From Local to Global Stability in Stochastic Processing Networks Through Quadratic Lyapunov Functions

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We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes jobs that have been least routed through the network. We show that the network is globally stable under this policy if there exists an appropriate quadratic local Lyapunov function that provides a negative drift with respect to nominal loads at servers. Applying this generic framework, we obtain stability results for our policy in many important examples of stochastic processing networks: open multiclass queueing networks, parallel server networks, networks of input-queued switches, and a variety of wireless network models with interference constraints. Our main novelty is the construction of an appropriate global Lyapunov function from quadratic local Lyapunov functions, which we believe to be of broader interest.
Publisher
INFORMS
Issue Date
2013-11
Language
English
Article Type
Article
Citation

MATHEMATICS OF OPERATIONS RESEARCH, v.38, no.4, pp.638 - 664

ISSN
0364-765X
DOI
10.1287/moor.2013.0588
URI
http://hdl.handle.net/10203/202762
Appears in Collection
EE-Journal Papers(저널논문)
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