Day-to-Day dynamical evolution of network traffic flow under bounded rational view

Abstract

The formation mechanism of network traffic flow and its evolution law are closely related to daily activities of travelers. The current studies indicate that the law of network traffic flow evolution is day-to-day; therefore, using days as the scale unit is an important way to illustrate the evolution of network traffic flow. In previous studies, travelers in the network were tacitly assumed to be entirely rational. When the rationality of travelers is limited, the dynamics of the evolution law needs to be re-examined. This paper presents the utility maximization hypothesis in a logit model by using the bounded rationality hypothesis and develops a bounded rational binary logit (BRBL) model. We apply the BRBL model to a day-to-day network traffic flow distribution and discuss the evolution law of day-to-day network traffic flow under the assumption of the limited rationality of travelers. Through a numerical experiment, this paper analyzes the evolution characteristics of network traffic flow. The results are as follows. Firstly, the final state of the network traffic flow process is not only correlated to the cost-sensitivity of travelers and dependence on actual cost, but also strongly related to the degree of the nationality of travelers. Secondly, the system will be either bifurcated or chaotic when either cost-sensitivity increases or dependence on actual cost increases. Moreover, within the group of travelers whose rationality level is low, no matter what the cost-sensitivity of travelers and the dependence on actual cost are, the evolution results are asymptotically stable. Finally, in particular, in certain circumstances, it is easy to achieve stability when the rationallty degree of travelers is very high or very low, while it is not easy to achieve stability when the rationality degree of travelers is medium.