Retransmissions over correlated channels.

Frequent failures characterize many existing communication networks, e.g. wireless ad-hoc networks, where retransmission- based failure recovery represents a primary approach for successful data delivery. Recent work has shown that retransmissions can cause power law delays and instabilities even if all traffic and network characteristics are super-exponential. While the prior studies have considered an independent channel model, in this paper we extend the analysis to the practically important dependent case. We use modulated processes, e.g. Markov modulated, to capture the channel dependencies. We study the number of retransmissions and delays when the hazard functions of the distributions of data sizes and channel statistics are proportional, conditionally on the channel state. Our results show that the tails of the retransmission and delay distributions are asymptotically insensitive to the channel correlations and are determined by the state that generates the lightest asymptotics. This insight is beneficial both for capacity planning and channel modeling since we do not need to account for the correlation details. However, these results may be overly optimistic when the best state is infrequent, since the effects of 'bad' states may be prevalent for sufficiently long to downgrade the expected performance.