The G/GI/N queue in the Halfin–Whitt regime
The G/GI/N queue in the Halfin–Whitt regime
复制标题
哈芬-惠特制度中的 G/GI/N 队列
DOI：
10.1214/09-aap609
复制
发表时间：
2009
影响因子：
1.8
通讯作者：
Josh E. Reed
中科院分区：
文献类型：
--
作者：
Josh E. Reed
在本文中，我们研究了 Halfin-Whitt 机制中的 $G/\mathit{GI}/N$ 队列。我们的第一个结果是获得系统中正确居中和缩放的客户数量的确定性流体限制，这可用于提供队列长度过程的一阶近似。我们的第二个结果是获得 Halfin-Whitt 体系中系统中客户数量的二阶随机近似。这是通过首先将队列长度过程以其确定性流体限制居中，然后通过适当的因子进行标准化来实现的。然后，我们继续获得极限近似的替代但等效的表征，其中涉及与服务时间分布相关的更新函数。这种替代表征简化为由 Halfin 和 Whitt [Oper.1] 获得的扩散过程。资源。 29 (1981) 567--588]在服务时间呈指数分布的情况下。
In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a first-order approximation to the queue length process. Our second result is to obtain a second-order stochastic approximation to the number of customers in the system in the Halfin--Whitt regime. This is accomplished by first centering the queue length process by its deterministic fluid limit and then normalizing by an appropriate factor. We then proceed to obtain an alternative but equivalent characterization of our limiting approximation which involves the renewal function associated with the service time distribution. This alternative characterization reduces to the diffusion process obtained by Halfin and Whitt [Oper. Res. 29 (1981) 567--588] in the case of exponentially distributed service times.