Robustness of Q-ary collision resolution algorithms in random access systems

The throughput characteristics of a random access system (RAS) which uses Q-ary tree algorithms (where Q is the number of groups into which colliding users are split) of the Capetanakis–Tsybakov–Mikhailov–Vvedenskaya type are analyzed for an infinite population of identical users generating packets. In the standard model packets are assumed to be generated according to a Poisson process. In this paper we greatly relax this assumption and consider a rich class of Markovian arrival processes, which, in general, are non-renewal. This class of arrival processes is known to lend itself very well to modeling bursty and correlated arrival processes commonly arising in computer and communication applications. Blocked and grouped channel access protocols are considered in combination with Q-ary collision resolution algorithms that exploit either binary (“collision or not”) or ternary (“collision, success or idle”) feedback. For the resulting RASs the corresponding maximum stable throughput is determined. It is concluded that the resulting RASs maintain their good stability characteristics under the wide range of arrival processes considered, thereby further extending the theoretical foundations of tree algorithms.