Quasi user equilibrium and its stability

In the historical studies of dynamic traffic assignment (or the so-called dynamic route choice modeling), user equilibrium is a fundamental paradigm to guide the final state of flow diversion for a transportation network. However, the user behavior of path selection had been observed and indicated that there exists an adaptive and learning process to adjust the daily travel decision as travel information is provided by intelligent transportation systems in particular. In this paper, a general structure of stimulus-response mechanism to formulate daily path adjustment is reviewed first. Quasi user equilibrium is then introduced in the same modeling framework but replacing a threshold-effect response term. A proof of the stability of quasi user equilibrium in the sense of Lyapunov is presented. Finally, a simple network is illustrated to show the verification of the proposed approach numerically.