Analysis of the 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 length, he joins either queue with probability ½. We show that the stationary queue length distribution can be represented by an infinite sum of product form solutions, which satisfy nice recurrence relations. Due to the recurrence relations, the successive terms of the infinite sum are easily calculated. Moreover, the convergence of the infinite sum is exponentially fast and we provide bounds for the error of each partial sum. Based on these properties, a numerically highly attractive algorithm is obtained.