Analysis of Dynamic Traffic Demand on a Paradoxical Phenomenon and Reachability With Input Constraints

Drivers in a traffic network behave selfishly so that they choose the paths to minimize their own travel time to destinations. Under the equilibrium of traffic flow distribution over paths, traffic network is not used efficiently, and there can be a paradoxical phenomenon in which an increase of traffic on a road can decrease the drivers' total travel time. Our contributions are that, on similar phenomenon, we provide analysis of converging points and some properties of equilibrium points on dynamic traffic demands. The properties are stability, price of anarchy and Pareto efficiency from the viewpoints of total average delay and total traffic demands on the network. Finally, we provide reachability analysis with some input constraints to the Pareto efficient traffic demands.