Performance of random medium access control, an asymptotic approach

Random Medium-Access-Control (MAC) algorithms have played an increasingly important role in the development of wired and wireless Local Area Networks (LANs) and yet the performance of even the simplest of these algorithms, such as slotted-Aloha, are still not clearly understood. In this paper we provide a general and accurate method to analyze networks where interfering users share a resource using random MAC algorithms. We show that this method is asymptotically exact when the number of users grows large, and explain why it also provides extremely accurate performance estimates even for small systems. We apply this analysis to solve two open problems: (a) We address the stability region of non-adaptive Aloha-like systems. Specifically, we consider a fixed number of buffered users receiving packets from independent exogenous processes and accessing the resource using Aloha-like algorithms. We provide an explicit expression to approximate the stability region of this system, and prove its accuracy. (b) We outline how to apply the analysis to predict the performance of adaptive MAC algorithms, such as the exponential back-off algorithm, in a system where saturated users interact through interference. In general, our analysis may be used to quantify how far from optimality the simple MAC algorithms used in LANs today are, and to determine if more complicated (e.g. queue-based) algorithms proposed in the literature could provide significant improvement in performance.