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

Eyal Castiel (1) , Sem Borst (2) , Laurent Miclo (3) , Florian Simatos (1) , Philip Whiting (4)

1 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace
2 Department of mathematics and computing science [Eindhoven]
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 Macquarie University

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 highly nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the $N/N^2$ 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 developed a new method for obtaining a fully coupled stochastic averaging principle.

Domaines: Probabilités [math.PR]

Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos, Philip Whiting. Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms. 2019. ⟨hal-02093957⟩