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Scheduling Stochastic Jobs with a Two-Point Distribution on Two Parallel Machines

Published online by Cambridge University Press:  27 July 2009

E.G. Coffman Jr ,
M. Hofri  and
G. Weiss
E.G. Coffman Jr
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey07974
M. Hofri
Affiliation:
Computer Science Department The Technion Haifa, Israel
G. Weiss
Affiliation:
School of ISyE Georgia Institute of Technology Atlanta, Georgia 30320
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Abstract

We analyze the optimal preemptive sequencing of n jobs on two machines to minimize expected total flow time. The running times of the jobs are independent samples from the distribution Pr(X = 1) = p, Pr(X = κ + 1) = 1 − p. We verify that the shortest-expected-remaining-processing-time (SERPT) policy, which is optimal for independent and identically distributed (i.i.d.) running times with a monotone hazard-rate distribution, is not optimal for this distribution. However, we prove that if p ≥ 1/κ, then the number of decisions where SERPT and an optimal policy disagree is bounded by a constant independent of n. For p < 1/k, we prove that the expected number of such decisions has a similar bound. In addition, bounds on the expected increase in flow times under SERPT are derived; these bounds are also independent of n.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 1 , January 1989 , pp. 89 - 116
Copyright
Copyright © Cambridge University Press 1989

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References

Agrawala, A., Coffman, E.G. JrGarey, M.R. & Tripathi, S. (1984). A stochastic optimiation algorithm minimizing expected flow times on uniform processors. IEEE Transactions on Computers C-33: 351–356.CrossRefGoogle Scholar
Bruno, J.L., Downey, P.J. & Frederickson, G.N. (1981). Sequencing tasks with exponential service times to minimize the expected flow time or makespan. Journal of the Association for Computing Machines 28: 100–113.Google Scholar
Chazan, D., Konheim, A.G. & Weiss, B. (1968). A note on time-sharing. Journal of Combinatorial Theory 5: 344–369.Google Scholar
Coffman, E.G. Jr, Flatto, L., Garey, M.R. & Weber, R.R. (1987). Minimizing expected makespans on uniform processor systems. Advances in Applied Probability 19: 177–201.Google Scholar
Feller, W. (1971). An introduction to probability theory and its applications, Vol. 11, 2nd Edidon, New York: John Wiley & Sons.Google Scholar
Gittins, J.C. (1979). Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society Series B 14: 148–177.Google Scholar
Glazebrook, K.D. (1979). Scheduling tasks with exponential service times on parallel processors. Journal of Applied Probability 16: 658–689.Google Scholar
Kämpke, T. (1987). On the optimality of static priority policies in stochastic scheduling on parallel machines. Journal of Applied Probability 24: 430–448.Google Scholar
Meilijson, I. & Weiss, G. (1977). Multiple feedback at a single server station. Stochastic Processes and Their Applications 5: 195–205.CrossRefGoogle Scholar
Papadimitriou, C. (1985). Games against nature. Journal of Computer and System Sciences 31: 288–301CrossRefGoogle Scholar
Ross, S. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
Sevcik, K.C. (1974). Scheduling for minimum total loss using service time distributions. Journal of the Association for Computing Machines 21: 66–75.CrossRefGoogle Scholar
Weber, R.R. (1982). Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flow time. Journal of Applied Probability 19: 167–182.CrossRefGoogle Scholar
Weber, R.R., Varaiya, P. & Walrand, J. (1986). Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flow time. Journal of Applied Probability 23: 841–847.CrossRefGoogle Scholar
Weiss, G. & Pinedo, M. (1980). Scheduling tasks with exponential service times on nonidentical processors to minimize various cost functions. Journal of Applied Probability 17: 187–202.Google Scholar