A methodology for robust multi-train trajectory planning under dwell-time and control-point uncertainty

Methods to optimise train movements to maintain time and avoid excessive energy consumption are becoming widely applied, but outcomes remain sensitive to uncertainties within the system. In this paper variability in station dwell-times and the points of application of planned train control (traction, coasting or braking) are taken as examples of typical rail system uncertain- ties, and are used to demonstrate an approach to multi-train trajectory optimisation that is resilient to them.

Trade-offs are explored between highly optimised train trajectories that are vulnerable to perturbation, and less optimal trajectories that are robust to typical disturbances. Beyond dwell and control variations the method has application for the many other common rail network uncertainties, e.g. differences in the traction characteristics of nominally identical trains or variable train loading. Relative to optimisation without consideration of uncertainty, the approach is shown to find control strategies of substantially increased robustness for the test cases examined, and offers a more principled way to plan a network than the ad-hoc use of recovery time to mitigate everyday operational disturbances.