Equivalences between analytical railway capacity methods

Capacity analysis is of central importance in railway operation. Existing methods divide the infrastructure of question into smaller sections when computing the consumed capacity, which makes them nontransferable for real-world operation. We first review and enhance the UIC compression method, which results in a combination–reconstruction (ComRec) method to compute the compressed timetable graph of the whole infrastructure. Secondly, we propose a triangular-gap-problem-based (TGP) method to compute the headway times of train pairs when no more than one train lies within the separation gap of two trains. Then we show TGP method produces an compressed timetable graph equivalent to that by the ComRec method. Max-plus algebra approach determines the consumed capacity by solving an eigenvalue problem, and the solution corresponds to a timed event network as the compressed timetable. And by their correspondence, we show that these three methods are equivalent. Finally, we establish correspondences between the capacity methods and linear programming models. In this way, we were able to specify the condition when they give the same result and how infrastructure dividing underestimates capacity.