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




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1 CMAP - Centre de Mathématiques Appliquées

Abstract : 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.

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





Author: Carl Graham -

Source: https://hal.archives-ouvertes.fr/



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