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.