Aggregation of stations in queueing network models of multiprogrammed computers

  • Authors:

  • Alexander Thomasian;Behzad Nadji

  • Affiliations:

  • Department of Electrical Engineering - Systems, University of Southern California, Los Angeles, California;Department of Electrical Engineering - Systems, University of Southern California, Los Angeles, California

  • Venue:
  • SIGMETRICS '81 Proceedings of the 1981 ACM SIGMETRICS conference on Measurement and modeling of computer systems
  • Year:
  • 1981

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Abstract

In queueing network models the complexity of the model can be reduced by aggregating stations. This amounts to obtaining the throughput of the flow-equivalent station for the subnetwork of stations to be aggregated. When the subnetwork has a separable solution, aggregation can be carried out using the Chandy-Herzog-Woo theorem. The throughput of the subnetwork can be expressed explicitly in terms of its parameters when the stations are balanced (have equal utilizations). This expression for throughput can be used as an approximation when the stations are relatively unbalanced. The basic expression can be modified to increase the accuracy of the approximation. A generating function approach was used to obtain upper bounds on the relative error due to the basic approximation and its modifications. Provided that the relative error bound is tolerable, a set of unbalanced stations can be replaced by a single aggregate station or a set of balanced stations. Finally, we propose a methodology to simplify the queueing network model of a large-scale multiprogrammed computer, which makes use of the previous aggregation results.