Asymptotic Analysis of Queueing Systems with Finite Buffer Space

In the paper, we consider a single-server loss system in which each customer has both service time and a random volume. The total volume of the customers present in the system is limited by a finite constant (the system’s capacity). For this system, we apply renewal theory and regenerative processes to establish a relation which connects the stationary idle probability P 0 with the limiting fraction of the lost volume, Q loss, provided the service time and the volume are proportional. Moreover, we use the inspection paradox to deduce an asymptotic relation between Q loss and the stationary loss probability P loss. An accuracy of this approximation is verified by simulation.