Résumé
We examine a queue-based random-access algorithm where ac-tivation 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 dependson some parameter of the algorithm and is not theN/N2scaling usuallyfound in functional central limit theorems; (2) the heavy traffic limit isdeterministic. We discuss how this nonstandard behavior arises from theidleness induced by the distributed nature of the algorithm. In order toprove our main result, we develop a new method for obtaining a fully cou-pled stochastic averaging principle.
Remplace
Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos et Phil Whiting, « Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms », TSE Working Paper, n° 20-1129, août 2020.
Référence
Eyal Castiel, Sem Borst, Laurent Miclo, Florian Simatos et Phil Whiting, « Induced idleness leads to deterministicheavy traffic limits for queue-basedrandom-access algorithms », Annals of Applied Probability, vol. 31, n° 2, avril 2021, p. 941–971.
Voir aussi
Publié dans
Annals of Applied Probability, vol. 31, n° 2, avril 2021, p. 941–971