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.

铁路运力是一种稀缺且昂贵的资源，必须以最佳方式加以利用。存在用于铁路容量的中短期规划和分析的许多方法。但是，缺乏用于长期（战略）规划的方法，无法提供高质量的复杂铁路网络容量估算。在本文中，我们通过可在预定时间段内运行的最大列车组来定义铁路网络的容量。这个最大的集合区分不同的火车类型和每种类型的数量，从而区分操作的异质性。

我们将容量确定形式化为一个优化问题，目的是找到最大数量的火车，以最大程度地减少相同类型火车之间的平均等待时间。我们通过计算一组火车占用基础设施的时间来测试一组火车的可行性。可行性测试不需要固定的时间表，因为要检查火车序列的样本。此外，可以通过调整输入参数来确定取决于服务约束的容量范围。

我们提出并测试两种不同的解决方案方法来确定铁路基础设施的容量：精确的分支定界算法和禁忌搜索启发式算法。容量确定框架的适用性在丹麦西南部的铁路网络上进行了演示，无论是否进行基础设施升级。我们分析计算时间，解决方案性能和灵敏度。结果说明了在几分钟内为真实网络获得高质量解决方案的能力。由于在交叉路口考虑了精确的基础设施特征，因此该方法能够量化基础设施升级的影响，这与长期（战略）规划阶段中使用的其他评估方法相反。