast train only stops at stations 1,7 and 9.In the cross-line situation,the model optimization strategy adopts the departure time window set to 120 s,and the stop time window set to 300 s.The optimization results show that the total train running time and departure delay time of all intercity trains increase by 6.9 % compared with that of no intercity trains.The cross-line operation of intercity trains increases the total starting delay of the original train of Shanghai Airport Line by 90 s,but does not affect the total starting time of the original train.Compared with the optimization results of the operation organization by the change of the intercity train crossing time when the proportion of the original train speed and slow train is 2 : 1,3 : 1,4 : 1 and 5 : 1,respectively,under the same other conditions,the adjacent departure operation of the intercity train and the regional fast train has the smallest impact on the original driving plan.In addition,with the increase of the proportion of fast and slow trains,the change of intercity train crossing time has similar influence on the original driving plan.