The multiclass GI/PH/N queue in the Halfin-Whitt regime
The multiclass GI/PH/N queue in the Halfin-Whitt regime
复制标题
Halfin-Whitt 制度中的多类别 GI/PH/N 队列
DOI：
10.1239/aap/1013540179
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发表时间：
2000
影响因子：
1.2
通讯作者：
M. Reiman
中科院分区：
文献类型：
--
作者：
A. Puhalskii;M. Reiman
我们考虑由 Halfin 和 Whitt 引入和研究的高流量状态下的多服务器队列，他们研究了具有指数分布服务时间的单个客户类别的情况。我们的目的是将他们的分析扩展到具有多个客户类别、优先级和阶段型服务分配的系统。我们证明了弱收敛极限定理，表明正确定义和归一化的队列长度过程收敛到特定的 K 维扩散过程，其中 K 是服务时间分布中的阶段数。我们还表明，适当标准化的等待时间过程收敛于队列长度的极限扩散的简单函数。
We consider a multiserver queue in the heavy-traffic regime introduced and studied by Halfin and Whitt who investigated the case of a single customer class with exponentially distributed service times. Our purpose is to extend their analysis to a system with multiple customer classes, priorities, and phase-type service distributions. We prove a weak convergence limit theorem showing that a properly defined and normalized queue length process converges to a particular K-dimensional diffusion process, where K is the number of phases in the service time distribution. We also show that a properly normalized waiting time process converges to a simple functional of the limit diffusion for the queue length.