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On extremal service disciplines in single-stage queueing systems

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter ,
J. George Shanthikumar  and
Genji Yamazaki
Rhonda Righter*
Affiliation:
Santa Clara University
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
Genji Yamazaki*
Affiliation:
Tokyo Metropolitan Institute of Technology
*
∗Postal address: Department of Decision and Information Sciences, Santa Clara University, Santa Clara, CA 95053, USA.
∗∗Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
∗∗∗Postal address: Department of Engineering Management, Tokyo Metropolitan Institute of Technology, Hino City, Tokyo 191, Japan.
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Abstract

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

Keywords

SINGLE-SERVER QUEUEFCFSLAST SERVICE DISCIPLINESNBUEDMRL SERVICE TIMESCONSERVATION IDENTITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 409 - 416
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Supported in part by NSF under grant ECS-8811234.

References

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