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  1. S. Aalto and U. Ayesta, Mean delay comparison among multilevel processor-sharing scheduling disciplines, Insitut Mittag-Leffler, 11, 2004/2005 fall, 2004 (pdf)(bib)
    Abstract: Multilevel Processor-Sharing (MLPS) scheduling disciplines permit to model a wide variety of non-anticipating scheduling disciplines. Such disciplines have recently attracted attention in the context of the Internet as an appropriate flow-level model for the bandwidth sharing obtained when priority is given to short TCP connections. In this article we compare the mean delay in an M/G/1 queue among MLPS disciplines when the hazard rate of the service time distribution is decreasing. The internal disciplines within levels may vary in the family $\\mathrmFB, \mathrmPS, \mathrmFCFS\$. Our main result states that, given an MLPS discipline, the mean delay is reduced whenever a level is added by splitting an existing one. Furthermore, we show that given an MLPS discipline, the mean delay is reduced when an internal discipline is changed from FCFS to PS (or from PS to FB). For service time distributions with increasing and bounded hazard rate, we obtain the corresponding inverse results. By numerical means we quantify the reduction on the mean delay after the addition of levels. We demonstrate that the mean delay of an MLPS discipline can get close to the minimum feasible delay (FB) with just a few levels. This supports the claim that in order to improve the flow-level performance in the Internet, a simple two-class classification (mice and elephants) might be sufficient.