Single-server queueing systems with exponential service times and threshold-based renovation

In this paper we study two types of GI/M/1 infinite capacity queues with the implemented threshold-based renovation mechanism. As usual renovation implies probabilistic dropping of customers from the queue upon service completions. In the systems of the first type there the threshold value (indication the queue length) controls the activation of the renovation mechanism. In the systems of the second type the threshold value not only triggers the renovation, but also specifies the area in the queue wherefrom the customers cannot be dropped. For both types of systems the main stationary characteristics are obtained. Numerical results are also provided, which illustrate the performance of the queues.