Poly-symmetry in processor-sharing systems

Thomas Bonald (), Céline Comte (), Virag Shah () and Gustavo Veciana ()
Additional contact information
Thomas Bonald: Télécom ParisTech
Céline Comte: Télécom ParisTech
Virag Shah: Microsoft Research - Inria Joint Centre
Gustavo Veciana: The University of Texas at Austin

Queueing Systems: Theory and Applications, 2017, vol. 86, issue 3, No 7, 327-359

Abstract: 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; 60K25 Queueing theory, 68M20 Performance evaluation; Queueing; Scheduling, 90B15 Network models, stochastic (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11134-017-9525-2

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