X. Luan, B. De Schutter, F. Corman, and G. Lodewijks, "Integrating dynamic signaling commands under fixed-block signaling systems into train dispatching optimization problems," Transportation Research Record, 2018.
In railway operations after a disruption has occurred, train dispatchers aim at adjusting the impacted schedule and reducing negative consequences during disruptions. As one of the most important components of the railway system, railway signals are used to guarantee the safety of train service. 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 been so far neglected in the railway train dispatching literature, and we innovatively propose a 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 are 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 the 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.