A load-balanced network with two servers

A load-balanced network with two queues Q(1) and Q(2) is considered. Each queue receives a Poisson stream of customers at rate lambda (i), i = 1, 2. In addition, a Poisson stream of rate lambda 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 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.