Equilibrium with predictive routeing in the online version of the Braess paradox

The agents of a distributed adaptive system perceive the current state of their environment and make decisions which action to perform. The actions are both reactive and proactive. Reactivity can be supported by the availability of real-time data and proactivity can be supported by anticipatory techniques. Recent investigations proved that if the agents use selfish strategy, then in some situations sometimes the system maybe worst off with real-time data than without real-time data, even if anticipatory techniques are applied to predict the future state of the environment. This study investigates that version of the Braess paradox, where each subsequent agent of the flow may select a different route, using real-time data and anticipatory techniques. The authors contribute to the state-of-the-art by proving that the traffic distribution in this Braess paradox approximates the Nash equilibrium.