A NOTE ON BOUNDS AND ERROR-BOUNDS FOR NONEXPONENTIAL BATCH ARRIVAL SYSTEMS

This note studies the comparison of finite-buffer and nonexponential b atch arrival systems of the form G(X)/M/c/c + N with the corresponding Systems, with N replaced by N', where N' can be smaller, larger, or i nfinite. If N' = infinity the service times can be arbitrarily distrib uted. Both comparison and error bounds are obtained for performance me asures such as the throughput, the idle probability, and the active se rver distribution. The results are of practical interest to establish computational reductions, either by infinite-space approximation or by reduced finite truncations. Two different proof techniques will be em ployed: the sample path approach and the Markov reward approach. The c omparison of these two techniques is of interest in itself, showing th e advantage and disadvantage of each.