Queueing delay of Stop-and-Wait ARQ over a wireless Markovian channel

In this paper, we present the analysis of the Stop-and-Wait ARQ (Automatic Repeat reQuest) protocol with the notable complication that the transmission errors occur in a bursty, correlated manner. Fixed-length packets of data are sent from transmitter to receiver over an error-prone channel. The receiver notifies the transmitter whether a packet was received correctly or not by returning a feedback message over the backward channel. If necessary, the packet is retransmitted until it is received correctly, after which the transmission of another packet starts. We model the transmitter side as a discrete-time queue with infinite storage capacity and independent and identically distributed (iid) packet arrivals. Arriving packets are stored in the queue until they are successfully transmitted over the channel. The probability of an erroneous transmission is modulated by a two-state Markov Chain, rather than assuming stationary channel errors. In previous work we have analysed the queue content distribution of the transmitter, while in the present paper, we give an intuitive derivation of the throughput of the system and the distribution of the packet delay. For the latter, we use the spectral decomposition theorem from linear algebra and give an accurate approximation for the asymptotic behaviour. Finally, we illustrate the importance of accounting for the error correlation by means of some numerical examples