Out of equilibrium functional central limit theorems for a large network where customers join the shortest of several queues

Carl Graham (1)

1 CMAP - Centre de Mathématiques Appliquées

Customers arrive at rate N times alpha on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate beta. We let N go to infinity.We prove a functional central limit theorem (CLT) for the tails of the empirical measures of the queue occupations,in a Hilbert space with the weak topology, with limit given by an Ornstein-Uhlenbeck process. The a priori assumption is that the initial data converge.This completes a recent functional CLT in equilibrium result for which convergence for the initial data was not known in advance, but was deduced a posteriori from the functional CLT.

Mots clés: Mean-field interaction; non-equilibrium fluctuations; inhomogeneous Ornstein-Uhlenbeck process in Hilbert space; infinite-dimensional analysis

Domaines: Probabilités [math.PR]

Carl Graham. Out of equilibrium functional central limit theorems for a large network where customers join the shortest of several queues. 2004. ⟨hal-00000958v2⟩