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.
Amit @cite_7 apply optimization techniques to solve train timetable optimization problems. Ghoseiri @cite_3 present a multi-objective optimization model for the passenger train scheduling problem on a railroad network. To adjust the arrival departure times of trains based on a dynamic behavior of demand, Canca @cite_10 develop a nonlinear integer programming model, which can be used to evaluate the train service quality. Considering the user satisfaction parameters, average travel time and energy consumption, Sun @cite_4 present a multi-objective optimization model of the train routing problem. Wang @cite_8 @cite_5 propose a real-time train scheduling model with stop-skipping and solve the problem with the mixed integer nonlinear programming (MINLP) approach and the mixed integer linear programming (MILP) approach. Sun @cite_6 propose an optimization method of train scheduling for metro lines with a train dwell time mode, and lagrangian duality theory is adopted to solve this optimization problem with high dimensionality.
@cite_4 @cite_7 @cite_8 @cite_3 @cite_6 @cite_5 @cite_10
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A major problem in wireless sensor network localization is erroneous local geometric realizations in some parts of the network due to the sensitivity to certain distance measurement errors, which may in turn affect the reliability of the localization of the whole or a major portion of the sensor network. This phenomenon is well-described using the notion of "flip ambiguity" in rigid graph theory. In a recent study by the coauthors, an initial formal geometric analysis of flip ambiguity problems has been provided. The ultimate aim of that study was to quantify the likelihood of flip ambiguities in arbitrary sensor neighborhood geometries. In this paper we propose a more general robustness criterion to detect flip ambiguities in arbitrary sensor neighborhood geometries in planar sensor networks. This criterion enhances the recent study by the coauthors by removing the assumptions of accurately knowing some inter- sensor distances. The established robustness criterion is found to be useful in two aspects: (a) Analyzing the effects of flip ambiguity and (b) Enhancing the reliability of the location estimates of the prevailing localization algorithms by incorporating this robustness criterion to eliminate neighborhoods with flip ambiguity from being included in the localization process. In subway systems, the energy put into accelerating trains can be reconverted into electric energy by using the motors as generators during the braking phase. In general, except for a small part that is used for onboard purposes, most of the recovery energy is transmitted backward along the conversion chain and fed back into the overhead contact line. To improve the utilization of recovery energy, this paper proposes a cooperative scheduling approach to optimize the timetable so that the recovery energy that is generated by the braking train can directly be used by the accelerating train. The recovery that is generated by the braking train is less than the required energy for the accelerating train; therefore, only the synchronization between successive trains is considered. First, we propose the cooperative scheduling rules and define the overlapping time between the accelerating and braking trains for a peak-hours scenario and an off-peak-hours scenario, respectively. Second, we formulate an integer programming model to maximize the overlapping time with the headway time and dwell time control. Furthermore, we design a genetic algorithm with binary encoding to solve the optimal timetable. Last, we present six numerical examples based on the operation data from the Beijing Yizhuang subway line in China. The results illustrate that the proposed model can significantly improve the overlapping time by 22.06 at peak hours and 15.19 at off-peak hours. 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. 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 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. SUMMARY Railway scheduling and timetabling are common stages in the classical hierarchical railway planning process and they perhaps represent the step with major influence on user's perception about quality of service. This aspect, in conjunction with their contribution to service profitability, makes them a widely studied topic in the literature, where, nowadays, many efforts are focused on improving the solving methods of the corresponding optimization problems. However, literature about models considering detailed descriptions of passenger demand is sparse. This paper tackles the problem of timetable determination by means of building and solving a nonlinear integer programming model that fits the arrival and departure train times to a dynamic behavior of demand. The optimization model results are then used for computing several measures to characterize the quality of the obtained timetables considering jointly both user and company points of view. Some aspects are discussed, including the influence of train capacity and the validity of Random Incidence Theorem. An application to the C5 line of Madrid rapid transit system is presented. Different measures are analyzed in order to improve the insight into the proposed model and analyze in advance the influence of different objectives on the resulting timetable. Copyright © 2014 John Wiley & Sons, Ltd.