Optimizing Capacity Utilization of Stations by Estimating Knock-on Train Delays

Document Type

Journal Article

Publication Date


Subject Area

operations - capacity, operations - traffic, infrastructure - station, ridership - commuting, mode - rail


Transportation industry, Transportation, Transport, Trains, Traffic delay, Speed, Railroad transportation, Railroad trains, Railroad stations, Rail transportation, Networks, Mathematical models


For scheduled train services, a trade-off exists between efficiently utilizing the capacity of railway networks and improving the reliability and punctuality of train operations. This paper proposes a new analytical stochastic model of train delay propagation in stations, which estimates the knock-on delays of trains caused by route conflicts and late transfer connections realistically. The proposed model reflects the constraints of signalling system and train protection operations rules. The stochastic variations of track occupancy times due to the fluctuations of train speed in case of different signal aspects are modelled with conditional probability distributions. The model is solved on the basis of a numerical approximation of the Stieltjes convolution of individual independent distributions and can be integrated into a larger computerized decision support tool for timetable design and train dispatching. Having been validated successfully with empirical data, the model is applied for optimizing the station capacity utilization in a case study of the Dutch railway station The Hague Holland Spoor. The model can determine the maximal frequency of trains passing the critical level crossing with a given maximum knock-on delay at a certain confidence level. It is found that when the scheduled buffer time between train paths at the level crossing decreases, the mean knock-on delay of all passing trains increases exponentially. (A) "Reprinted with permission from Elsevier".


Transportation Research Part B Home Page: http://www.sciencedirect.com/science/journal/01912615