Mean Delay Analysis of Multi Level Processor Sharing Disciplines
Mean Delay Analysis of Multi Level Processor Sharing Disciplines
复制标题
多级处理器共享规则的平均延迟分析
DOI：
10.1109/infocom.2006.262
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
U. Ayesta
中科院分区：
文献类型：
--
作者：
S. Aalto;U. Ayesta
多级处理器共享（MLP）调度学科允许建模各种非期望的调度学科。这些学科最近在Internet的背景下引起了人们的关注，作为当优先使用短TCP连接的优先级时获得的带宽共享的适当流级模型。在本文中，我们比较了MLPS学科中M/G/1队列的平均延迟，假设服务时间分布属于降低危险率（DHR）。我们能够证明，鉴于MLP纪律，只要在某些情况下添加现有的级别时，平均延迟就会减少。例外涉及PS内部学科将高层分裂。但是，我们的数值示例表明，即使在这种情况下，分裂的水平也有利。此外，我们表征了在级别内改变内部学科的平均延迟的影响。通过数值手段，我们证明了MLPS学科的平均延迟只能在几个级别的情况下接近最小最佳延迟。随着MLP纪律中水平的数量增加，MLP队列模仿了前景 - 背景队列的行为，众所周知，这可以最大程度地减少所有学科之间的平均延迟。因此，我们的结果提供了一种建设性的方式来证明FB的最佳性。
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 paper, we compare the mean delay in an M/G/1 queue among MLPS disciplines under the assumption that the service time distribution belongs to class Decreasing Hazard Rate (DHR). We are able to prove that, given an MLPS discipline, the mean delay is reduced whenever a level is added by splitting an existing one in several cases. The exceptions concern splitting the upper levels with PS internal discipline. Our numerical examples, however, indicate that the level splitting be advantageous even in these cases. Furthermore, we characterize the effect on the mean delay of changing internal disciplines within levels. By numerical means we demonstrate that the mean delay of an MLPS discipline can get close to the minimum optimal delay with just a few levels. As the number of levels increases in an MLPS discipline, the MLPS queue mimics closer and closer the behavior of a Foreground- Background queue, which is known to minimize the mean delay among all disciplines. Thus, our result provides a constructive way to demonstrate the optimality of FB.