An Analytical Method for Studying a Queuing System with Jump-Changing Information Flows
In this paper, for the first time, an accurate analytical method for studying the behavior of a queuing system with abruptly changing information flows is presented. It based on the method of the fundamental matrix of the Kolmogorov system. It is important to note that it possible to study analytically the transient mode of the system when it is turned on and off or input flows are changed by using this method. As example the method is applied for the system M|M|1|n. In the paper it is analyzed the transient mode of the system, and it is obtained the analytical expressions for the system state probabilities as the functions of time, as well as the expressions of the transient mode duration, the throughput, and the number of packets received and processed during the transient mode duration. In accordance with the presented model the numerical calculations are presented too. The calculation results for the considered particular cases fully correspond to the early obtained analytical and numerical results for the M|M|1|n system in the stationary mode.