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Minimizing expected makespans on uniform processor systems

Published online by Cambridge University Press:  01 July 2016

E. G. Coffman Jr ,
L. Flatto ,
M. R. Garey  and
R. R. Weber
E. G. Coffman Jr*
Affiliation:
AT&T Bell Laboratories
L. Flatto*
Affiliation:
AT&T Bell Laboratories
M. R. Garey*
Affiliation:
AT&T Bell Laboratories
R. R. Weber*
Affiliation:
Queens’ College, Cambridge
*
∗Postal address: AT&T Bell Laboratories, Murray Hill, NJ 07974, USA.
∗Postal address: AT&T Bell Laboratories, Murray Hill, NJ 07974, USA.
∗Postal address: AT&T Bell Laboratories, Murray Hill, NJ 07974, USA.
∗∗ Postal address: Queens’ College, Cambridge CB3 9ET, UK.
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Abstract

We study the problem of scheduling n given jobs on m uniform processors to minimize expected makespan (maximum finishing time). Job execution times are not known in advance, but are known to be exponentially distributed, with identical rate parameters depending solely on the executing processor. For m = 2 and 3, we show that there exist optimal scheduling rules of a certain threshold type, and we show how the required thresholds can be easily determined. We conjecture that similar threshold rules suffice for m > 3 but are unable to prove this. However, for m > 3 we do obtain a general bound on problem size that permits Bellman equations to be used to construct an optimal scheduling rule for any given set of m rate parameters, with the memory required to represent that scheduling rule being independent of the number of remaining jobs.

Keywords

SCHEDULINGSCHEDULINGSTOCHASTIC OPTIMIZATION ALGORITHMS
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 1 , March 1987 , pp. 177 - 201
Copyright
Copyright © Applied Probability Trust 1987 

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References

1. Agrawala, A. K., Coffman, E. G. Jr., Garey, M. R. and Tripathi, S. K. (1984) A stochastic optimization algorithm minimizing expected flow times on uniform processors. IEEE Trans, on Computers, 33, 351–356.Google Scholar
2. Lin, W. and Kumar, P. R. (1982) Optimal control of a queueing system with two heterogeneous servers. Preprint.Google Scholar
3. Walrand, J. (1983) A note on optimal control of a queueing system with two heterogeneous servers. Technical Report, EECS, University of California, Berkeley.Google Scholar