A Train Holding Model for Urban Rail Transit Systems

Urban rail transit lines are subject to disruptions that can adversely affect passenger level of service and routine operations. This paper focuses upon the development of a real-time disruption response model with an emphasis on the train holding strategy. The paper also discusses the short-turning control strategy which is often used in conjunction with holding for longer disruptions. The holding problem is modeled as a non-linear mixed-integer program and a two-step solution procedure is designed to solve it quickly, yielding solution times of less than 10 seconds. The model is applied to a disruption scenario on a simplified representation of the MBTA Red Line. The sensitivity of the optimal holding strategy to the assumptions of finite train capacity and the value of in-vehicle time are also investigated. The results show a high level of regularity in the headway distribution for the control strategy when in-vehicle time is not considered. When accounting for in-vehicle delay, the optimal holding strategy consists of only a few trains being held at a few stations. Overall, the results suggest the present formulation yields control strategies that are simple enough to be implemented by transit practitioners and that the solution times are feasible for real-time implementation.