Mathematics – Probability
Scientific paper
2003-12-17
Mathematics
Probability
A new preprint math.PR/0403538, has been written as a combined version of the present preprint and the preprint math.PR/031233
Scientific paper
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.
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