On Markov---Krein characterization of the mean waiting time in M/G/K and other queueing systems

Authors:
Varun Gupta;Takayuki Osogami
Affiliations:
Carnegie Mellon University, Pittsburgh, USA;IBM Research--Tokyo, Kanagawa, Japan
Venue:
Queueing Systems: Theory and Applications
Year:
2011

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Abstract

We propose a new research direction to reinvigorate research into better understanding of the M/G/K and other queueing systems--via obtaining tight bounds on the mean waiting time as functions of the moments of the service distribution. Analogous to the classical Markov---Krein theorem, we conjecture that the bounds on the mean waiting time are achieved by service distributions corresponding to the upper/lower principal representations of the moment sequence. We present analytical, numerical, and simulation evidence in support of our conjectures.