Queueing Systems

, Volume 86, Issue 3–4, pp 327–359 | Cite as

Poly-symmetry in processor-sharing systems

  • Thomas Bonald
  • Céline Comte
  • Virag Shah
  • Gustavo de Veciana
Article

Abstract

We consider a system of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and Pareto-efficient in such systems, which ensures that the performance metrics, when computable, will provide robust insights into the real performance of the system considered. We first show that these performance metrics can be evaluated with a complexity that is polynomial in the system size if the system is partitioned into a finite number of parts, so that queues are exchangeable within each part and asymmetric across different parts. This in turn allows us to derive stochastic bounds for a larger class of systems which satisfy less restrictive symmetry assumptions. These results are applied to practical examples of tree data networks, such as backhaul networks of Internet service providers, and computer clusters.

Keywords

Processor-sharing queueing systems Performance Balanced fairness Poly-symmetry 

Mathematics Subject Classification

60K25 Queueing theory 68M20 Performance evaluation; Queueing; Scheduling 90B15 Network models, stochastic 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Thomas Bonald
    • 1
  • Céline Comte
    • 1
  • Virag Shah
    • 2
  • Gustavo de Veciana
    • 3
  1. 1.Télécom ParisTechParisFrance
  2. 2.Microsoft Research - Inria Joint CentrePalaiseauFrance
  3. 3.Department of ECEThe University of Texas at AustinAustinUSA

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