THE FLUID LIMIT OF A HEAVILY LOADED PROCESSOR SHARING QUEUE
THE FLUID LIMIT OF A HEAVILY LOADED PROCESSOR SHARING QUEUE
复制标题
高负载处理器共享队列的流量限制
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Ruth J. Williams
中科院分区：
文献类型：
--
作者：
H. C. Gromoll;Amber L. Puha;Ruth J. Williams
考虑一个具有更新到达和i.i.d.的单服务器队列。服务器在处理器共享服务规程下操作的服务时间。为了描述这个系统的演变，我们使用一个测度值的过程，在任何给定的时间跟踪系统中的所有作业的剩余服务时间。从这个度量值的过程，可以恢复传统的性能过程，包括队列长度和工作负载。本文提出并研究了一个重负载处理器共享队列的临界流体模型（或形式大数定律近似）。流体模型的状态描述子是一个测度值函数，其动态由一个非线性积分方程控制。在适当的假设下，我们证明了流体模型解的存在唯一性。此外，我们证明临界流体模型作为一个重负荷的处理器共享队列的一阶近似，当适当地重新缩放，对应于一个序列的重负荷的处理器共享队列的测量值的过程收敛分布的限制，几乎肯定是一个流体模型的解决方案。
Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We propose and study a critical fluid model (or formal law of large numbers approximation) for a heavily loaded processor sharing queue. The fluid model state descriptor is a measure valued function whose dynamics are governed by a nonlinear integral equation. Under mild assumptions, we prove existence and uniqueness of fluid model solutions. Furthermore, we justify the critical fluid model as a first order approximation of a heavily loaded processor sharing queue by showing that, when appropriately rescaled, the measure valued processes corresponding to a sequence of heavily loaded processor sharing queues converge in distribution to a limit that is almost surely a fluid model solution.