Keywords: railways, railway capacity, absolute capacity, return paths, cycles.

Railways are an important mode of transportation. They are, however, large and complex and their construction, management, and operation is time consuming and costly. Evidently, planning the current and future activities is vital. Part of that planning process is an analysis of capacity. To determine what volume of traffic can be achieved over time, a variety of railway capacity analysis techniques have been created. A generic analytical approach that incorporates more complex train paths, however, has yet to be provided. This paper provides such an approach. This paper extends a mathematical model for determining the theoretical capacity of a railway network. The main contribution of this paper is the modelling of more complex train paths whereby each section can be visited many times in the course of a train's journey. Three variant models are formulated and then demonstrated in a case study. This paper's numerical investigations have successively shown the applicability of the proposed models and how they may be used to gain insights into system performance.

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