A quasi-birth-and-death process approach for integrated capacity and reliability modeling of railway systems

• Published in: Journal of rail transport planning & management 2017-12, Vol.7 (3), p.114-126
• Main Authors: Weik, Norman, Nießen, Nils
• Format: Article
• Language: English
• Subjects: Capacity; Infrastructure planning; Performance modelling; Quasi-birth-and-death-processes; Queueing; Railways; Reliability
• ISSN: 2210-9706; 2210-9714
• DOI: 10.1016/j.jrtpm.2017.06.001

A railway system's capacity is an important performance indicator allowing to assess different infrastructure variants and to devise market-compliant schedules. Existing approaches in capacity analysis assume the unrestricted availability and peak performance of all system components. Disruptions leading to infrastructure unavailability and reduced system performance are not considered in long- and medium term tactical planning of capacity. We present a quasi-birth-and-death process approach for the integrated modelling of capacity and reliability. By allowing for phase-type distributed arrival, service and repair processes the model permits to describe a wide range of schedule and operational characteristics. At the same time, the solvability of Markovian processes and the information on the queue length distribution are preserved. The model is solved using a Krylov-subspace method, which allows to effectively deal with large state spaces and transition matrices. The approach is compatible to existing queueing-based models in the capacity analysis of railway lines and junctions. The functionality of the method is demonstrated in a case study of a mixed service railway line with infrastructure unavailability.