Towards Efficient, Stable, and Fair Random Access Networks: A Conjectural Equilibrium Approach

For wireless LANs, such as IEEE 802.11 networks, the channel utilization efficiency, the system stability, and the fairness of bandwidth allocation are three important criteria for designing medium access control (MAC) protocols. This paper aims to design a simple access mechanism optimized for all the aforementioned issues from a game theoretic perspective. In particular, this paper enables nodes to form simple internal belief functions on how their competitors would react to their transmission actions. The steady-state outcome of this multiuser interaction can be characterized as a conjectural equilibrium (CE). We propose a distributed algorithm, Conjecture-based Random Access (CBRA), which enables nodes to independently update their transmission probabilities based on their internal beliefs and local observations. For CBRA, we first derive the sufficient conditions that guarantee its local stability and global convergence. We analytically show that all the achievable operating points in the throughput region are essentially stable CE corresponding to different belief initializations. Moreover, we show that CBRA approximately achieves the weighted fairness for the nodes carrying different traffic classes. Numerical simulations verify that the system performance significantly outperforms existing protocols, such as the 802.11 DCF and the priority based fair medium access control (P-MAC) protocol, in terms of throughput, fairness, convergence, and stability.