Lateness probability of a retransmission scheme for error control on a two-state Markov channel

In this paper, we study the performance of a simple retransmission-based error-control strategy for delay-constrained data communications over a bursty channel. Correlated errors are modeled as a two state Markov process. A retransmission algorithm is used to correct errors, and the probability that a packet is not successfully delivered within D slots of its arrival is computed. In the presence of a smoothing buffer at the receiver, this is the probability that the jitter experienced by a packet is too large to be absorbed by the buffer itself. The cases of zero and nonzero roundtrip delay are studied separately, as are the conditions of perfect and imperfect feedback. Our results relate the achievable quality of service and the amount of traffic that can be served to the packet-error process parameters, which in turn are induced by the physical layer specifications. This relationship between the traffic and the channel parameters can be useful in making admission control decisions and in assessing the effect of physical layer design on the performance of higher layer protocols.