Variability ordering for the backlog in buffer models fed by on-off fluid sources

In the context buffer models fed by independent on-off fluid sources, we explore conditions under which “determinism minimizes the stationary backlog.” These comparison results are couched in terms of the convex ordering for distributions. We show that increased variability in the on-duration rv results in greater variability of the corresponding backlog. While it appears that in general increased variability in the off-duration rv does not necessarily imply greater variability of the backlog, it is however the case when the on-period duration rv B is exponentially distributed. The discussion is organized around a representation of the stationary backlog in terms of the stationary waiting time rv for an auxiliary stable GI|GI|1 queue.