Railway capacity estimation considering vehicle circulation: Integrated timetable and vehicles scheduling on hybrid time-space networks

Abstract

Railway capacity is a vague concept, related to the possibility to run a maximal transport performance given a set of available resources. While most approaches focus only on infrastructure resources (i.e. availability of train paths), we include both infrastructure and vehicle resources in a capacity estimation problem. We study the railway capacity estimation problem applying an associated timetable saturation method; in other words, the capacity is related to a timetable where no additional trains can be added. We use optimization methods to find such a timetable integrating explicitly variables and constraints from vehicle circulation. A hybrid time–space network describes the integrated timetabling and vehicles scheduling problem, based on which an integer programming model can be formulated, to maximize the overall transportation performance. A Lagrangian relaxation-based decomposition algorithm is proposed to solve the problem, and is shown able to scale to large instances efficiently. The integrated scheduling problem is decomposed into a timetabling sub-problem and a vehicle circulation sub-problem by dualizing the consistency constraints linking the two. A new heuristic, based on the concept of timetable intensity, is employed to improve the quality of the feasible (non-relaxed) solution found. The experimental result shows the benefit of the approach, which can evaluate transportation performance and relate it to various fleet sizes, vehicle depot locations, and minimum headways.