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.