Train regulation for mass transit systems

The train regulation problem is of particular importance among the scheduling problems found in mass transit systems, being characterized by trains running in urban regions taking passengers from one location to another. If the desired headway between trains, dwell-times in platforms and running times between platforms are determined and known a-priori, the steady state solution (timetable) can be calculated. However, real systems are subject to disturbances such as passengers preventing doors from closing, mechanical or electrical failures, etc., that can deviate the trains from the steady state. In this context, this work is concerned with the determination of a control law, i.e. a law for the determination of the arrival and departure times of each train on each platform in the system's cycles in order to reestablish and maintain the timetable (reference solution). The proposed control law is based on max-plus algebra concepts. The desired arrival and departure times of each train on each platform are calculated from the last occurrence instants of the system's events and from a set of matrices defined in max-plus algebra.