Variability Ordering for the Backlog in Buffer Models Fed by On-Off Fluid Sources

摘要

In the context buffer models fed by independent on-off fluid sources, the author explores conditions under which 'determinism minimizes the stationary backlog.' These comparison results are couched in terms of the convex ordering for distributions. He shows that increased variability in the on-duration random variable results in greater variability of the corresponding backlog. While it appears that, in general, increased variability in the off- duration random variable does not necessarily imply greater variability of the backlog, it is the case when the on-period duration random variable B is exponentially distributed. The discussion is organized around a representation of the stationary backlog in terms of the stationary waiting time random variable for an auxiliary stable GI.