The Queueing System with Threshold-Based Direct and Inverse General Renovation Mechanism

The paper considers a single-server queuing system with a single-threshold mechanism for probabilistic dropping of applications accepted into the system (general renovation). On the one hand, unlike the previously considered systems with general renovation, this system introduces a certain threshold value in the queue as a control parameter of the renovation mechanism, which not only determines the moment when the probabilistic dropping of applications accepted into the system is enabled, but also sets a safe area in the queue from which applications accepted into the system cannot be reset. A general renovation is a probabilistic reset of an arbitrary number of applications from the queue outside the safe zone, which occurs at the end of the application service on the device. For this system, the main probabilistic-time characteristics are obtained for two types of general renovation: the direct general renovation—applictions are dropped from the queue in the order of arrival, and the inverse general renovation—applictions are dropped from the queue starting from the last one. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.