A stimulus-response model of day-to-day network dynamics

A general structure of stimulus-response formula is presented to specify the interacted network dynamics in a day-to-day time scale under the assumption of a learning and adaptive behavioral process. By taking the time derivative of system variable as a reaction in stimulus-response equation the evolution of whole system is formulated as a dynamical system. Issue of stability for the proposed differential equations are briefly discussed. Approximation of time dependent route-choice model is derived from the addressed path flow dynamics. The threshold effect on path flow dynamics is developed in term of defining a discontinuous stimulus. Quasi user equilibrium is researched to be a steady state when all users feel indifferent between experienced travel time and predicted travel time provided by Advanced Traveler Information Systems. The proposed quasi user equilibrium is reduced to Wardrop´s user equilibrium if threshold effect is vanishing.