Price of Anarchy in mmWave Backhaul Routing and Link Scheduling

In this paper we present and evaluate the performance of a routing and link scheduling algorithm for millimeter wave backhaul networks. The proposed algorithm models the access point behavior as being selfish by considering access points always aiming to maximize their individual utility, rather than the global optimization objective. Our system utilizes popular concepts from the economics and fairness literature. Specifically, in order to forward packets between the access points that comprise the backhaul network, the Shapley value method is applied, which is shown to induce solutions with reduced latency. The performance of the proposed algorithm is evaluated in terms of total delay and price of anarchy, which represents the inefficiency of a scheduling policy when users are allowed to adapt their rates in a selfish manner and reach an equilibrium. A relaxed version of the problem is also presented, providing a lower bound on the value of the optimal solution. According to simulation results, the system that employs the proposed algorithm outperforms in terms of delay and price of anarchy a system that considers a First-In-First-Out packet forwarding policy, and a system that employs local search global optimization, under which users aim at optimizing the overall network delay.