The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1-Reference-Cited by-同舟云学术

The distribution of the maximum number of customers present simultaneously during a busy period for the queueing systems M/G/1 and G/M/1

Published:1967-11 Issue:1 Volume:4 Page:162-179
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Cohen J. W.

Abstract

The distribution of the maximum number of customers simultaneously present during a busy period is studied for the queueing systems M/G/1 and G/M/1. These distributions are obtained by using taboo probabilities. Some new relations for transition probabilities and entrance time distributions are derived.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference3 articles.

1. Markov Chains with Stationary Transition Probabilities

2. On the maximum of the queue GI/M/1

Cited by 19 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Analyzing the Busy Period of the M/M/1 Queue via Order Statistics and Record Values;2021 11th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS);2021-09-22

2. FIRST-PASSAGE TIMES FOR SOME LINDLEY PROCESSES IN CONTINUOUS TIME;Sequential Analysis;2002-05-20

3. On extreme values of orbit lengths in $M/G/1$ queues with constant retrial rate;OR-Spektrum;2001-08

4. First exit times for integer valued continuous time markov chains;Sequential Analysis;2000-01

5. Some exact expressions for the bulk-arrival queue mx/M/1;Queueing Systems;1989-03