Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
EnglishFrançais
Advances in Applied Probability Advances in Applied Probability

Article contents

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

Gideon Weiss
Gideon Weiss
Affiliation:
Georgia Tech
Get access
Rights & Permissions[Opens in a new window]

Abstract

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

Keywords

STOCHASTIC PROCESSING TIMES HOLDING COSTS GITTINS PRIORITY RULE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B35: Scheduling theory, deterministic 90C40: Markov and semi-Markov decision processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 821 - 839
Copyright
Copyright © Applied Probability Trust 1995 

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

Footnotes

Research supported by NSF grants DDM-8914863 and DDM-9215233, and the fund for the promotion of research at the Technion.

References

[1] Bruno, J., Downey, P. and Frederickson, G. (1981) Sequencing tasks with exponential service times to minimize the expected flowtime or makespan. J. ACM 28, 100–113.CrossRefGoogle Scholar
[2] Chazan, D., Konheim, A. G. and Weiss, B. (1968) A note on time sharing. J. Combinatorial Theory 5, 344–369.CrossRefGoogle Scholar
[3] Coffman, E. G., Hofri, M. and Weiss, G. (1989) Scheduling stochastic jobs with a two point distribution on two parallel machines. Prob. Eng. Inf. Sci. 3, 89–116.CrossRefGoogle Scholar
[4] Gittins, J. (1979) Bandit processes and dynamic allocation indices. J. R. Statist. Soc. B 14, 148–167.Google Scholar
[5] Gittins, J. (1989). Bandit Processes and Dynamic Allocation Indices. Wiley, New York.Google Scholar
[6] Gittins, J. (1982) Forward induction and dynamic allocation indices. In Deterministic and Stochastic Scheduling, Dempster, M. A. H. et al. pp. 125–156. Reidel, Dordrecht.CrossRefGoogle Scholar
[7] Huang, C. C. and Weiss, G. (1992) Preemptive scheduling of stochastic jobs with a two stage processing time distribution on M + 1 parallel machines. Prob. Eng. Inf. Sci. 6, 171–191.CrossRefGoogle Scholar
[8] Kawaguchi, T. and Kyan, S. (1986) Worst case bound for an LRF schedule for the mean weighted flowtime problem. SIAM J. Computing 15, 1119–1129.CrossRefGoogle Scholar
[9] Kleinrock, L. (1976) Queueing Systems, Vol. II: Computer Applications. Wiley, New York.Google Scholar
[10] Lawler, E. L., Lenstra, J. K., Rinnooy-Kan, A. H. G. and Shmoys, D. B. (1989) Sequencing and Scheduling: Algorithms and Complexity. Technical Report BS-R8909, Center for Mathematics and Computer Science, Amsterdam, The Netherlands.Google Scholar
[11] Lenstra, J. K., Rinnooy-Kan, A. H. G. and Brucker, P. (1977) Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362.CrossRefGoogle Scholar
[12] Mcnaughton, R. (1959) Scheduling with deadlines and loss functions. Management Sci. 6, 1–12.CrossRefGoogle Scholar
[13] Pinedo, M. and Weiss, G. (1979) Scheduling of stochastic tasks on two parallel processors. Naval Res. Logist. Quart. 26, 527–535.CrossRefGoogle Scholar
[14] Smith, W. E. (1956) Various optimizers for single stage production. Naval Res. Logist. Quart. 3, 59–66.CrossRefGoogle Scholar
[15] Spaccamela, A. M., Rhee, W. S., Stoughie, L. and Van De Geer, S. (1992) Probabilistic analysis of the minimum weighted flowtime problem. Operat. Res. Lett. 11, 67–71.CrossRefGoogle Scholar
[16] Weber, R. R. (1982) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime. J. Appl. Prob. 19, 167–182.Google Scholar
[17] Weber, R. R., Varaiya, P. and Walrand, J. (1986) Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. J. Appl. Prob. 23, 841–847.CrossRefGoogle Scholar
[18] Weiss, G. (1990) Approximation results in parallel machines stochastic scheduling. Ann. Operat. Res. Special Volume on Production Planning and Scheduling, ed. Queyranne, M., 26, 195–242.Google Scholar
[19] Weiss, G. (1992) Turnpike optimality of Smith's rule in parallel machines stochastic scheduling. Math. Operat. Res. 17, 255–270.CrossRefGoogle Scholar
[20] Weiss, G. and Pinedo, M. (1980) Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Prob. 17, 187–202.CrossRefGoogle Scholar
[21] Wolff, R. N. (1989) Stochastic Modeling and the Theory of Queues. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 16 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 22nd January 2021. This data will be updated every 24 hours.

3 Cited by
Hostname: page-component-76cb886bbf-4qfsd Total loading time: 0.463 Render date: 2021-01-22T00:17:04.744Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *