NDLI: Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

Content Provider	Springer Nature Link
Author	Cheung, Sing Kong Berg, Hans Boucherie, Richard J.
Copyright Year	2006
Abstract	This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads to insensitive upper bounds requiring only knowledge of the traffic intensity and the initial job size. Interestingly, the upper bounds involve polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained.
Starting Page	7
Ending Page	18
Page Count	12
File Format	PDF
ISSN	02570130
Journal	Queueing Systems
Volume Number	53
Issue Number	1-2
e-ISSN	15729443
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	M/G/1 PS Conditional sojourn time Moments Insensitive bounds Instantaneous sojourn time Euler's number triangle Moment ordering Permanent customers Computer Communication Networks Systems Theory, Control Probability Theory and Stochastic Processes Operations Research/Decision Theory Production/Logistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Management Science and Operations Research Computational Theory and Mathematics Computer Science Applications

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Explicit formulas for the moments of the sojourn time in the m/g/1 processor sharing queue with permanent jobs (2005).

Insensitive Bounds for the Moments of the Sojourn Times in M/GI Systems Under State-Dependent Processor Sharing

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Explicit formulas for the moments of the sojourn time in the M/G/1 processor sharing queue with permanent jobs

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Explicit formulas for the moments of the sojourn time in the M/G/1 processor sharing queue with permanent jobs

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