## The Annals of Mathematical Statistics

### On the Characteristics of the General Queueing Process, with Applications to Random Walk

#### Abstract

The authors continue the study (initiated in [1]) 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 [1]; the necessary results of [1] are quoted. No previous knowledge of the theory of queues is required for reading either [1] or the present paper.

#### Article information

Source
Ann. Math. Statist., Volume 27, Number 1 (1956), 147-161.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177728354

Digital Object Identifier
doi:10.1214/aoms/1177728354

Mathematical Reviews number (MathSciNet)
MR77019

Zentralblatt MATH identifier
0070.36602

JSTOR