Analyzing the impact of timetable elements on railway line capacity

Train timetabling poses inherent challenges, prompting the need to enhance existing schedules by extracting valuable insights from the current timetable structure. By such philosophy, this paper studies the impact of timetable elements on the consumed capacity. These elements primarily encompass train operation parameters, including running times and stop plans. Their impact is defined as the deviation of consumed capacity relative to their variations. We initially establish a link between consumed capacity and timetable elements. This relationship is articulated as the signed sum of timetable elements along a designated ”critical path”. Then, the limited impact of any timetable element is clarified, namely changing an element can impact the consumed capacity with its neighbor trains in a combinatorial way. With this knowledge, we analyze the impact of a single element, using stop plans for example. This result is then generalized into analyzing the impact of several dependent and independent stop plans. The findings on capacity calculation and impact analysis of a single element are tested through real-world numerical computations and then extended to analyzing various capacity factors, such as average speed and heterogeneity.