Distribution-valued heavy-traffic limits for the $\mathbf{{G/\mathit{GI}/\infty}}$ queue
Distribution-valued heavy-traffic limits for the $\mathbf{{G/\mathit{GI}/\infty}}$ queue
复制标题
$mathbf{{G/mathit{GI}/infty}}$ 队列的分布值大流量限制
DOI：
10.1214/14-aap1027
复制
发表时间：
2009
影响因子：
1.8
通讯作者：
Rishi Talreja
中科院分区：
文献类型：
--
作者：
Josh E. Reed;Rishi Talreja
We study the $G/\mathit{GI}/\infty$ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distribution-valued processes. We find that our diffusion limits are tempered distribution-valued Ornstein-Uhlenbeck processes.
