A Load-Balanced Network with Two Servers

Authors:
I. A. Kurkova
Affiliations:
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, B.C.188, 4, place Jussieu, 75252 Paris cedex 05, France kourkova@ccr.jussieu.fr
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Proceedings of the 5th International Conference on Queueing Theory and Network Applications

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Abstract

A load-balanced network with two queues Q1 and Q2 is considered. Each queue receives a Poisson stream of customers at rate λi, i=1,2. In addition, a Poisson stream of rate λ arrives to the system; the customers from this stream join the shorter of two queues. After being served in the ith queue, i=1,2, customers leave the system with probability 1−pi*, join the jth queue with probability p(i,j), j=1,2, and choose the shortest of two queues with probability p(i,{1,2}). We establish necessary and sufficient conditions for stability of the system.