Modeling User Equilibrium and the Day-to-day Traffic Evolution based on Cumulative Prospect Theory

Abstract

With the rapid development of ATIS, the effect of information provision on travellers' route choice behaviour has received much attention. In this paper, we develop a dynamical traffic system within the frame of bounded rationality by an integration of the BNN dynamic and Cumulative Prospect Theory to characterize travellers' day-to-day route switching behaviours and investigate the process and conditions of achieving UE under ATIS. Under three mild constraints, we prove that no matter what the initial state is and whether travellers' reference points are fixed or updated under certain rules, the dynamical system can eventually evolve to UE, at which the link flow pattern is uniquely determined and globally asymptotical stable, while uniqueness and asymptotic stability of the route flow pattern cannot be ensured, which call for a further exploration of the network topology and link performance. Finally, we demonstrate the above conclusions and illustrate the process of achieving UE through a numerical experiment.

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