The throughput characteristics of contention-based random access channels which use Q-ary splitting algorithms (where Q is the number of groups into which colliding users are split) are analyzed. The algorithms considered are of the Capetanakis-Tsybakov- Mikhailov-Vvedenskaya (CTMV) type and are studied for infinite populations of identical users generating packets according to a discrete time batch Markovian arrival process (D-BMAP). D-BMAPs are a class of tractable Markovian arrival processes, which, in general, are non-renewal. Free channel-access is assumed in combination with Q-ary collision resolution algorithms that exploit either binary or ternary feedback. For the resulting schemes, tree structured Quasi-Birth-Death (QBD) Markov chains are constructed and their stability is determined. The maximum achievable throughput is determined for a variety of arrival processes and splitting factors Q. It is concluded that binary (Q=2) and ternary (Q=3) algorithms should be preferred above other splitting factors Q as the throughput for Q > 3 quickly degrades when subject to bursty arrival streams. If packets arrivals are correlated and bursty, higher throughput rates can be achieved by making use of biased coins.
"Throughput of Q-Ary Splitting Algorithms for Contention Resolution in Communication Networks." Commun. Inf. Syst. 4 (2) 135 - 164, 2004.