A discrete day-to-day link flow dynamic model considering travelers’ heterogeneous inertia patterns

This study investigates the impact of heterogeneous psychological inertia of travelers on link flow evolution process on a day-to-day basis. The psychological inertia of a traveler is defined as his/her reluctance to reconsider his/her route choice, and is characterized by a sequence of binary parameters along time. Travelers are grouped into different classes by their inertia patterns. Based on these classes, a variational inequality formulation for the multi-class user equilibrium problem is presented. We develop a generic day-to-day link flow dynamic model by considering heterogeneous inertia patterns of the travelers. The convergence properties of the model are rigorously demonstrated. The developed model is formulated in a general form under mild assumptions. We further consider a special case of the generic model. We examine properties of this special case model, and investigate its relationship with existing models in the literature. Numerical experiments are conducted to demonstrate our theoretical results.