RT Journal Article
SR 00
ID 10.1214/20-AAP1609
A1 Castiel, Eyal
A1 Borst, Sem
A1 Miclo, Laurent
A1 Simatos, Florian
A1 Whiting, Phil
T1 Induced idleness leads to deterministicheavy traffic limits for queue-basedrandom-access algorithms
JF Annals of Applied Probability
YR 2021
FD 2021-04
VO vol. 31
IS n°2
SP 941
OP 971
AB 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.
PB Institute of Mathematical Statistics
SN 1050-5164
LK https://publications.ut-capitole.fr/id/eprint/42349/
UL http://tse-fr.eu/pub/125191