A comprehensive stochastic programming model for transfer synchronization in transit networks

We investigate the stochastic transfer synchronization problem, which seeks to synchronize the timetables of different routes in a transit network to reduce transfer waiting times, delay times, and unnecessary in-vehicle times. We present a sophisticated two-stage stochastic mixed-integer programming model that takes into account variability in passenger walking times between bus stops, bus running times, dwell times, and demand uncertainty. Our model incorporates new features related to dwell time determination by considering passenger arrival patterns at bus stops which have been neglected in the literature on transfer synchronization and timetabling. We solve a sample average approximation of our model using a problem-based scenario reduction approach, and the progressive hedging algorithm. As a proof of concept, our computational experiments on instances using transfer nodes in the City of Toronto, with a mixture of low- and high-frequency routes, demonstrate the potential advantages of the proposed model. Our findings highlight the necessity and value of incorporating stochasticity in transfer-based timetabling models.