Stability of processor sharing networks with simultaneous resource requirements

Details Stability of processor sharing networks with simultaneous resource requirements Stability of processor sharing networks with simultaneous resource requirements

2006-05-17

arxiv.org/abs/math/0605477v2

Mathematics

Probability

minor revisions - corresponds to published version

Scientific paper

We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to met 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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