On the Optimal Stochastic Scheduling of Out-Forests

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...

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Vydáno v:	Operations research Ročník 40; číslo 1-supplement-1; s. S67 - S75
Hlavní autoři:	Coffman, E. G., Liu, Zhen
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Linthicum, MD INFORMS 01.01.1992 Operations Research Society of America Institute for Operations Research and the Management Sciences
Témata:	Applied sciences Counterexamples Exact sciences and technology Forest conservation Job shops Mathematical analysis network/graphs: tree algorithms Operational research and scientific management Operational research. Management science Operations research Optimal policy Parallel processing Plant roots Probabilities production/scheduling: stochastic sequencing Random variables Roots of functions Scheduling Scheduling, sequencing Stochastic models Trees Tree(graph) Processor Forest(graph) Scheduling Graph theory Stochastic method Optimization
ISSN:	0030-364X, 1526-5463
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1
ISSN:	0030-364X 1526-5463
DOI:	10.1287/opre.40.1.S67