Determination of infrastructure capacity in railway networks without the need for a fixed timetable

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, place - europe, planning - methods, operations - capacity


Railways, Absolute capacity, Capacity analysis, Tabu search, Branch-and-bound


Railway capacity is a scarce and expensive resource that has to be utilised in the best way possible. Many methods exist for medium- and short-term planning and analysis of railway capacity. Yet, there is a lack of methods for long term (strategic) planning that provides high quality estimates of capacity in complex railway networks. In this paper, we define capacity of a railway network by a maximal set of trains that can be operated in a predefined period. This maximal set distinguish between different train types and the number of each type, and thus the heterogeneity of the operation.

We formalise the capacity determination as an optimisation problem with the objective of finding the maximal set of trains that minimises the average waiting time between trains of the same type. We test for feasibility of sets of trains by computing the time a set of trains occupies the infrastructure. A fixed timetable is not needed for the feasibility tests as samples of train sequences are examined. Furthermore, it is possible to determine a span of capacity depending on service constraints by adjusting input parameters.

We propose and test two different solution approaches to determine the capacity of railway infrastructure: an exact branch-and-bound algorithm and a tabu search heuristic. The applicability of the capacity determination framework is demonstrated on the railway network of Southwestern Denmark, with and without infrastructure upgrades. We analyse computation time, solution performance and sensitivity. The results illustrate the ability to obtain quality solutions for a real network within the order of minutes. As precise infrastructure characteristics are considered in junctions, the method is able to quantify the effect of the infrastructure upgrades, contrary to other assessment methods used in the long term (strategic) planning phase.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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