Rational behavior adjustment process with boundedly rational user equilibrium

Abstract

This paper extends the framework of "rational behavior adjustment process" (RBAP) to incorporating the "boundedly rational user equilibrium" (BRUE). The proportional-switch adjustment process (PSAP) and the network tatonnement process (NTP) are extended to the BRUE case, and their dynamical equations are shown to be Lipschitz continuous, which guarantees the global uniqueness of the classical solutions. A special group of the BRUE-RBAP is proposed, for which the path flows would increase if the paths are in an acceptable path set, and would decrease otherwise. Classical solutions to this special group of models may not exist. Stability of the BRUE-RBAP with classical solutions is proved with separable link travel cost functions. For nonseparable link travel cost functions, the stability of the BRUE-PSAP is proved. Numerical examples are presented to demonstrate the evolution processes of BRUE-PSAP and BRUE-NTP under various bounded rationality thresholds and different initial states. The applicability of BRUE-PSAP in larger networks with asymmetric link travel cost functions is also illustrated.