A Short-Term Throughput Measure for Communications with ARQ Protocols

The renewal-reward theorem has been widely used in the literature to provide the expected throughput of ARQ systems when the inter-arrival intervals between consecutive message acknowledgements (ACKs) are iid random variables. In cases however when the channel error probability may be allowed to vary with time the above approach cannot accurately estimate the desired throughput time-average. For such scenarios we propose a "short-term" measure for the expected throughput of ARQ systems up to some predefined number r of received ACKs and explicitly show that it converges asymptotically to the "long-term" renewal-reward result when r to infinity. A Maximum Zero-outage short-term Throughput (MZT
_s-t
) metric is further introduced. Its value is shown to be greater than the respective value (MZT
_l-t
) for the "longterm" case.We conclude that use of the renewal-reward theorem in cases of varying error probabilities may underestimate the maximum possible transmission rate and the short-term measure is more appropriate.