On the stochastic continuity of the queuing systems of type $G|G|1$

A one-line queueingi system is considered with an arbitrary flow of calls, arbitrary service and infinite queue.
The behaviour of virtual waiting times is investigated and the problem of continuity of sequences of these waiting times as functions of the determining sequences (in the sense of the author's paper [2]) is posed. A number of well-known metrics are used such as the uniform metric, the Lévy–Prohorov metric, the distance of the convergence in probability etc. With respect to these metrics, explicit quantitative estimates for continuity effects are constructed in the general case as well as in particular case of $G|G|1$ type systems. Some of the results of this paper were formulated, without proof, in the author's note [3].