Buffer times are an important factor in railway timetable design preventing the propagation of delays and ensuring timetable robustness. Determining the required amount of buffer times, such that a certain level of service quality is achieved, falls within the responsibility of railway capacity analysis. This is why capacity analysis is intrinsically linked to delay propagation modelling. Currently, delay propagation modelling in this context relies on the assumption of random, exponentially distributed or deterministic buffer times.Real-world timetables tend to deviate from this behaviour, such that a more general modelling of buffer time distributions is desirable. In this paper the impact of different buffer time distributions on the build-up of knock-on delays in delay propagation modelling is analysed using a Monte-Carlo simulation approach. It is shown that the choice of distribution has a significant impact on performance metrics. In a sensitivity analysis line capacity is observed to vary by as much as 17% as a function of the underlying buffer time statistics in the investigated scenarios.
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.
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