Analysis of Stop-and-Wait ARQ for a wireless channel

In this paper, we study the behavior of the transmitter buffer of a system working under a Stop-and-Wait retransmission protocol. The buffer at the transmitter side is modeled as a discrete-time infinite-capacity queue. The numbers of information packets entering the buffer during consecutive slots are assumed to be independent and identically distributed random variables. The packets are sent over an unreliable channel and transmission errors occur in a correlated manner. Specifically, the probability of an erroneous transmission is modulated by a two-state Markov chain. An expression is derived for the probability generating function of the buffer content. This expression is then used to derive several queue-length characteristics and the mean packet delay. Numerical examples illustrate the strong effect of error correlation on the system performance. The obtained analytical results are also compared with appropriate simulations.