Modeling route choice inertia in network equilibrium with heterogeneous prevailing choice sets

• A precise definition of route choice inertia in the transportation network is presented.
• The model of inertial user equilibrium is proposed and its variational inequality formulation is established.
• Equilibrium preservation associated with UE and IUE, and the impact of information provision are analyzed.
• The relationship between IUE and ε-BRUE is briefly discussed.

The notion of inertia is originally a term in physics that describes the tendency of an object sustaining the same mode and its resistance of change in the state of motion. In the context of social and behavioral sciences, inertia is often understood as the endurance of stable relationships or reluctance in adjustment of status quo. In this paper, a precise definition of inertia under the criteria of route choice in the transportation network is presented. We then incorporate the concept of route choice inertia into the traffic assignment problem and propose a model of inertial user equilibrium (IUE). The inertial user equilibrium is compatible with the standard user equilibrium and extends UE with heterogeneous route choice inertia patterns. The variational inequality formulation is established. We show how travelers’ heterogeneous inertia patterns may redistribute traffic flow and affect the original network equilibrium. Useful equivalent conditions for equilibrium preservation are obtained. The impact of traffic information provision to alleviate inertia is analyzed. The relationship between IUE and ε-BRUE is briefly discussed. And a number of numerical examples are conducted.