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On the Optimal Stochastic Scheduling of Out-Forests

Author

Listed:
  • E. G. Coffman

    (AT&T Bell Laboratories, Murray Hill, New Jersey)

  • Zhen Liu

    (INRIA, Valbonne, France)

Abstract

This paper presents new results on the problem of scheduling jobs on K ≥ 1 parallel processors to stochastically minimize the makespan. The jobs are subject to out-forest precedence constraints, i.e., each job has at most one immediate predecessor, and job running times are independent samples from a given exponential distribution. We define a class of uniform out-forests in which all subtrees are ordered by an embedding relation. We prove that an intuitive greedy policy is optimal for K = 2, and that if out-forests satisfy an additional, uniform root-embedding constraint, then the greedy policy is optimal for all K ≥ 2.

Suggested Citation

  • E. G. Coffman & Zhen Liu, 1992. "On the Optimal Stochastic Scheduling of Out-Forests," Operations Research, INFORMS, vol. 40(1-supplem), pages 67-75, February.
  • Handle: RePEc:inm:oropre:v:40:y:1992:i:1-supplement-1:p:s67-s75
    DOI: 10.1287/opre.40.1.S67
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