BOUNDING THE STATIONARY DISTRIBUTION OF THE M/G/1 QUEUE SIZE-Reference-Cited by-同舟云学术

BOUNDING THE STATIONARY DISTRIBUTION OF THE M/G/1 QUEUE SIZE

Published:2006-09-19 Issue:4 Volume:20 Page:571-574
ISSN:0269-9648
Container-title:Probability in the Engineering and Informational Sciences
language:en
Short-container-title:Prob. Eng. Inf. Sci.

Author:

Ross Sheldon M.

Abstract

We start with a simple derivation of an identity connecting the conditional expected residual service time as seen by an arrival and the steady-state tail distribution function of the number of customers in the system, which was previously proven by Mandelbaum and Yechiali. We then show how to use it to obtain bounds on the the stationary distribution of the number of customers in the M/G/1 queue.

Publisher

Cambridge University Press (CUP)

Subject

Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability

Reference3 articles.

1. Shaked, M. & Shanthikumar, J.G. (1994).Stochastic orders and their applications.New York:Academic Press.

2. Mandelbaum, A. & Yechiali, U. (1979).Individual optimization in the M/GI/1queue, Appendix A.Technical Report,Department of Statistics, Tel Aviv University.

3. Fakinos, D. (1982).The expected remaining service time in a single server queue.Operations Research 30(5):1014–1017.

Cited by 4 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. Compound geometric approximation under a failure rate constraint;Journal of Applied Probability;2016-09

2. On the Stability of Random Multiple Access With Stochastic Energy Harvesting;IEEE Journal on Selected Areas in Communications;2015-03

3. Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service;Queueing Systems;2007-11-17

4. Stationary remaining service time conditional on queue length;Operations Research Letters;2007-09