有限容量处理器共享队列中的逗留时间

S. Borst, O. Boxma, N. Hegde
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引用次数: 35

摘要

由于需要开发简单的简化模型来评估无线数据系统的性能,我们考虑了有限容量的处理器共享系统。对于这样的系统,我们分析了停留时间分布,这为网页等文件的传输延迟提供了一个有用的度量。服务速率允许是状态相关的,以便捕捉这样一个事实,即由于调度增益或信道冲突,无线数据系统中的吞吐量可能随着活动用户的数量而变化。我们导出了逗留时间分布的Laplace-Stieltjes变换的一组线性方程,该方程以到达时的用户数量为条件。对这组方程进行了求解,得到了LST的倒置,得到了无条件停留时间的相位型分布。给出了数值结果,并提出了两种近似,大大减少了计算量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sojourn times in finite-capacity processor-sharing queues
Motivated by the need to develop simple parsimonious models for evaluating the performance of wireless data systems, we consider finite-capacity processor-sharing systems. For such systems, we analyze the sojourn time distribution, which presents a useful measure for the transfer delay of documents such as Web pages. The service rates are allowed to be state-dependent, to capture the fact that the throughput in wireless data systems may vary with the number of active users due to scheduling gains or channel collisions. We derive a set of linear equations for the Laplace-Stieltjes transforms of the sojourn time distributions, conditioned on the number of users upon arrival. This set of equations is solved, and the resulting LST's are inverted, resulting in a phase-type distribution for the unconditional sojourn time. Numerical results are provided, and two types of approximations are proposed that substantially reduce the computational effort.
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