A framework is proposed for determining the least expected cost path in a schedule-based time-expanded public transit network where travel times, and thus bus arrival and departure times at stops, are stochastic. Transfer reliability is incorporated in a label-correcting algorithm with a penalty function for the expected waiting time when transferring that reflects the likelihood of making a successful transfer. The algorithm is implemented in transit assignment on an Austin, Texas test network, using actual bus arrival and departure time distributions from vehicle location data. Assignment results are compared with those of a deterministic shortest path based on the schedule and from a calibrated transit assignment model. Simulations of the network and passenger paths are also conducted to evaluate the overall path reliability. The reliable shortest path algorithm is found to penalize transferring and provide paths with improved transfer and overall reliability. The proposed model is realistic, incorporating reliability measures from vehicle location data, and practical, given the efficient shortest path approach and application to transit assignment. / text