  In this paper continuity theorems are established for the number of losses
during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing
system where the service time probability distribution, slightly different in a
certain sense from the exponential distribution, is approximated by that
exponential distribution. Continuity theorems are obtained in the form of one
or two-sided stochastic inequalities. The paper shows how the bounds of these
inequalities are changed if further assumptions, associated with specific
properties of the service time distribution (precisely described in the paper),
are made. Specifically, some parametric families of service time distributions
are discussed, and the paper establishes uniform estimates (given for all
possible values of the parameter) and local estimates (where the parameter is
fixed and takes only the given value). The analysis of the paper is based on
the level crossing approach and some characterization properties of the
exponential distribution.
