Law of large numbers limits for many-server queues
Law of large numbers limits for many-server queues
复制标题
大数定律对多服务器队列的限制
DOI：
10.1214/09-aap662
复制
发表时间：
2007
影响因子：
1.8
通讯作者：
K. Ramanan
中科院分区：
文献类型：
--
作者：
H. Kaspi;K. Ramanan
抽象的。这项工作考虑了一个多服务器排队系统，其中具有独立同分布的客户，一般分布服务时间按到达顺序进入服务。系统的动态表现为描述系统中客户总数的过程，以及跟踪服务中客户年龄的度量值过程。在服务时间分布的温和假设下，随着服务器数量趋于无穷大，这对进程建立了大数（或流动）限制定律。该极限被描述为一对耦合积分方程的唯一解，它允许相当明确的表示。作为推论，还获得了其他几个感兴趣的函数的流体限制，例如等待时间。此外，当到达过程是时间均匀的时，流体极限显示出收敛到其平衡。在此过程中，获得了一些独立感兴趣的结果，包括连续映射结果和流体极限的最大值属性。研究这些系统的动机是它们作为计算机数据系统和呼叫中心的模型而出现。
Abstract. This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system are represented in terms of a process that describes the total number of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service. Under mild assumptions on the service time distribution, as the number of servers goes to infinity, a law of large numbers (or fluid) limit is established for this pair of processes. The limit is characterised as the unique solution to a coupled pair of integral equations, which admits a fairly explicit representation. As a corollary, the fluid limits of several other functionals of interest, such as the waiting time, are also obtained. Furthermore, when the arrival process is time-homogeneous, the fluid limit is shown to converge to its equilibrium. Along the way, some results of independent interest are obtained, including a continuous mapping result and a maximality property of the fluid limit. A motivation for studying these systems is that they arise as models of computer data systems and call centers.