Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the inapproximability of M/G/K: whytwomoments of job size distribution arenotenough

On the inapproximability of M/G/K: whytwomoments of job size distribution arenotenough The M/G/K queueing system is one of the oldest models for multiserver systems and has been the topic of performance papers for almost half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (nonnumerical) approximations in the literature are based on (at most) the first two moments of the job size distribution. In this paper we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we provide a lower bound on the inapproximability ratio, which we refer to as “the gap.” This is the first such result in the literature to address “the gap.” The proof technique behind this result is novel as well and combines mean value analysis, sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into the effect of higher moments of the job size distribution on the mean waiting time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Queueing Systems Springer Journals

On the inapproximability of M/G/K: whytwomoments of job size distribution arenotenough

Download PDF
44 pages

Loading next page...
 
/lp/springer-journal/on-the-inapproximability-of-m-g-k-why-two-moments-of-job-size-83E1Prbx10

References (63)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Business and Management; Operation Research/Decision Theory; Computer Communication Networks; Probability Theory and Stochastic Processes; Supply Chain Management; Systems Theory, Control
ISSN
0257-0130
eISSN
1572-9443
DOI
10.1007/s11134-009-9133-x
Publisher site
See Article on Publisher Site

Abstract

The M/G/K queueing system is one of the oldest models for multiserver systems and has been the topic of performance papers for almost half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (nonnumerical) approximations in the literature are based on (at most) the first two moments of the job size distribution. In this paper we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we provide a lower bound on the inapproximability ratio, which we refer to as “the gap.” This is the first such result in the literature to address “the gap.” The proof technique behind this result is novel as well and combines mean value analysis, sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into the effect of higher moments of the job size distribution on the mean waiting time.

Journal

Queueing Systems – Springer Journals

Published: Aug 5, 2009

There are no references for this article.