Delay analysis of selective repeat ARQ for a Markovian source over a wireless channel

In this paper, we analyze the mean delay experienced by a Markovian source over a wireless channel with time-varying error characteristics. The wireless link implements the selective-repeat automatic repeat request (ARQ) scheme for retransmission of erroneous packets. We obtain good approximations of the total delay, which consists of transport and resequencing delays. The transport delay, in turn, consists of queueing and transmission delays. In contrast to previous studies, our analysis accommodates both the inherent correlations between packet interarrival times (i.e., traffic burstiness) and the time-varying nature of the channel error rate. The probability generating function (PGF) of the queue length under the "ideal" SR ARQ scheme is obtained and combined with the retransmission delay to obtain the mean transport delay. For the resequencing delay, the analysis is performed under the assumptions of heavy traffic and small window sizes (relative to the channel sojourn times). The inaccuracy due to these assumptions is observed to be negligible. We show that ignoring the autocorrelations in the arrival process or the time-varying nature of the channel state can lead to significant underestimation of the delay performance, particularly at high channel error rates. Some interesting effects of key system parameters on the delay performance are observed.