Running times on railway sections with heterogeneous train traffic

In contemporary railway traffic, different train services often run on the same track of a railway section. Since these train services generally trave l at different speed, this may result in delays due to fast trains being ca ught behind slower ones. This note investigates these delays developing a s tochastic model capturing both scheduled and unscheduled train movements. R unning time distributions for each train service can be obtained solving a system of linear differential equations. This system can be solved explicit ly when free running times for all train services are deterministic. The ma thematical model falls in the class of infinite server resequencing queues, and the results generalise existing results for such queues, allowing depe ndence between consecutive interarrival times, as well as between interarri val times and service times. A case study of a railway section in the Dutch railway network illustrates the practical value of the model, both for lon g and short term railway planning. (C) 2001 Elsevier Science Ltd. All right s reserved.