Scheduling bus holding times in time horizons considering transfer synchronization and service regularity

Transfers between public transport modes hinder the traveling by public transport due to the unreliability and long waiting times. Nonetheless, public transport operators are mainly interested in maintaining the regularity of different lines without accounting for the transfer waiting times. This work focuses on the application of bus holding to reduce the transfer waiting times, in-vehicle waiting times, and the deviation from the target headways. The determination of optimal holding times is performed in time horizons (e.g., hourly time periods) where past events are fixed, while future events are considered in the optimization process. This study models the bus holding problem which considers transfer synchronization as a nonlinear convex program (NLP) that can be solved by off-the-shelf solvers. Our approach is tested against state-of-the-art bus holding methods in a case study on the bus network of Almere (Netherlands) demonstrating a significant reduction in the transferring waiting times.