An M/M/1 dual-stage vacation queueing system with a system disaster is analysed in this paper. This work is motivated by the dual-stage sleep mode mechanism in the MAC (Media Access Control) and the physical layer of a WiMAX system with Denial of Service. In this model, the server switches to two types of vacation called stage-I and stage-II vacation. Disaster can occur at any stage of the system and subsequent repair is considered. For this system, explicit expressions for transient and steady-state probabilities are computed. Further, performance indices like the mean, variance of the system size, the probability that the server is on vacation mode and busy mode, and system throughput have been computed. Finally, numerical illustrations are presented to understand the effect of the parameters on the system performance.

安米/米_/1双阶段休假排队系统具有系统灾难分析。这项工作的动机是 MAC（媒体访问控制）中的双阶段睡眠模式机制和具有拒绝服务的 WiMAX 系统的物理层。在此模型中，服务器切换到两种类型的假期，称为第一阶段假期和第二阶段假期。系统的任何阶段都可能发生灾难，并考虑进行后续修复。对于该系统，计算瞬态和稳态概率的显式表达式。此外，还计算了性能指标，例如平均值、系统大小的方差、服务器处于休假模式和忙碌模式的概率以及系统吞吐量。最后，通过数值说明来了解参数对系统性能的影响。