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.
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. During rail operations, unforeseen events may cause timetable perturbations, which ask for the capability of traffic management systems to reschedule trains and to restore the timetable feasibility. Based on an accurate monitoring of train positions and speeds, potential conflicting routes can be predicted in advance and resolved in real time. The adjusted targets (location-time-speed) would be then communicated to the relevant trains by which drivers should be able to anticipate the changed traffic circumstances and adjust the train's speed accordingly. We adopt a detailed alternative graph model for the train dispatching problem. Conflicts between different trains are effectively detected and solved. Adopting the blocking time model, we ascertain whether a safe distance headway between trains is respected, and we also consider speed coordination issues among consecutive trains. An iterative rescheduling procedure provides an acceptable speed profile for each train over the intended time horizon. After a finite number of iterations, the final solution is a conflict-free schedule that respects the signaling and safety constraints. A computational study based on a hourly cyclical timetable of the Schiphol railway network has been carried out. Our automated dispatching system provides better solutions in terms of delay minimization when compared to dispatching rules that can be adopted by a human traffic controller In this paper we survey the main studies dealing with the train timetabling problem in its nominal and robust versions. Roughly speaking, the nominal version of the problem amounts of determining “good” timetables for a set of trains (on a railway network or on a single one-way line), satisfying the so-called track capacity constraints, with the aim of optimizing an objective function that can have different meanings according to the requests of the railway company (e.g. one can be asked to schedule the trains according to the timetables preferred by the train operators or to maximize the passenger satisfaction). Two are the main variants of the nominal problem: one is to consider a cyclic (or periodic) schedule of the trains that is repeated every given time period (for example every hour), and the other one is to consider a more congested network where only a non-cyclic schedule can be performed. In the recent years, many works have been dedicated to the robust version of the problem. In this case, the aim is to determine robust timetables for the trains, i.e. to find a schedule that avoids, in case of disruptions in the railway network, delay propagation as much as possible. We present an overview of the main works on train timetabling, underlining the differences between models and methods that have been developed to tackle the nominal and the robust versions of the problem.