Modeling and analysis of the multi-channel queueing system transient behavior for piece-wise constant arrival rates

The problem of analyzing transient mode of multi-channel queueing system with a finite buffer is considered in this paper. The transient mode of multi-channel queueing system characterizes a switching on/off process or system rebooting process. The transitional time is one of the important transient metrics and it is calculated by using proposed approach. The case of inoperative queueing system is especially relevant at the stage of the first launch of such systems or in the case of a sudden change in the number of incoming applications. That is why in order to avoid any troubles and unforeseen situations, it is necessary to thoroughly examine working capacity of the system depending on the workload. The multi-channeled queueing system M|M|n|m with two servicing devices (n=2) and a finite buffer (m=3) has been analyzed in the paper. State probabilities of the queueing system at the arbitrary point of time have been found by means of the matrix method of fundamental solutions on the base of the system of Kolmogorov equations. The loss probability, the throughput in transient mode have been estimated by using proposed approach.