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April 2021 Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms
Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos, Phil Whiting
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Ann. Appl. Probab. 31(2): 941-971 (April 2021). DOI: 10.1214/20-AAP1609

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.

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Eyal Castiel. Sem Borst. Laurent Miclo. Florian Simatos. Phil Whiting. "Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms." Ann. Appl. Probab. 31 (2) 941 - 971, April 2021. https://doi.org/10.1214/20-AAP1609

Information

Received: 1 February 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1609

Subjects:
Primary: 60K25
Secondary: 60K35

Keywords: CSMA algorithms , state space collapse , stochastic averaging principle

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2021
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