The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 27, Number 1 (1956), 147-161.
On the Characteristics of the General Queueing Process, with Applications to Random Walk
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.
Ann. Math. Statist., Volume 27, Number 1 (1956), 147-161.
First available in Project Euclid: 28 April 2007
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Kiefer, J.; Wolfowitz, J. On the Characteristics of the General Queueing Process, with Applications to Random Walk. Ann. Math. Statist. 27 (1956), no. 1, 147--161. doi:10.1214/aoms/1177728354. https://projecteuclid.org/euclid.aoms/1177728354