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

Authors:
Andreas Brandt;Manfred Brandt
Affiliations:
Wirtschaftswissenschaftliche Fakultät, Humboldt-Universität zu Berlin, Berlin, Germany D-10178;Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Berlin, Germany D-14195
Venue:
Queueing Systems: Theory and Applications
Year:
2006

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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.