Stochastic Models for Capacity Analysis in Railway Networks - An Approach Capturing Network Effects and Component Failures


Norman Weik


+49 241 80 25185



Railway capacity planning aims to determine the number of trains which can be operated concurrently on a given infrastructure such that a pre-defined level of service is satisfied. In medium and long-term planning of infrastructure and traffic concepts stochastic models have found widespread application in capacity analysis. Existing approaches rely on a decomposition of the network into line segments, stations and route nodes which are analyzed individually.

Current models in this area lack precision for two reasons: First, the decomposition approach tends to overestimate network capacity as it neglects correlation effects. Second, the state of the underlying infrastructure is not accounted for. Malfunctions and breakdowns have so far only been considered implicitly as a source of primary delays.

By integrating failure and restoration processes giving rise to uncertain infrastructure availability the doctoral project aims to improve current models used in capacity investigations of railway tracks and stations. The goal is to develop an integrated approach for capacity and reliability modeling which allows to determine a railway system’s capacity as a function of infrastructure availability at network level. This is expected to provide valuable insights into the interplay between train operations and the state of the railway infrastructure. Apart from allowing for a more realistic assessment of the available and marketable capacity the methodology is thought to be beneficial for infrastructure and maintenance planning by identifying critical elements and facilitating cost-revenue analysis, for instance.

In a first step, existing local capacity models on line and station-scale, which rely on stochastic delay propagation or queueing theory (cf. Nießen, 2014; Weik, 2016) have been analyzed and extended. In Weik (2017) an integrated capacity-reliability model based on a queueing process in a random environment describing failure and maintenance states in the system has been described. Currently, the local modelling approaches are extended to network level in a bi-layer approach and validated against discrete event simulation of railway operations. The outcomes of this approach will form the main part of the PhD thesis which will be completed in mid 2019.

Within UnRAVeL the project is closely linked to the work of Matthias Volk’s PhD project “Verifying Fault Trees for Railway Safety”. While the present project focuses on the performance aspect of railway operations on infrastructure with uncertain availability the latter strives for an evaluation of failure modes, their importance and the overall quality of the system. Currently, Dynamic Fault Trees are investigated in a joint attempt to introduce formal modelling approaches in reliability modelling of railway operations. Here, the goal is to provide insights into the criticality of infrastructure elements to facilitate maintenance investment planning. Besides that, a constant exchange within the railway focus area in UnRAVeL (additionally comprising the PhD projects of Stephan Zieger. Rebecca Haehn) is maintained.


N. Nießen, ”Queueing“, in Hansen, Pachl (eds): ”Railway Timetabling & Operations”, Eurailpress, 2014
N. Weik, N. Niebel, and N. Nießen, “Capacity analysis of railway lines in Germany ‑ A rigorous discussion of the queueing based approach”, Journal of Rail Transport Planning & Management 6 (2), pp. 99-115 (2016)

N. Weik and N. Nießen, “A quasi-birth-and-death process approach for integrated capacity and reliability modeling of railway system”, Journal of Rail Transport Planning & Management 7 (3), pp. 114-126 (2017)