Regenerative exact simulation for multiserver job model

Perfect/exact sampling has been used in situations, where the underlying distribution from which random samples are of interest is unknown or complex, for more than three decades now. However, to apply perfect sampling techniques to specific models, additional techniques are required. In this paper,...

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Veröffentlicht in:Cluster computing Jg. 28; H. 14; S. 937
Hauptverfasser: Golovin, Alexander, Rumyantsev, Alexander, Chakravarthy, Srinivas
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.11.2025
Springer Nature B.V
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Abstract Perfect/exact sampling has been used in situations, where the underlying distribution from which random samples are of interest is unknown or complex, for more than three decades now. However, to apply perfect sampling techniques to specific models, additional techniques are required. In this paper, the perfect sampling technique is adapted to study a workload process as well as the per-class waiting times of customers in a computing cluster model (also known as the multiserver job model) by using stochastic comparison to a single-server queue, for the first time. Numerical experiments demonstrate the effectiveness of the method in scenarios when the service times have heavy-tailed (Pareto), phase-type, and exponential distributions.
AbstractList Perfect/exact sampling has been used in situations, where the underlying distribution from which random samples are of interest is unknown or complex, for more than three decades now. However, to apply perfect sampling techniques to specific models, additional techniques are required. In this paper, the perfect sampling technique is adapted to study a workload process as well as the per-class waiting times of customers in a computing cluster model (also known as the multiserver job model) by using stochastic comparison to a single-server queue, for the first time. Numerical experiments demonstrate the effectiveness of the method in scenarios when the service times have heavy-tailed (Pareto), phase-type, and exponential distributions.
ArticleNumber 937
Author Rumyantsev, Alexander
Golovin, Alexander
Chakravarthy, Srinivas
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  surname: Golovin
  fullname: Golovin, Alexander
  organization: SMITS Lab, Institute of Applied Mathematical Research, Karelian Research Center of RAS, Department of Applied Mathematics and Cybernetics, Petrozavodsk State University
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  givenname: Alexander
  surname: Rumyantsev
  fullname: Rumyantsev, Alexander
  email: ar0@krc.karelia.ru
  organization: SMITS Lab, Institute of Applied Mathematical Research, Karelian Research Center of RAS, Department of Applied Mathematics and Cybernetics, Petrozavodsk State University
– sequence: 3
  givenname: Srinivas
  surname: Chakravarthy
  fullname: Chakravarthy, Srinivas
  organization: Kettering University
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Keywords Workload vector
65C20
Perfect sampling
Multiserver job model
Stochastic monotonicity
Kiefer–Wolfowitz recursion
Busy cycle
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Snippet Perfect/exact sampling has been used in situations, where the underlying distribution from which random samples are of interest is unknown or complex, for more...
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SubjectTerms Algorithms
Computer Communication Networks
Computer Science
Equilibrium
Expected values
Operating Systems
Processor Architectures
Queuing theory
Sampling methods
Simulation
Supercomputers
Workloads
Title Regenerative exact simulation for multiserver job model
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