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Stochastic dispatching of multi-priority jobs to heterogeneous processors

Published online by Cambridge University Press:  14 July 2016

Susan H. Xu ,
Pitu B. Mirchandani ,
Srikanta P. R. Kumar  and
Richard R. Weber
Susan H. Xu*
Affiliation:
Pennsylvania State University
Pitu B. Mirchandani*
Affiliation:
The University of Arizona
Srikanta P. R. Kumar*
Affiliation:
Northwestern University
Richard R. Weber*
Affiliation:
University of Cambridge
*
∗ Postal address: Department of Management Science, Pennsylvania State University, University Park, PA 16802, USA.
∗∗ Postal address: Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, USA.
∗∗∗ Postal address: Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA.
∗∗∗∗ Postal address: Department of Engineering, University of Cambridge, Mill Lane, Cambridge CB2 1RX, UK.
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Abstract

A number of multi-priority jobs are to be processed on two heterogeneous processors. Of the jobs waiting in the buffer, jobs with the highest priority have the first option of being dispatched for processing when a processor becomes available. On each processor, the processing times of the jobs within each priority class are stochastic, but have known distributions with decreasing mean residual (remaining) processing times. Processors are heterogeneous in the sense that, for each priority class, one has a lesser average processing time than the other. It is shown that the non-preemptive scheduling strategy for each priority class to minimize its expected flowtime is of threshold type. For each class, the threshold values, which specify when the slower processor is utilized, may be readily computed. It is also shown that the social and the individual optimality coincide.

Keywords

STOCHASTIC SCHEDULINGMULTI-SERVER SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 852 - 861
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This work has been partially supported by the FMS Program in the Center for Manufacturing Productivity and Technology Transfer, Rensselaer Polytechnic Institute, Troy, NY 12180–3590, USA.

References

Agra Wala, A. K., Coffman, E. G. Jr., Garey, M. R. and Tripathi, S. K. (1984) A stochastic optimization algorithm minimizing expected flowtime on uniform processors. IEEE Trans. Computers 33, 351–357.CrossRefGoogle Scholar
Coffman, E. G., Flatto, L., Garey, M. R. and Weber, R.R. (1987) Minimizing expected makespan on uniform processors systems. Adv. Appl. Prob. 19, 177–201.CrossRefGoogle Scholar
Kumar, P. R. and Walrand, J. (1985) Individually optimal routing in parallel systems. J. Appl. Prob. 22, 989–995.CrossRefGoogle Scholar
Mirchandani, P. B. and Xu, S. H. (1989) Optimal dispatching of multi-priority jobs to two heterogeneous workstations. IIFMS 2, 25–42.Google Scholar
Ross, S. M. (1983) Introduction to Stochastic Dynamic Programming. Wiley, New York.Google Scholar
Weber, R. R. (1981) Scheduling jobs on parallel machines to minimize makespan or flowtime. In Proc. Conf. on Applied Probability, Computer Science: The Interface, Boca Raton. CrossRefGoogle Scholar
Weber, R. R. (1982) Scheduling jobs with stochastic process requirements on parallel machines to minimize makespan or flowtime. J. Appl. Prob. 19, 167–182.CrossRefGoogle Scholar
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
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