zbMATH — the first resource for mathematics

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.

90B22 Queues and service in operations research
Full Text: DOI