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International Conference on Modelling Techniques and Tools for Computer Performance Evaluation

TOOLS 1994: Computer Performance Evaluation Modelling Techniques and Tools pp 111–122Cite as

Waiting time distributions for processor sharing queues with state-dependent arrival and service rates

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 794))

Abstract

Several variants of multiple server queues with Poisson input, exponentially distributed service demands and processor sharing discipline are considered, in which the arrival rate and the service capacity may depend on the actual number of customers in the system. These queues are approximated by a sequence 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. Numerical examples are provided for open and closed M/M/N processor sharing queues. In particular the effect of the number of parallel processors on the response time distribution under the condition of fixed total service capacity is discussed.

The main part of this research was carried out at the Technische Universität Braunschweig. The author is now with Siemens AG, Bereich Verkehrstechnik, Ackerstraße 22, D-38126 Braunschweig

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Author information

Authors and Affiliations

  1. Institut für Mathematische Stochastik, Technische Universität Braunschweig, Deutschland

    Jens Braband

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  1. Jens Braband
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Günter Haring Gabriele Kotsis

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© 1994 Springer-Verlag Berlin Heidelberg

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Braband, J. (1994). Waiting time distributions for processor sharing queues with state-dependent arrival and service rates. In: Haring, G., Kotsis, G. (eds) Computer Performance Evaluation Modelling Techniques and Tools. TOOLS 1994. Lecture Notes in Computer Science, vol 794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58021-2_6

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  • DOI: https://doi.org/10.1007/3-540-58021-2_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58021-8

  • Online ISBN: 978-3-540-48416-5

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