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

  • Authors:

  • Yves Dallery;Rajan Suri

  • Affiliations:

  • Harvard University, Division of Applied Sciences, Cambridge, MA;Harvard University, Division of Applied Sciences, Cambridge, MA

  • Venue:
  • SIGMETRICS '86/PERFORMANCE '86 Proceedings of the 1986 ACM SIGMETRICS joint international conference on Computer performance modelling, measurement and evaluation
  • Year:
  • 1986

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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 &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.