Stability and performance of stack algorithms for random access communication modeled as a tree structured quasi birth–death Markov chain

In this paper, we introduce an analytical model to study the stability and the main performance measures of a binary stack algorithm for random multiple access communication. The input traffic is a discrete time Batch Markovian Arrival Process. The analytical model is nearly exact (one minor approximation is required) and the analysis is based on recent results obtained from tree structured Quasi-Birth–Death Markov chains. Apart from studying the stability of the protocol, we are also able to calculate the mean delay and other important performance measures. The method deployed in this paper can also be extended to evaluate other medium access control protocols with an underlying stack structure.