Computer Science Department
School of Computer Science, Carnegie Mellon University
Adam Wierman, Takayuki Osogami, Mor Harchol-Balter, Alan Scheller-Wolf
We model this situation as an M/GI/k queue with m preemptive-resume priority classes, presenting the first analysis of this system with more than two priority classes under a general phase-type service distribution. (Prior analyses of the M/GI/k with more than two priority classes are approximations that, we show, can be highly inaccurate.) Our analytical method is very different from the prior literature: it combines the technique of dimensionality reduction with Neuts' technique for determining busy periods in multiserver systems, and then uses a novel recursive iteration technique. Our analysis is approximate, but, unlike prior techniques, can be made as accurate as desired, and is verified via simulation.