Approximate disaggregation and performance bounds for queueing networks with multiple-server stations

Abstract

We introduce the concept of approximate disaggregation which enables us to replace a station by a subnetwork, i.e. a set of stations, such that the performance of the derived network is close to the performance of the initial network. We use this concept to disaggregate any multiple-server station into a set single-server stations. Using two different disaggregations, we are able to bound the performance of the initial network by the performance of a “lower” and an “upper” network each consisting of single-server stations, whose performance can in turn be bounded by the Balanced Job Bounds (or other known bounds). Several examples show the useful information provided by these bounds at a very low cost: for Κ stations and Ν customers, the computational complexity here is Ο ( Κ ) which is significantly less than the Ο ( ΚΝ 2 ) operations required for exact solution. Indeed, despite the multiple server stations, the computational complexity of our bounds is the same as that of Balanced Job Bounds.