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On the Characteristics of the General Queueing Process, with Applications to Random Walk
J. Kiefer and J. Wolfowitz
The Annals of Mathematical Statistics
Vol. 27, No. 1 (Mar., 1956), pp. 147-161
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2236981
Page Count: 15
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The authors continue the study (initiated in ) of the general queueing process (arbitrary distributions of service time and time between successive arrivals, many servers) for the case $(\rho < 1)$ where a limiting distribution exists. They discuss convergence with probability one of the mean waiting time, mean queue length, mean busy period, etc. Necessary and sufficient conditions for the finiteness of various moments are given. These results have consequences for the theory of random walk, some of which are pointed out. This paper is self-contained and may be read independently of ; the necessary results of  are quoted. No previous knowledge of the theory of queues is required for reading either  or the present paper.
The Annals of Mathematical Statistics © 1956 Institute of Mathematical Statistics