Approximate Performability and Dependability Analysis using Generalized Stochastic Petri Nets

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Abstract

Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task. To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described. In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness.
Original languageUndefined
Pages (from-to)61-78
Number of pages18
JournalPerformance evaluation
Volume18
Issue number18
DOIs
Publication statusPublished - 1993

Keywords

  • generalized stochastic Petri nets
  • truncation
  • performability
  • reversibility
  • Approximations
  • IR-18265
  • Dependability
  • Error bounds
  • EWI-7888
  • METIS-118785
  • Markov chains

Cite this

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title = "Approximate Performability and Dependability Analysis using Generalized Stochastic Petri Nets",
abstract = "Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task. To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described. In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness.",
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year = "1993",
doi = "10.1016/0166-5316(93)90027-R",
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volume = "18",
pages = "61--78",
journal = "Performance evaluation",
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Approximate Performability and Dependability Analysis using Generalized Stochastic Petri Nets. / Haverkort, Boudewijn R.H.M.

In: Performance evaluation, Vol. 18, No. 18, 1993, p. 61-78.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Approximate Performability and Dependability Analysis using Generalized Stochastic Petri Nets

AU - Haverkort, Boudewijn R.H.M.

N1 - Imported from research group DACS (ID number 450)

PY - 1993

Y1 - 1993

N2 - Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task. To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described. In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness.

AB - Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task. To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described. In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness.

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