Modeling train movements through complex rail networks

Abstract

Trains operating in densely populated metropolitan areas typically encounter complex trackage configurations. To make optimal use of the available rail capacity, some portions of the rail network may consist of single-track lines while other locations may consist of double- or triple-track lines. Because of varying local conditions, different points in the rail network may have different speed limits. We formulate a graphical technique for modeling such complex rail networks; and we use this technique to develop a deadlock-free algorithm for dispatching each train to its destination with nearly minimal travel time while (a) abiding by the speed limits at each point on each train's route, and (b) maintaining adequate headways between trains. We implemented this train-dispatching algorithm in a simulation model of the movements of passenger and freight trains in Los Angeles County, and we validated the simulation as yielding an adequate approximation to the current system performance.