Asymptotic analysis of queueingnetworks

Abstract

This paper presents limit theorems for the vector queue length process associated with a closed queueing network as the total number of customers n goes to infinity. The first theorem states that the queue process normalized by the factor n-1converges in probability as n → x to a deterministic function which can be characterized as the unique solution of a certain differential inclusion. The second theorem gives an approximation via reflected diffusion process for the sequence of deviations of normalized queue length process from the deterministic limit, expanded by nl2

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