A cost-effective approximation for SRD traffic in arbitrary multi-buffered networks
Abstract The question When may short range dependence (SRD) traffic be modelled by uncorrelated traffic with negligible error? is addressed in terms of performance metrics such as stationary queue length distribution (QLD), marginal blocking probability (BP) and mean queue length (MQL) for generic queueing network models (QNMs) of some multi-buffered communication systems such as asynchronous transfer mode (ATM) switch architectures and other high-speed networks with output port queueing. To this end, a cost-effective queue-by-queue decomposition algorithm is devised for the approximate analysis of arbitrary open first-come-first-served (FCFS) discrete-time QNMs with SRD arrivals, deterministic (D) service times, departure first (DF) buffer management simultaneity policy and repetitive service blocking with random destination (RS-RD). The shifted generalised geometric (sGGeo) batch renewal process, which exhibits geometrically declining count and interval covariances, is adopted to model external SRD traffic. To facilitate tractability with a tolerable accuracy and, thus, the understanding of the quantitative behaviour of SRD traffic in the interior of the network, the sGGeo process is approximated by an ordinary generalised geometric (GGeo) process whose first two moments of the count distribution match the corresponding first two sGGeo moments. Consequently, the sGGeo/D/1/N and GGeo/D/1/N queues, in conjunction with GGeo-type flow approximation formulae, play the role of analytic building blocks within the proposed decomposition scheme. Typical numerical tests are presented to (i) determine empirical conditions at a single queue level for there to be negligible approximation error in some performance metrics as a result of using a GGeo process in place of the sGGeo process, (ii) illustrate at a queueing network level the credibility of the decomposition algorithm via simulation and (iii) investigate the effect of external sGGeo-type traffic with varying degree of correlation upon network performance.