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Stability of Processor Sharing Networks with Simultaneous Resource Requirements

  • Jennie Hansen (a1), Cian Reynolds (a1) and Stan Zachary (a1)

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.

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Copyright

Corresponding author

Postal address: Actuarial Mathematics and Statistics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
∗∗ Email address: jhansen@ma.hw.ac.uk

References

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