Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T07:15:04.448Z Has data issue: false hasContentIssue false
  • English
  • Français

On the starshapeness of G/G/c queueing systems

Published online by Cambridge University Press:  01 July 2016

J. George Shanthikumar  and
Couchen Wu
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
Couchen Wu*
Affiliation:
University of California, Berkeley
*
∗Postal address: Walter A. Haas School of Business, University of California at Berkeley, Berkeley, CA 94720, USA.
∗∗Postal address: Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, CA 94720, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we show that the waiting and the sojourn times of a customer in a single-stage, multiple-server, G/G/c queueing system are increasing and starshaped with respect to the mean service time. Usefulness of this result in the design of the optimal service speed in the G/G/c queueing system is also demonstrated.

Keywords

SECOND-ORDER PROPERTIESSINGLE-STAGE QUEUEING SYSTEMSSTOCHASTIC STARSHAPENESSSTOCHASTIC CONVEXITYDESIGN
Type
Letter
Information
Advances in Applied Probability , Volume 23 , Issue 2 , June 1991 , pp. 431 - 435
Copyright
Copyright © Applied Probability Trust 1991 

Footnotes

Supported in part by NSF Grant ECS–8811234.

References

Harel, A. (1990) Convexity results for single-server queues and for multiserver queues with constant service times. J. Appl. Prob. 27, 465–468.CrossRefGoogle Scholar
LiYanage, L. and Shanthikumar, J. G. (1990) Second order properties of single stage queueing systems. Technical Report, Walter A. Haas School of Business, University of California, Berkeley, CA.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and its Applications . Academic Press, New York.Google Scholar
Meester, L. E. and Shanthikumar, J. G. (1990) Concavity of the throughput of tandem queueing systems with finite buffer storage space. Adv. Appl. Prob. 22, 764–767.Google Scholar
Shanthikumar, J. G. and Yao, D. (1988) Stochastic convexity and its applications in parametric optimization of queueing systems. Proc. 27th IEEE Conf. Decision and Control , Austin, TX, 657–662.CrossRefGoogle Scholar
Shanthikumar, J. G. and Yao, D. (1989) Second-order stochastic properties in queueing systems. Proc. IEEE 77, 162–170.Google Scholar
Shanthikumar, J. G. and Yao, D. (1991) Strong stochastic convexity: closure properties and applications. J. Appl. Prob. 28, 131–145.CrossRefGoogle Scholar
Tu, H. and Kumin, H. (1983) A convexity result for a class of GI/G/1 queueing systems. Operat. Res. 31, 948–950.Google Scholar
Weber, R. (1983) A note on waiting times in single server queues. Operat. Res. 31, 950–951.Google Scholar