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

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. © 2011 Springer Science+Business Media, LLC.