Delay-Based Network Utility Maximization

It is well known that max-weight policies based on a queue backlog index can be used to stabilize stochastic networks, and that similar stability results hold if a delay index is used. Using Lyapunov Optimization, we extend this analysis to design a utility maximizing algorithm that uses explicit delay information from the head-of-line packet at each user. The resulting policy is shown to ensure deterministic worst-case delay guarantees, and to yield a throughput-utility that differs from the optimally fair value by an amount that is inversely proportional to the delay guarantee. Our results hold for a general class of 1-hop networks, including packet switches and multi-user wireless systems with time varying reliability.