approximate disaggregation and performance bounds for queueing networks with multiple-server stations
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 &Kgr; stations and &Ngr; customers, the computational complexity here is &Ogr; ( &Kgr; ) which is significantly less than the &Ogr; ( &Kgr;&Ngr; 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.
approximate disaggregation performance bounds closed queueing networks product form networks