Synchronizing different transit lines at common stops considering travel time variability along the day

Synchronizing different lines at common stops can increase the level of service in transit systems, particularly for different lines in overlapping route segments or common stops (e.g. branching lines and limited-stop lines). In this study, we propose a measure of synchronization that penalizes the deviation from proposed arrivals' separation times of different lines at common stops. Then, we define two optimization problems that maximize the proposed measure considering bus speeds that dependents on the departure times. We implement a commercial solver and a Genetic Algorithm to obtain good quality solutions in short time for randomly generated instances. Finally, we implement our optimization approach for two branching lines of Redbus Urbano, an agency in Santiago, Chile. Numerical results show that it is possible to properly separate arrivals of different lines at common stops which benefits to passengers who may use more than one line.