Studies on the impact of the fixed-speed approximation for the real time Railway Traffic Management Problem

The real-time Railway Traffic Management Problem is the problem of selecting train routes and schedules to minimize delay propagation in case of perturbation. A frequent approximation used to solve it is named fixed-speed, where the accelerations and decelerations resulting from train rerouting or rescheduling are neglected. In this paper, we assess for the first time the ability of this approximation to drive the search of optimization algorithms on large infrastructures with numerous trains. This is done through a statistical analysis on a number of perturbed scenarios on different railway control areas, for various objective functions commonly used in the literature. For each scenario, we compare the ranking of hundreds of solutions, assessed with both the fixed-speed approximation and the simulated variable-speed dynamics. Our results indicate that the fixed-speed approximation is able to capture the relative solution quality with all considered objective functions, although some differences exist. This justifies the use of the fixed-speed approximation in optimization algorithms, to obtain practically reliable results with higher efficiency compared to more sophisticated approximations methods We also assess a modified fixed-speed approximation that better reflects the behavior of train speed dynamics, but no remarkable difference is observable as for the quality of the approximation.