Chaotic behavior in the dynamical evolution of network traffic flow and its control

Abstract

This paper presents the day-to-day dynamic evolution of network traffic flow in a simple two-route network. Firstly, a day-to-day dynamical assignment model is formulated, which can depict the evolution of network traffic flow. We have proved that the fixed point of the dynamical system, which is the stochastic user equilibrium solution, exists and is unique. Secondly, based on nonlinear dynamics theory, an equilibrium stability condition for the network is derived. Moreover, the evolution of network traffic flow is investigated through numerical experiments. Meanwhile, periodic and chaotic flows are discovered under certain conditions. Finally, a chaotic control method is derived considering OD demand as control variable.