The present paper deals with an \(M^{X}/M/c\) Bernoulli feedback queueing system with variant multiple working vacations and impatience timers which depend on the states of the servers. Whenever a customer arrives at the system, he activates an random impatience timer. If his service has not been completed before his impatience timer expires, the customer may abandon the system. Using certain customer retention mechanism, the impatient customer can be retained in the system. After getting incomplete or unsatisfactory service, with some probability, each customer may comeback to the system as a Bernoulli feedback. Using the probability generating functions (PGFs), we derive the steady-state solution of the model. Then, we obtain useful performance measures. Moreover, we carry out an economic analysis. Finally, numerical study is performed to explore the effects of the model parameters on the behavior of the system.

中文翻译：

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$$ M ^ {X} / M / c $$ MX / M / c Bernoulli反馈队列，其中包含多个工作假期和不耐烦的客户：绩效和经济分析

本文讨论的是\（M ^ {X} / M / c \）Bernoulli反馈排队系统，具有可变的多个工作休假和不耐烦计时器，具体取决于服务器的状态。每当客户到达系统时，他都会激活一个随机的急躁计时器。如果在其急躁计时器到期之前尚未完成其服务，则客户可以放弃该系统。使用某些客户保留机制，可以将急躁的客户保留在系统中。在获得不完整或不令人满意的服务后，每位客户都有可能作为伯努利的反馈返回系统。使用概率生成函数（PGF），我们可以得出模型的稳态解。然后，我们获得有用的性能指标。此外，我们进行了经济分析。最后，