2003/12/17 by Carl Graham, Graham, Carl
Business, Management and Accounting · Mathematics · Physics and Astronomy · #60K25 #60K35 #Advanced Queuing Theory Analysis #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60K25 #msc:60K35
paper · pdf · doi:10.48550/arxiv.math/0312335
A new preprint math.PR/0403538, has been written as a combined version of the present preprint and the preprint math.PR/0312334. It is recommended to read the new combined version instead of the two others
openalex publication_date 2003/12/17 · arxiv created 2004/03/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.