Multilevel processor sharing scheduling disciplines have recently been resurrected in papers that focus on the differentiation between short and long TCP flows in the Internet. We prove that, for M/G/1 queues, such disciplines are better than the processor sharing discipline with respect to the mean delay whenever the hazard rate of the service time distribution is decreasing. © 2004 Elsevier B.V. All rights reserved. Keywords: Scheduling; Multilevel processor sharing; Mean delay; Unfinished truncated work; M/G/
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