An M/M/1 queueing system subjected to multiple differentiated vacations, customer impatience and a waiting server is analyzed. The explicit transient probabilities of system size are derived using probability generating function technique, Laplace transform, continued fractions and some properties of confluent hypergeometric function. Further, the time-dependent mean and variance are obtained as the performance measures. A numerical example is presented in order to study the behavior of the system.

中文翻译：

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M / M / 1排队系统的多重差异休假，不耐烦的客户和等待服务器的瞬态分析及其在IEEE 802.16E节电机制中的应用

分析了一个具有多个差异休假，客户急躁和等待服务器的M / M / 1排队系统。系统大小的显式暂态概率是使用概率生成函数技术，Laplace变换，连续分数和汇合超几何函数的某些属性导出的。此外，获得时间相关的均值和方差作为性能指标。给出了一个数值示例，以研究系统的行为。