Integrating dynamic signaling commands under fixed-block signaling systems into train dispatching optimization problems

In railway operations, when a disruption occurs, train dispatchers aim to adjust the affected schedule and to minimize negative consequences during and after the disruption. As one of the most important components of the railway system, railway signals are used to guarantee the safety of train services. We study the train dispatching problem with consideration of railway signaling commands under the fixed-block signaling system. In such a system, signaling commands dynamically depend on the movement of the preceding trains in the network. We clarify the impact of the signaling commands on train schedules, which has so far been neglected in the literature on railway train dispatching, and we propose an innovative set of signaling constraints to describe the impact. The determination of the signal indicators is presented using “if-then” constraints, which are further transformed into linear inequalities by applying two transformation properties. Activation of the train speed limits that result from the signaling commands is the core purpose of the signaling constraints, and this is implemented by using the signal indicators. Moreover, we formulate the Greenwave (GW) policy, which requires that trains always proceed under green signals, and we further investigate the impact of the GW policy on delays. In numerical experiments, the proposed signaling constraints are employed within a time-instant optimization problem, which is a mixed-integer linear programming (MILP) problem. The experimental results demonstrate the effectiveness of the proposed signaling constraints and show the impact of the signaling commands and GW policy on the train dispatching solution.