A sample path relation for the sojourn times in G/G/1?PS systems and its applications |
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Authors: | Andreas Brandt Manfred Brandt |
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Institution: | 1. Wirtschaftswissenschaftliche Fakult?t, Humboldt-Universit?t zu Berlin, Spandauer Str. 1, D-10178, Berlin, Germany 2. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, D-14195, Berlin, Germany
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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.
Mathematics Subject Classification (MSC 2000) 60K25· 68M20· 60G17· 60G10
This work was supported by a grant from the Siemens AG. |
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Keywords: | G/G/1 G/D/1 G/GI/1 Processor sharing Sojourn time Waiting time Busy period Sample path First come first served Comparative analysis Mean sojourn time approximation |
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