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On the optimal stochastic scheduling of out-forests

Abstract : This paper presents new results on the problem of scheduling jobs on K ³ 1 parallel processors so as to minimize stochastically 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 greddy policy is optimal for all K ³ 2.
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https://hal.inria.fr/inria-00075402
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Submitted on : Wednesday, May 24, 2006 - 6:09:04 PM
Last modification on : Friday, February 4, 2022 - 3:22:03 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 10:57:54 PM

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  • HAL Id : inria-00075402, version 1

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Edward G. Coffman, Zhen Liu. On the optimal stochastic scheduling of out-forests. [Research Report] RR-1156, INRIA. 1990. ⟨inria-00075402⟩

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