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A sample path relation for the sojourn times in G/G/1−PS systems and its applications

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Abstract

For the single server system under processor sharing (PS) a sample path result for the sojourn times in a busy period is proved, which yields a sample path relation between the sojourn times under PS and FCFS discipline. This relation provides a corresponding one between the mean stationary sojourn times in G/G/1 under PS and FCFS. In particular, the mean stationary sojourn time in G/D/1 under PS is given in terms of the mean stationary sojourn time under FCFS, generalizing known results for GI/M/1 and M/GI/1. Extensions of these results suggest an approximation of the mean stationary sojourn time in G/GI/1 under PS in terms of the mean stationary sojourn time under FCFS.

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Authors and Affiliations

  1. Wirtschaftswissenschaftliche Fakultät, Humboldt-Universität zu Berlin, Spandauer Str. 1, D-10178, Berlin, Germany

    Andreas Brandt

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

    Manfred Brandt

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

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Mathematics Subject Classification (MSC 2000) 60K25· 68M20· 60G17· 60G10

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

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Brandt, A., Brandt, M. A sample path relation for the sojourn times in G/G/1−PS systems and its applications. Queueing Syst 52, 281–286 (2006). https://doi.org/10.1007/s11134-006-6264-1

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  • DOI: https://doi.org/10.1007/s11134-006-6264-1

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