Heavy-traffic limits for waiting times in many-server queues with abandonment
Heavy-traffic limits for waiting times in many-server queues with abandonment
复制标题
高流量限制多服务器队列中的等待时间并放弃
DOI：
10.1214/09-aap606
复制
发表时间：
2008
影响因子：
1.8
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
Rishi Talreja;W. Whitt
我们建立了大流量的随机过程限制在多服务器队列中的等待时间与客户放弃。如果系统是渐近临界加载，在质量和效率驱动（QED）制度，然后一个有界参数表明，放弃不影响等待时间的过程。相反，如果系统是过载的，如在效率驱动（艾德）的制度，按照曼德尔鲍姆等[Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication，Control and Computing（1999）1095- 1104]，我们通过研究到达在某个时间关闭的排队模型的限制行为来处理客户放弃。然后，一个无限耐心的顾客在时间t到达的等待时间就是排队清空所需的额外时间。为了证明虚拟等待时间的随机过程限制，我们建立了一个双参数版本的Puhalskii的第一次通过时间的不变性原理。这反过来又涉及到证明复合映射和逆映射的两个参数版本适当地保持收敛。
We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding argument shows that the abandonment does not affect waiting-time processes. If instead the system is overloaded, as in the efficiency-driven (ED) regime, following Mandelbaum et al. [Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control and Computing (1999) 1095--1104], we treat customer abandonment by studying the limiting behavior of the queueing models with arrivals turned off at some time $t$. Then, the waiting time of an infinitely patient customer arriving at time $t$ is the additional time it takes for the queue to empty. To prove stochastic-process limits for virtual waiting times, we establish a two-parameter version of Puhalskii's invariance principle for first passage times. That, in turn, involves proving that two-parameter versions of the composition and inverse mappings appropriately preserve convergence.