Stability of processor sharing networks with simultaneous resource requirements

Jennie Hansen, Cian Reynolds, Stan Zachary

Research output: Contribution to journalArticle

Abstract

We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to meet demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through poor control, and that, for a variety of network topologies, only small modifications to controls are required in order to ensure stability. For controls which possess a natural monotonicity property, we give some new results for the classification of the corresponding Markov processes, which lead to conditions both for stability and for instability. © Applied Probability Trust 2007.

Original languageEnglish
Pages (from-to)636-651
Number of pages16
JournalJournal of Applied Probability
Volume44
Issue number3
DOIs
Publication statusPublished - Sep 2007

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Markov processes
Topology
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Keywords

  • Entrainment
  • Processor sharing network
  • Stability

Cite this

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Stability of processor sharing networks with simultaneous resource requirements. / Hansen, Jennie; Reynolds, Cian; Zachary, Stan.

In: Journal of Applied Probability, Vol. 44, No. 3, 09.2007, p. 636-651.

Research output: Contribution to journalArticle

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AB - We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to meet demand, the requirement for simultaneous availability of resources means that a network may nevertheless be unstable. We show that instability occurs through poor control, and that, for a variety of network topologies, only small modifications to controls are required in order to ensure stability. For controls which possess a natural monotonicity property, we give some new results for the classification of the corresponding Markov processes, which lead to conditions both for stability and for instability. © Applied Probability Trust 2007.

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