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Stability analysis of symmetrical two-route traffic flow with feedback information delay

Traffic information feedback strategies have the potential to improve the efficiency of traffic flow. There is a processing delay in providing the information, and the delay sometimes makes the traffic flow unstable. In this study, a relationship between the stability of traffic flow of the Symmetrical Two-Route with providing traffic information and the information delay is analyzed. The type of provided traffic information is vehicle number on each route. It is assumed that drivers choose one route by reference to the information. The dynamics of the traffic flow is described by the delay differential equation. By analyzing the equation, a sufficient condition for stability of the traffic flow is presented. Moreover, the validity of the condition is confirmed by numerical simulations using the Stochastic Optimal Velocity model, which is one of the realistic traffic models.