Transit Service and Path Choice Models in Stochastic and Time-Dependent Networks

This paper develops a new path choice model that incorporates both time-dependent and stochastic transit service characteristics, and allows passengers to update path choice decisions while waiting. To develop this model, a new transit service model is proposed that represents route segments using a shuttle model. Such a model balances requirements for stochastic and time-dependent service modeling with the ability to aggregate to a larger transit corridor or network. This service model leads to a dynamic model of transit path choice, in which the passenger may wait until a vehicle is about to depart before making a boarding decision. A formal definition of this dynamic path choice model is given, and its differences with previous path choice models are noted. Based on this definition, two mathematical formulations of the dynamic model are developed. The first formulation assumes that the passenger will use the dynamic model for all possible vehicle departure times in the future, and is formulated as an optimal control problem. It is shown mathematically that this problem formulation is a less-constrained version of previous path choice models. However, because of some analytic and behavioral difficulties with this first model, a more well-behaved constrained formulation is also presented. A small corridor example demonstrates the significant differences in path choices and travel times between the constrained dynamic model and more traditional path choice models. Limitations of these dynamic path choice models are also discussed.