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On the stability of the multi-queue multi-server processor sharing with limited service

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Abstract

We consider a multi-queue multi-server system with n servers (processors) and m queues. At the system there arrives a stationary and ergodic stream of m different types of requests with service requirements which are served according to the following k-limited head of the line processor sharing discipline: The first k requests at the head of the m queues are served in processor sharing by the n processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes’ monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the m separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of n=k=1.

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Authors and Affiliations

  1. Institut für Operations Research, Humboldt-Universität zu Berlin, Spandauer Str. 1, 10178, Berlin, Germany

    Andreas Brandt

  2. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany

    Manfred Brandt

Authors
  1. Andreas Brandt
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  2. Manfred Brandt
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Correspondence to Andreas Brandt.

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This work was supported by a grant from the Siemens AG.

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Brandt, A., Brandt, M. On the stability of the multi-queue multi-server processor sharing with limited service. Queueing Syst 56, 1–8 (2007). https://doi.org/10.1007/s11134-007-9022-0

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  • DOI: https://doi.org/10.1007/s11134-007-9022-0

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