Stop-skipping in rolling horizons

Stop-skipping (also known as expressing) is a typical control strategy in public transit operations with a dual objective: (i) reduce the trip delays and (ii) improve the travel times of on-board passengers. Dynamic stop-skipping approaches decide about the stop-skipping strategy of each bus trip in isolation, neglecting the effect of the skipped stops on future trips. To rectify this, we introduce a rolling horizon stop-skipping model that determines the stop-skipping strategies of several trips within a rolling horizon. Then, we model the rolling horizon stop-skipping problem as an integer nonlinear program, and we prove that it is (at least) an NP-complete decision problem which can be solved to global optimality for small-scale scenarios. Simulation-based tests using real data from bus line 15L in Denver demonstrate a potential performance improvement of 13% when using our rolling horizon stop-skipping approach in the presence of travel time uncertainty.