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Random Quantum Allocation: A new approach to waiting time distributions for M/M/N processor sharing queues

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Messung, Modellierung und Bewertung von Rechen- und Kommunikationssystemen

Part of the book series: Informatik aktuell ((INFORMAT))

Abstract

Several variants of multiple server queues with Poisson input, exponentially distributed service demands and processor sharing discipline are considered. These queues are approximated by sequences of models featuring a new natural discipline called Random Quantum Allocation (RQA) operating in discrete time. This approach can be used for the numerical approximation of waiting and response time distributions for processor sharing queues. In the particular case of the M/M/1-RQA model we derive the generating function of the waiting time distribution of a tagged customer conditioned on service demand and number of customers in the system and the corresponding first two moments. The results are compared with the results for the M/M/1 processor sharing queue. Additionally we discuss the effect of the number of parallel processors on the response time distribution under the condition of fixed total service capacity.

Since 1st February 1993 the first author is with Siemens AG, Bereich Verkehrstechnik, Ackerstraße 22, D-38126 Braunschweig

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References

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Author information

Authors and Affiliations

  1. Institut für Mathematische Stochastik, Technische Universität Braunschweig, Pockelsstraße 14, D-38106, Braunschweig, Germany

    Jens Braband & Rolf Schaßberger

Authors
  1. Jens Braband
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  2. Rolf Schaßberger
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Kommunikationsnetze, RWTH Aachen, Kopernikusstr. 16, 52074, Aachen, Germany

    B. Walke

  2. Lehrstuhl für Informatik IV, RWTH Aachen, Ahornstr. 55, 52074, Aachen, Germany

    O. Spaniol

  3. Rheinisch-Westfälische Technische Hochschule Aachen, Germany

    O. Spaniol

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© 1993 Springer-Verlag Berlin Heidelberg

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Braband, J., Schaßberger, R. (1993). Random Quantum Allocation: A new approach to waiting time distributions for M/M/N processor sharing queues. In: Walke, B., Spaniol, O. (eds) Messung, Modellierung und Bewertung von Rechen- und Kommunikationssystemen. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78495-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-78495-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57201-5

  • Online ISBN: 978-3-642-78495-8

  • eBook Packages: Springer Book Archive

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