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Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.

Abstract. Delays and disruptions reduce the reliability and stability of the rail operations.Railway tra c rescheduling includes ways to manage the operations during and after the occurrence of such disturbances. In this study, we consider the simultaneous presence of large disruptions (temporary full or partial blockage of tracks) as well as stochastic variation of operations as a source of disturbance. The occurrence time of blockage and its recovery time are given. We designed a simulation-based optimization model that incorporates dynamic dispatch priority rules with the objective of minimizing the total delay time of trains. We, moreover, designed a variable neighborhood search meta-heuristic scheme for handling tra c under the limited capacity close to the blockage. The new plan includes a set of new departure times, dwell times, and train running times. We evaluated the proposed model on a set of disruption scenarios covering a large part of the Iranian rail network. The result indicates that the developed simulation-based optimization approach has substantial advantages in producing practical solution quickly, when compared to commercial optimization software. In addition, the solutions have a lower average and smaller standard deviation than the currently accepted solutions, determined by human dispatcher or by standard software packages.

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