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On an oversaturated urban rail transit line, passengers at downstream stations have to wait for more trains until they get aboard, resulting in service imbalance problem. To improve the service quality, this paper proposes an integrated optimization approach combining the train timetabling and collaborative passenger flow control, with the aim of minimizing indicators associated with the passenger service imbalance and train loading capacity utilization. Considering train regulation constraints and passenger loading dynamics, a mixed-integer linear programming model is formulated. Based on the linear weighting technique, an iterative heuristic algorithm combining the tabu search and Gurobi solver is designed to solve the proposed model. Finally, a simple case with different-scale instances is used to verify that the proposed algorithm can obtain near-optimal solution efficiently. Moreover, a real-world case of Beijing Subway Batong Line is implemented to compare performances of the proposed approach with those under the original timetable and noncollaborative passenger flow control. [ABSTRACT FROM AUTHOR]

Last train coordination aims to synchronize the arrival and departure times of the last feeder trains and the last connecting trains at transfer stations to improve the transfer accessibility of urban rail networks. This study focuses on the transfer accessibility between last trains with considering heterogeneous transfer walking time. Three mathematical models are developed on the last train timetable optimization. The first model fine-tunes the last train timetable under the given bound of the dwell time. The second one aims to allow the mutual transfers with the prolonged dwell time to maximize the transfer accessibility. A biobjective function is proposed to seek the trade-off between the maximal transfer accessibility and the minimal extension of dwell time. The third model considers the heterogeneity of transfer walking time that is represented as a random variable following a probability distribution. A discrete approximation method is proposed to reformulate the nonlinear model. The embedded Branch & Cut algorithm of CPLEX is applied to solve the models. A real case on the Shenzhen metro network is conducted to demonstrate the performance of the models. The three models all provide better last train timetable than the current timetable in practice. The sensitivity analysis manifests that the third model are always advantageous in the optimization of successful transfer passengers. [ABSTRACT FROM AUTHOR]

Energy-efficient metro operation has received increasing attention because of the energy cost and environmental concerns. This paper developed an integrated optimization model on train control and timetable to minimize the net energy consumption. The extents of train motoring and braking as well as timetable configurations such as train headway and interstation runtime are optimized to minimize the net energy consumption with consideration of utilizing regenerative energy. An improved model on train control is proposed to reduce traction energy by allowing coasting on downhill slopes as much as possible. Variations of train mass due to the change of onboard passengers are taken into account. The brute force algorithm is applied to attain energy-efficient speed profiles and an NS-GSA algorithm is designed to attain the optimal extents of motoring/braking and timetable configurations. Case studies on Beijing Metro Line 5 illustrate that the improved train control approach can save traction energy consumption by 20% in the sections with steep downhill slopes, in comparison with the commonly adopted train control sequence in timetable optimization. Moreover, the integrated model is able to significantly prolong the overlapping time between motoring and braking trains, and the net energy consumption is accordingly reduced by 4.97%. [ABSTRACT FROM AUTHOR]

This paper proposes a bi-level model to solve the timetable design problem for an urban rail line. The upper level model aims at determining the headways between trains to minimize total passenger cost, which includes not only the usual perceived travel time cost, but also penalties during travel. With the headways given by the upper level model, passengers’ arrival times at their origin stops are determined by the lower level model, in which the cost-minimizing behavior of each passenger is taken into account. To make the model more realistic, explicit capacity constraints of individual trains are considered. With these constraints, passengers cannot board a full train, but wait in queues for the next coming train. A two-stage genetic algorithm incorporating the method of successive averages is introduced to solve the bi-level model. Two hypothetical examples and a real world case are employed to evaluate the effectiveness of the proposed bi-level model and algorithm. Results show that the bi-level model performs well in reducing total passenger cost, especially in reducing waiting time cost and penalties. And the section loading-rates of trains in the optimized timetable are more balanced than the even-headway timetable. The sensitivity analyses show that passenger’s desired arrival time interval at destination and crowding penalty factor have a high influence on the optimal solution. And with the dispersing of passengers' desired arrival time intervals or the increase of crowding penalty factor, the section loading-rates of trains become more balanced. [ABSTRACT FROM AUTHOR]

• A collaborative transportation plan of passengers and freight on urban rail lines. • Both the dedicated freight trains and existing passenger trains to transport goods. • A MILP model to jointly optimize train stopping plans and schedules. • An iterative scheduling approach to solve the problem. • A case study based on the UP Express in Toronto and Beijing New Airport Line. This paper develops an operational strategy in which urban rail transit is used for freight transport. An environment-friendly urban freight transportation alternative is analyzed by employing optimization techniques to support the collaborative transportation of passengers and freight. Practical cases are investigated to test the technical feasibility of this transportation scheme. The paper formulates the train service design problem on a single urban rail line with passenger and freight. Passenger trains have a prescribed timetable which is allowed to be slightly modified to facilitate the freight service. Freight can be transported by inserting dedicated freight trains or utilizing the extra space inside the passenger train carriages. Station platforms are able to load and unload both goods and passengers. An optimization model for combined train service design is proposed to maximize profit resulting from the balance of revenues and costs brought by the freight service. The efficient schedules of trains and freight allocation plans are to be determined. This problem is formulated as a mixed-integer linear programming model. An iterative scheduling approach which includes a pre-processing method and two heuristic iterative algorithms is designed to solve the model. Two numerical examples are introduced to demonstrate the efficiency of the proposed model and the iterative scheduling approach. [ABSTRACT FROM AUTHOR]