$$G/{ GI}/N(+{ GI})$$G/GI/N(+GI) queues with service interruptions in the Halfin–Whitt regime
$$G/{ GI}/N(+{ GI})$$G/GI/N(+GI) queues with service interruptions in the Halfin–Whitt regime
复制标题
Halfin–Whitt 体系中存在服务中断的 $$G/{ GI}/N(+{ GI})$$G/GI/N(+GI) 队列
DOI：
10.1007/s00186-015-0523-z
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发表时间：
2016
影响因子：
1.2
通讯作者：
Yuhang Zhou
中科院分区：
文献类型：
--
作者：
Hongyuan Lu;G. Pang;Yuhang Zhou
我们研究了 Halfin–Whitt 机制中具有交替更新服务中断的 $$G/GI/N(+GI)$$G/GI/N(+GI) 队列。系统经历上下交替周期。在正常运行期间，系统按照通常的 $$G/GI/N(+GI)$$G/GI/N(+GI) 队列正常运行，遵循非空闲先到先服务的服务规则。在停机期间，到达的航班继续进入系统，但所有服务器都会停止运行，而每个客户收到的服务量将得到保留，并且服务将在下一个停机时段开始时恢复。对于被放弃的模型，中断不会影响客户的耐心时间。我们假设上升周期与服务时间具有相同的顺序，但与服务时间相比，下降周期渐近可以忽略不计。我们为这些模型中的队列长度过程和虚拟等待时间过程建立了功能中心极限定理，其中极限过程表示为由跳跃过程驱动的随机积分卷积方程。这些极限定理的收敛性在具有 Skorohod $$M_1$$M1 拓扑的空间 $${\mathbb D}$$D 中得到证明。
We study $$G/GI/N(+GI)$$G/GI/N(+GI) queues with alternating renewal service interruptions in the Halfin–Whitt regime. The systems experience up and down alternating periods. In the up periods, the systems operate normally as the usual $$G/GI/N(+GI)$$G/GI/N(+GI) queues with non-idling first-come–first-served service discipline. In the down periods, arrivals continue entering the systems, but all servers stop functioning while the amount of service that each customer has received will be conserved and services will resume when the next up period starts. For models with abandonment, interruptions do not affect customers’ patience times. We assume that the up periods are of the same order as the service times but the down periods are asymptotically negligible compared with the service times. We establish the functional central limit theorems for the queue-length processes and the virtual-waiting time processes in these models, where the limit processes are represented as stochastic integral convolution equations driven by jump processes. The convergence in these limit theorems is proved in the space $${\mathbb D}$$D endowed with the Skorohod $$M_1$$M1 topology.