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

Document Type

Journal Article

Publication Date


Subject Area

infrastructure - fleet management, mode - rail, operations - capacity, operations - performance, operations - scheduling


Railway capacity, Timetable, Vehicle circulation, Integrated optimization, Time-space network, Lagrangian relaxation


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.


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


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