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

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.

Replaced by

Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos, and Phil Whiting, “Induced idleness leads to deterministicheavy traffic limits for queue-basedrandom-access algorithms”, Annals of Applied Probability, vol. 31, n. 2, April 2021, pp. 941–971.

Reference

Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos, and Phil Whiting, “Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms”, TSE Working Paper, n. 20-1129, August 2020.