A Railway Timetable Scheduling Model based on a Max-Plus-Linear System

A max-plus-linear (MPL) system is applied to the problem of organizing railway timetables. Standard MPL systems are used to schedule production systems. In such systems, jobs are typically processed on a first-in-first-out basis, where the job order remains fixed. In contrast, railway systems include a variety of services (e.g., local and express trains), which changes the order in which trains arrive and depart. For example, an express train that arrives at a station after a local train may then depart again before the local train does. Such changes in the processing order of jobs cannot be expressed in existing MPL systems contents. We therefore extend an MPL model to apply it to a railway timetable problem. We demonstrate the algorithm and its validity with numerical calculations.