Transient Behavior of the MAP/M/1/N Queuing System

Abstract

This paper investigates the characteristics of the MAP/M/1/N queuing system in the transient mode. The matrix method for solving the Kolmogorov equations is proposed. This method makes it possible, in general, to obtain the main characteristics of the considered queuing system in a non-stationary mode: the probability of losses, the time of the transient mode, the throughput, and the number of customers in the system at time t. The developed method is illustrated by numerical calculations of the characteristics of the MAP/M/1/3 system in the transient mode.

Keywords

• queuing system
• transient mode
• <i>MAP</i> flow
• matrix method
• Kolmogorov equations