The Uniqueness of Stationary Distributions for the GI/G/S Queue

Kiefer and Wolfowitz (Kiefer, J., J. Wolfowitz. 1955. On the theory of queues with many servers. Amer. Math. Soc.78 1–18.) showed that there exists a unique proper stationary limiting distribution for the stochastic process representing the workload at arrival epochs in a multiple-server queue when the utilization per server is less than one. An alternate proof of the uniqueness is presented here which avoids using approximating discrete-state Markov chains.