A two-phase utility maximization framework for wireless medium access control

In multi-hop wireless networks, the optimal medium access control (MAC) design is challenging, partially due to the time-varying nature of the PHY-layer communication channels and the network topology. In this paper, we take a utility maximization approach to study fair MAC design towards QoS provisioning. To this end, we first identify two key challenges of wireless access control, namely the topology dependency and the channel dependency therein. Based on the observation that the topology change and channel variation occur on different time scales, we decompose the utility maximization to two phases: a "global" optimization phase addresses the topology dependency, and arbitrates fair channel access across the links by adapting the persistence probability to achieve long-term fairness, and a "local" optimization phase deals with the channel dependence, and determines the transmission duration based on local channel conditions while maintaining short-term fairness. Observing that the MAC throughput depends on the realizations of channel contention in random access networks, we use stochastic approximation to investigate in depth the MAC design with the adaptive persistence mechanism in the global phase. Using Lyapunov's Stability Theorems and LaSalle's Invariance Theorem, we establish the stability of the proposed algorithm for the global phase and analyze the fairness under (w→, κ)-fair utility functions. Our findings reveal that under the large network assumption, there exists a single equilibrium point for the proposed (w→, κ)-fair MAC algorithm provided that κ > 1. We also present the solution to the local optimization phase under general fairness constraints.