Stochastic inequalities for single-server loss queueing systems

The present paper provides some new stochastic inequalities for the characteristics of the $M\mathrm{/}GI\mathrm{/}1\mathrm{/}n$ and $GI\mathrm{/}M\mathrm{/}1\mathrm{/}n$ loss queueing systems. These stochastic inequalities are based on substantially deepen up- and down-crossings analysis, and they are stronger than the known stochastic inequalities obtained earlier. Specifically, for a class of $GI\mathrm{/}M\mathrm{/}1\mathrm{/}n$ queueing system, two-side stochastic inequalities are obtained.