Approximate analysis of networks of PH|PH|1|K queues with customer losses: Test results

We address the approximate analysis of large, open networks of general finite-buffer queues. We start from the analysis of large, open infinite-buffer queueing networks (QNs), as proposed by Kühn and later extended by Whitt, in which large QNs are decomposed into a number of individual GI|G|1 queues, characterized by the first and second moment of the service and interarrival time distribution. We restrict ourselves by focusing on PH|PH|1 queues for which matrix-geometric and general Markovian techniques can be used, and allow for the inclusion of finite-buffers, i.e. we address networks of PH|PH|1|K queues in which customers arriving at completely filled queues are lost. In doing so, the above decomposition can not be done in a single step but should be done iteratively, i.e. we propose a fixed-point scheme for the solution of networks of PH|PH|1|K queues. In this paper we focus on the accuracy of the fixed-point approach. To keep the current paper self-contained, we describe the theory as well. We have tested our approach on a large set of examples and compared the results with simulations. It turns out that our approach does not only yield accurate results (mostly within a few percent of simulation results) but is also very fast in obtaining them (in comparison with simulation). To the best of our knowledge, it is currently the only approach for analysing large networks of finite-buffer PH|PH|1|K queues.