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A discrete-time technique for solving closed queueing network models of computer systems

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Book cover Messung, Modellierung und Bewertung von Rechensystemen

Part of the book series: Informatik-Fachberichte ((INFORMATIK,volume 61))

Summary

We give a discrete-time model for a central server computer system, and show that the equilibrium distribution is of product-form Given the requests for workload at the different stations of a cycle, we compute the conditional cycle time distribution, which is linear in that requests.

Zusammenfassung

Wir stellen ein zeit-diskretes Modell für Rechensysteme vor. Es wird gezeigt, daß die Gleichgewichtsverteilung des Systems eine Produktform besitzt. Für gegebene Bedienungszeitforderungen an den einzelnen Stationen eines Zyklus wird die bedingte Zyklusverteilung berechnet; diese ist linear in den Anforderungen.

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References

  1. BARBOUR, A.D.; SCHASSBERGER, R.: Insensitive Average Residence Times in Generalized Semi-Markov-Processes, Adv.Appl.Prob. 13, 720–735, 1981

    Article  MathSciNet  MATH  Google Scholar 

  2. BUZEN, J.P.: Computational Algorithms for Closed Queueing Networks with Exponential Servers, Comm. ACM (16), 527–531, 1973

    Article  MathSciNet  MATH  Google Scholar 

  3. COHEN, J.W.: The Multiple Phase Service Network with Generalized Processor Sharing, Acta Informatica, 12,245–284, 1979

    Article  MathSciNet  MATH  Google Scholar 

  4. KELLY, F.P.: Reversibility and Stochastic Networks, Wiley, 1979

    MATH  Google Scholar 

  5. KLEINROCK, L.: Queueing Systems, Vol.11, Wiley, 1976

    MATH  Google Scholar 

  6. KLEINROCK, L.: Time-shared Systems:A Theoretical Treatment, J.A.C.M. 14,242–261, 1967

    MathSciNet  MATH  Google Scholar 

  7. SAKATA, M.; NOGUCHI, S.; OIZUMI, J.: An Analysis of the M/G/1 Queue Under Round-Robin Scheduling, Oper.Res.19,371–385, 1971

    Article  MATH  Google Scholar 

  8. SALZA, S.; LAVENBERG, S.S.: Approximating Response Time Distributions in Closed Queueing Network Models of Computer Performance, Proc.Performance 81, 133–145, 1981

    Google Scholar 

  9. SCHASSBERGER, R.: The Doubly Stochastic Server: A Time-sharing Model, ZOR 25, 179–189, 1981

    Article  MathSciNet  MATH  Google Scholar 

  10. SCHASSBERGER, R.: Residence Time in the M/G/1 Processor Sharing Queue, Preprint 1982

    Google Scholar 

  11. SCHASSBERGER, R.; DADUNA, H.: A Discrete Time Round-Robin Queue with Bernoulli Input and General Arithmetic Sercice Time Distribution, Acta Informatica, 15, 251–263, 1981

    Article  MathSciNet  MATH  Google Scholar 

  12. SCHASSBERGER, R.; DADUNA, H.: Networks of Queues in Discrete Time, Preprint 1982

    Google Scholar 

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© 1983 Springer-Verlag Berlin Heidelberg

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Schassberger, R., Daduna, H. (1983). A discrete-time technique for solving closed queueing network models of computer systems. In: Kühn, P.J., Schulz, K.M. (eds) Messung, Modellierung und Bewertung von Rechensystemen. Informatik-Fachberichte, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68830-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-68830-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11990-6

  • Online ISBN: 978-3-642-68830-0

  • eBook Packages: Springer Book Archive

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