Transient behavior of the M|M|1|n queuing system with piecewise-constant information flows

Konstantin Vytovtov, Elizaveta Barabanova, Vladimir Vishnevsky
The analysis of transient behavior of the M|M|1|n queuing system with abruptly changing information flows is presented in this paper for the first time. The proposed method is based on the conception of fundamental matrix of the system of the Kolmogorov equations and allows studying the transient and stationary modes of functioning different types of queuing system. The conception of transient time for the queuing system has been introduced and the formulas for calculation of such transient performance metrics as throughput, the number of received and processed packets and others have been obtained for the first time.