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Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms

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  • Castiel, Eyal
  • Borst, Sem
  • Miclo, Laurent
  • Simatos, Florian
  • Whiting, Phil

Abstract

We examine a queue-based random-access algorithm where activation and deactivation rates are adapted as functions of queue lengths. We establish its heavy traffic behavior on a complete interference graph, which turns out to be nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the N/N2 scaling usually found in functional central limit theorems; (2) the heavy traffic limit is deterministic. We discuss how this nonstandard behavior arises from the idleness induced by the distributed nature of the algorithm. In order to prove our main result, we develop a new method for obtaining a fully coupled stochastic averaging principle.

Suggested Citation

  • Castiel, Eyal & Borst, Sem & Miclo, Laurent & Simatos, Florian & Whiting, Phil, 2020. "Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms," TSE Working Papers 20-1129, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:124587
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    References listed on IDEAS

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    2. Ohad Perry & Ward Whitt, 2013. "A Fluid Limit for an Overloaded X Model via a Stochastic Averaging Principle," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 294-349, May.
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    6. Otis B. Jennings, 2010. "Averaging Principles for a Diffusion-Scaled, Heavy-Traffic Polling Station with K Job Classes," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 669-703, August.
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