On Modeling Contention-Based MAC Protocols Using Markov Chains

Using discrete-time Markov chains to analyze the performance of contention-based medium access control (MAC) protocols has been a common practice since its initial proposal by Bianchi in his seminal paper published in 2000. The way these methods work is by modeling each individual node competing for the medium in a wireless network as a Markov chain. Performance metrics of the whole system, such as throughput, delays and losses, can then be obtained from the model. However, these methods implicitly assume that Markov chains modeling individual nodes are independent from each other, which is not necessarily true in most situations. In this work we propose a more realistic model in which the whole network with all of its nodes is modeled using a single Markov chain, and in which assuming independence is no longer necessary. We reduce the complexity of the problem, both in processing and memory requirements, by taking advantage of its inherent symmetry, which allows us to work with only a few selected representative states. We evaluate how results from both types of methods compare to each other and to simulations. Our findings show that the old method has a very poor performance as compared to the new one.