The Urban Rail Transit (URT) has been one of the major trip modes in cities worldwide. As the passengers arrive at variable rates in different time slots, e.g., rush and non-rush hours, the departure frequency at a site directly relates to perceived service quality of passengers; the high departure frequency, however, incurs more operation cost to URT. Therefore, a tradeoff between the interest of railway operator and the service quality of passengers needs to be addressed. In this paper, we develop a model on the operation method of train operation scheduling using a Stackelberg game model. The railway operator is modeled as the game leader and the passengers as the game follower, and an optimal departure frequency can be determine the tradeoff between passengers' service quality and operation cost. We present several numerical examples based on the operation data from Nanjing transit subway at China. The results demonstrate that the proposed model can significantly improve the traffic efficiency.
In order to maintain a satisfying level of quality of experience, optimization models have been widely adopted to determine the optimal Urban rail transit (URT) train operation with different objectives, such as travel time @cite_9 , waiting time @cite_12 , operation cost [16-18] and robustness @cite_2 .
@cite_9 @cite_12 @cite_2
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This paper proposes an optimization method of train scheduling for metro lines with a train dwell time model according to passenger demand. An optimization problem of train scheduling is established with constraints of a headway equation, passenger equation, and train dwell time equation, where the train dwell time is modeled as a function of boarding and alighting passenger volumes. The aim of the optimization problem is to minimize the waiting time of passengers and train operation cost. Lagrangian duality theory is adopted to solve this optimization problem with high dimensionality. Finally, simulation results illustrate that this method is efficient to generate the train schedule, which meets the passengers' exchanging requirements between trains and platforms. The contribution of this paper is that a dwell time model is introduced in train schedule optimization, which provides the possibility of reducing the operation cost in the precondition that the exchanging time of passengers between platforms and trains is assured. This paper develops a multi-objective optimization model for the passenger train-scheduling problem on a railroad network which includes single and multiple tracks, as well as multiple platforms with different train capacities. In this study, lowering the fuel consumption cost is the measure of satisfaction of the railway company and shortening the total passenger-time is being regarded as the passenger satisfaction criterion. The solution of the problem consists of two steps. First the Pareto frontier is determined using the [var epsilon]-constraint method, and second, based on the obtained Pareto frontier detailed multi-objective optimization is performed using the distance-based method with three types of distances. Numerical examples are given to illustrate the model and solution methodology. This paper describes the development and use of a model designed to optimise train schedules on single line rail corridors. The model has been developed with two major applications in mind, namely: as a decision support tool for train dispatchers to schedule trains in real time in an optimal way; and as a planning tool to evaluate the impact of timetable changes, as well as railroad infrastructure changes. The mathematical programming model described here schedules trains over a single line track. The priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay, as well as the current delay. This priority is used in a branch and bound procedure to allow and optimal solution to reasonable size train scheduling problems to be determined efficiently. The use of the model in an application to a "real life" problem is discussed. The impacts of changing demand by increasing the number of trains, and reducing the number of sidings for a 150 km section of single line track are discussed. It is concluded that the model is able to produce useful results in terms of optimal schedules in a reasonable time for the test applications shown here. The real-time train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the operation of trains. Based on the passenger demand in the urban rail transit system, the optimal departure times, running times, and dwell times are obtained by solving the scheduling problem. A new iterative convex programming (ICP) approach is proposed to solve the train scheduling problem. The performance of the ICP approach is compared with other alternative approaches, i.e., nonlinear programming approaches, a mixed-integer nonlinear programming (MINLP) approach, and a mixed-integer linear programming (MILP) approach. In addition, this paper formulates the real-time train scheduling problem with stop-skipping and shows how to solve it using an MINLP approach and an MILP approach. The ICP approach is shown, via a case study, to provide a better tradeoff between performance and computational complexity for the real-time train scheduling problem. Furthermore, for the train scheduling problem with stop-skipping, the MINLP approach turns out to have a good tradeoff between the control performance and the computational efficiency.