On a Computational Method for Two Asymmetric Parallel Queues

Abstract

This paper addresses a well-known problem in queuing theory: the asymmetric shortest queue problem. The system consists of two parallel queues fed by a common Poisson arrival stream with rate λ. Upon arrival, each customer joins the shortest queue and
remains there until being served. If the two queues have the same length, the arriving customer chooses the queue 1 with probability α and the queue 2 with probability 1−α. Service times are exponentially distributed, with rate μ₁ for the queue 1 and rate μ₂ for the queue 2. No jockeying is permitted between the two queues. An easy and efficient method is presented for computing the steady state solution of the system.