2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101249The present paper provides some new stochastic inequalities for the characteristics of the $M/GI/1/n$ and $GI/M/1/n$ 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 $GI/M/1/n$ queueing system, two-side stochastic inequalities are obtained.17 pages, 11pt To appear in Stochastic Analysis and ApplicationsProbability60K25, 60E15text