  Some important results on the variance of the $M|G|\infty$ queue busy period
are presented. Often, this parameter depends on the whole structure of the
service time distribution. So, the importance of the bounds presented,
depending only on some parameters. Also, some bounds for service time
distributions important in reliability theory, with technological and financial
applications, are presented and a particular stochastic ordination is explored
to explain those results. Finally, an interesting result about the
exponentiality of the MGInf queue busy period, resulting from the coefficient
of variation study is shown.
