Queuing system with threshold-based general renovation mechanism

The paper considers a single-line 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