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A load-balanced network with two servers. (English) Zbl 1017.90022
Summary: A load-balanced network with two queues $$Q_1$$ and $$Q_2$$ is considered. Each queue receives a Poisson stream of customers at rate $$l_i$$, $$i=1,2$$. In addition, a Poisson stream of rate $$l$$ 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 $$1-p_i^*$$, join the $$j$$th 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.

MSC:
 90B22 Queues and service in operations research
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