Limiting Distribution of the Asymmetric Shortest Queue Problem

摘要

In this paper, we consider a queueing system consisting of two parallel servers. Each server has its own queue with unlimited capacity. Customers arrive according to a Poisson stream and that service times have an arbitrary distribution function. An arriving customer joins the shortest queue and jockeying between the queues is not permitted. If both queues have equal length, the arrival joins the first queue with probability p (0 < p < 1), and the second one with probability 1 -p. By using Markov skeleton processes theory, we obtain the concrete formula and conditions for the existence of the limit distribution of the joint-queue length.