Limit Distributions of Additive-Type Functionals in a Particular Queuing Problem

The limit distribution functions as $t\to\infty$ for the total number $w_t$ of lost calls in an interval $(0,t)$ by the $GI|M|n|n+m$ queuing system are investigated for the cases $m=0$ and $m\ne0$. The asymptotic normality of the additive functional wt as $t\to\infty$ is proved, and the parameters of the corresponding limit distributions are calculated. Examples are given.