Heavy-traffic limits for many-server queues with service interruptions
Heavy-traffic limits for many-server queues with service interruptions
复制标题
多服务器队列的大流量限制导致服务中断
DOI：
10.1007/s11134-009-9104-2
复制
发表时间：
2009
期刊：
影响因子：
1.2
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
G. Pang;W. Whitt
我们为G/M/n+M排队模型建立了多服务器大流量限制，允许客户放弃（+M），受外生再生服务中断的影响。在服务中断时间未缩放的情况下，我们得到了队列长度进程的FWLLN，其极限是双状态随机环境下的常微分方程。在服务中断渐近可忽略的情况下，我们得到了队列长度过程的FCLT，其极限被表征为具有跳变的随机积分方程的路径唯一解。当到达是更新的，中断周期时间是指数的，极限是一个马尔可夫过程，在QED状态下是一个跳跃扩散过程，在ED状态下是一个由Levy过程驱动的O-U过程（对于无限服务器队列）。得到了极限过程在ED区域（和无限服务器队列）的稳态分布的一个随机分解性质。
We establish many-server heavy-traffic limits for G/M/n+M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queue-length process, where the limit is an ordinary differential equation in a two-state random environment. With asymptotically negligible service interruptions, we obtain a FCLT for the queue-length process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. When the arrivals are renewal and the interruption cycle time is exponential, the limit is a Markov process, being a jump-diffusion process in the QED regime and an O–U process driven by a Levy process in the ED regime (and for infinite-server queues). A stochastic-decomposition property of the steady-state distribution of the limit process in the ED regime (and for infinite-server queues) is obtained.