Optimal Train Dispatching at Railway Stations: A Discrete Event Dynamic System Approach

Reliability of transfers in a transportation network largely influences the level of service of trip chains. Especially in low-frequency service networks like (long-distance) railway networks. Running and dwell times are typically subject to random variations resulting in arrival delays during operation. If a scheduled transfer connection is endangered, process operators can decide to secure the tansfer by holding the connecting train until the passengers of the delayed feeder train(s) have arrived. However, a large departure delay may result in severe delay propagation. The effect of dispatching is thus very complex and can not be foreseen without advanced mathematical models. This paper proposes a mathematical model for computing optimal train waiting times depending on the actual state of delays in the train service network. The optimal strategy determines the transfers that must be secured or cancelled with respect to estimated arrival delays. Several objectives may be pursued, including the minimization of total delay or the minimization of weighted passenger waiting time. The incorporated delay propagation model explores the compensating effect of recovery times to arrival delays and is modelled as a discrete event dynamic system (DEDS), and in particular as a max-plus linear system. The optimal train waiting time strategies can be computed offline for each scenario of arrival delays. The optimal strategies result in critical passage times at reference points about 10 minutes before the railway stations. If the actual passage time exceeds the relevant critical passage time then the associated connection at the railway station is cancelled. The results can be incorporated in a decision support system to assist process operators at railway stations or traffic operators at traffic control centra