M/G/∞M/G/∞ transience, and its applications to overload detection

When controlling communication networks, it is of crucial importance to have procedures that are capable of checking whether there are unanticipated load changes. In this paper we develop techniques for detecting such load changes, in a setting in which each connection consumes roughly the same amount of bandwidth (with VoIP as a leading example). For the situation of exponential holding times an explicit analysis can be performed in a large-deviations regime, leading to approximations of the test statistic of interest (and, in addition, to results for the transient of the M/M  /∞∞ queue, which are of independent interest). Since this procedure is applicable to exponential holding times only, and is rather numerically involved, we develop an approximate procedure for general holding times. In this procedure we record the number of trunks occupied at equidistant points in time Δ,2Δ,…Δ,2Δ,…, where ΔΔ is chosen sufficiently large to safely assume that the samples are independent; this procedure is backed by results on the transient of the M/G/∞M/G/∞ queue, thus complementing earlier results on relaxation times. The validity of the testing procedures is demonstrated through an extensive set of numerical experiments.