Domains and Solutions of the Braess Paradox

The Braess paradox in road planning presents a case, where adding a new connection in a road network may lead to delayed arrival because of violation of the balance in the traffic flow. The paper discusses a generalization of this paradox. The initial, the asymmetrical, and the Pareto optimal domain are identified. Administrative solution with the participation of a controller is introduced, which aims to minimize the time of arrival, and thus has an environmental aspect. The preferences of the groups of passengers in the vehicles are modeled by an analytical arctan-approximated utility. Nash arbitration is employed to find an optimal solution that maximizes the Nash utility criterion. It is performed over the optimal Pareto domain that is outlined in four stages. A numerical example with 40 vehicles and five types of preferences of the passengers demonstrates the ideas.