Analysis of the symmetric shortest queue problem

In this paper we study a system consisting of two identical servers, each with exponentially distributed service times. Jobs arrive according to a Poisson stream. On arrival a job joins the shortest queue and in case both queues have equal lengths, he joins either queue with probability 1/2. By using a compensation method, we show that the stationary queue length distribution can be expressed as an infinite linear combination of product forms. Explicit relations are found for these product forms, as well as for the coefficients in the linear combination. These analytic results offer an elegant and efficient numerical algorithm, with effective bounds on the error of each partial sum.