Transient Behaviour of Finite-Source Single-Line Queueing Systems With Jumps of Network Traffic

Vladimir Vishnevsky, Konstantin Vytovtov, Elizaveta Barabanova, Georgiy Vytovtov
In this paper, the accurate analytical method for studying the transient behavior of finite-source single-line queueing systems with jumps of network traffic is presented. It based on the method of the probability translation matrix. The mathematical model allows us to analyze the transient mode of Local Area Network when a switch has been turned on or an arrived or serviced rate has been changed. It is obtained the analytical expressions for the system state probabilities including the expression for the loss probability and the transient time. The numerical calculations for the five-state queuing system M/M/1/n are presented too. The calculation results for the considered particular cases fully correspond to the well-known analytical and numerical results for the system in the stationary mode.