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The completion time of a job on multimode systems

Published online by Cambridge University Press:  01 July 2016

V. G. Kulkarni ,
V. F. Nicola  and
K. S. Trivedi
V. G. Kulkarni*
Affiliation:
University of North Carolina, Chapel Hill
V. F. Nicola*
Affiliation:
University of North Carolina, Chapel Hill
K. S. Trivedi*
Affiliation:
Duke University
*
∗Postal address: Department of Operations Research, University of North Carolina, Chapel Hill, NC 27514, USA.
∗∗Postal address: Department of Computer Science, Duke University, Durham, NC 27706, USA.
∗∗Postal address: Department of Computer Science, Duke University, Durham, NC 27706, USA.
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Abstract

In this paper we present a general model of the completion time of a single job on a computer system whose state changes according to a semi-Markov process with possibly infinite state-space. When the state of the system changes the job service is preempted. The job service is then resumed or restarted (with or without resampling) in the new state at, possibly, a different service rate. Different types of preemption disciplines are allowed in the model. Successive aggregation and transform techniques are used to obtain the Laplace–Stieltjes transform of the job completion time. We specialize to the case of Markovian structure-state process. We demonstrate the use of the techniques developed here by means of two applications. In the first we derive the distribution of the response time in an M/M/1 queueing system under the processor-sharing discipline (PS). In the second we derive the distribution of the completion time of a job when executed on a system subject to mixed types of breakdowns and repair.

Keywords

SEMI-MARKOV CHAINSPERFORMANCE OF MULTISTATE COMPUTER SYSTEMSFAILURE–REPAIR MODELSPRE-EMPTIONSJOB COMPLETION
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 932 - 954
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported in part by the Air Force Office of Scientific Research under grants AFOSR-86–0132 and AFOSR-84–0140, by the Army Research Office under contract DAAG29–84–0045 and by the National Science Foundation under grant MCS-830200.

References

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