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: | , |
| 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: | |
| ISSN: | 0030-364X, 1526-5463 |
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| 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. |
|---|---|
| AbstractList | New results are presented on the problem of scheduling jobs on K greater than or equal to one parallel processors to stochastically minimize the makespan. The jobs are subject to out-forest precedence constraints, with each job having at most one immediate predecessor. Job running times are independent samples from a given exponential distribution. A class of uniform out-forests is defined in which all subtrees are ordered by an embedding relation. It is proved that an intuitive greedy policy is optimal for K equals 2 and that, if out-forests satisfy an additional, uniform root-embedding constraint, then the greedy policy is optimal for all K greater than or equal to 2. 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. 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. |
| Author | Coffman, E. G. Liu, Zhen |
| Author_xml | – sequence: 1 givenname: E. G. surname: Coffman fullname: Coffman, E. G. – sequence: 2 givenname: Zhen surname: Liu fullname: Liu, Zhen |
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| Copyright | Copyright 1992 Operations Research Society of America 1992 INIST-CNRS Copyright Institute for Operations Research and the Management Sciences Jan/Feb 1992 |
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| DOI | 10.1287/opre.40.1.S67 |
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| Keywords | Tree(graph) Processor Forest(graph) Scheduling Graph theory Stochastic method Optimization |
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| Snippet | 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... 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... New results are presented on the problem of scheduling jobs on K greater than or equal to one parallel processors to stochastically minimize the makespan. The... |
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| SubjectTerms | 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 |
| Title | On the Optimal Stochastic Scheduling of Out-Forests |
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