A stochastic transit assignment model using a dynamic schedule-based network

Using the schedule-based approach, in which scheduled time-tables are used to describe the movement of vehicles, a dynamic transit assignment model is formulated. Passengers are assumed to travel on a path with minimum generalized cost which consists of four components: in-vehicle time; waiting time; walking time; and a time penalty for each line change. With the exception of in-vehicle time, each of the other cost components is weighted by a sensitivity coefficient which varies among travelers and is defined by a density function. This time-dependent and stochastic minimum path is generated by a specially developed branch and bound algorithm. The assignment procedure is conducted over a period in which both passenger demand and train headways are varying. Due to the stochastic nature of the assignment problem, a Monte Carlo approach is employed to solve the problem. A case study using the Mass Transit Railway System in Hong Kong is given to demonstrate the model and its potential applications.