Delay analysis of the stop-and-wait ARQ protocol over a correlated error channel
Stijn De Vuyst, Sabine Wittevrongel, Herwig Bruneel · 2004
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. For the Stop-and-Wait protocol, no other packets are transmitted while the transmitter waits for a feedback message. We model the transmitter side as a discrete-time queue with infinite storage capacity and indepen-dent 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. Our analysis is based on the use of probability generating functions (pgf) and is exact at the packet level. 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 in the analysis by means of some numerical examples. 1