On continuity of queueing systems with refusals

L. Szeidl

Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 3, Tome 87 (1979), pp. 125-142

Résumé

In this paper is considered the queueing system of type $G|G|m|0$. It is introduced the series of random variables $Y=\{Y_n,n=0,1,2,\dots\}$ (where $Y_n$ is the number of the occupied apparatus at the moment of the call with number $n$) connected with the defining series $X=\{X_n,n=0,1,2,\dots\}$ by the rule (I) of this paper. This rule determines the mapping $F\colon\mathfrak X\to Y$, where $\mathfrak X$ is a set of the defining series $X$ and $Y$ is the set of the corresponding series $Y$. By the method of V. M. Zolotarev it is studied the continuity of mapping $F$ with choosen metrics in $\mathfrak X$ and $Y$. Quantitative estimations of general type are obtained. If is proved that if $m\to\infty$ then the estimations will be transformed into those of the corresponding case $G|G|\infty$ of paper [2].