QNAUT: approximately analyzing networks of PH|PH|1|K queues

With QNAUT we can perform the (approximate) analysis of possibly large, open networks of PH|PH|1 and PH|PH|1|K queues. Since up till now there are no exact means available to study such queueing networks (QNs), the approach supported by QNAUT is currently the best alternative. Starting point of our approach is the analysis of large open QNs as proposed by W. Whitt (known as QNA) in which large QNs are decomposed into individual GI|G|1 queues, characterized by the first and second moments of the service and interarrival time distributions. In order to come to this decomposition, the first- and second-order traffic (flows) equations need to be solved. The first-order equations are well-known and also normally solved when addressing Jackson networks, however, the second-order equations require the investigation of the joint effect of interarrival time variability, queue utilization and service time variability. Once solved, the latter equations provide the second moments of the job streams between queues. On the basis of these results, individual nodes can then be analyzed using the Kramer and Langenbach-Belz approximation for GI|G|1 queues.