Two Types of Single-Server Queueing Systems with Threshold-Based Renovation Mechanism

This work is devoted to the analysis of two GI/M/1 infinite capacity queuing systems with threshold control of the renovation mechanism, which is responsible for the probabilistic dropping of claims entered into the system upon service completions. In the system of the first type, the threshold value is the value of the queue length, upon passing which the renovation mechanism is activated. For a system of the second type, the threshold value not only activates the renovation, but also specifies the area in the queue where from the customers cannot be dropped. For both systems, the main stationary time-probabilistic characteristics are derived and also the results of simulation, which illustrate the performance of the queues, are presented. © 2021, Springer Nature Switzerland AG.