Sojourn Times In The M/G/1 FB Queue With Light-Tailed Service Times

Authors:
M. Mandjes;M. Nuyens
Affiliations:
CWI, Amsterdam, The Netherlands, and, KdV Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands, E-mail: michel.mandjes@cwi.nl;Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, E-mail: mnuyens@few.vu.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2005

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Abstract

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the foreground–background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times, the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimizes the decay rate in the class of work-conserving disciplines.