Multi-constrained bus holding control in time windows with branch and bound and alternating minimization

This work proposes a periodic bus holding control method where the bus holding times of all running trips are computed simultaneously within each optimization time period; thus, increasing the coordination among running buses for avoiding bus bunching. This paper considers the adverse effects of the bus holding control in the in-vehicle travel times of on-board passengers and performs holistic bus holding decisions by modelling the bus holding problem as a discrete, nonlinear, constrained optimization problem. Given the computational complexity of the bus holding problem, an alternating minimization approach is introduced for computing the optimal holding times at each optimization instance. The performance of the periodic control method is evaluated against the performance of event-based control methods using 5-month automated vehicle location and automated passenger count data from bus line 1 in Stockholm for contacting simulation-based experiments.