Recent advances from the theory of multivariate stochastic orderings
can be used to formalize the “folk theorem” that positive
correlations lead to larger buffer levels at a discrete-time infinite
capacity multiplexer queue. In particular, it is known that if the
input traffic is larger than its independent version in the
supermodular (sm) ordering, then their corresponding buffer contents
are similarly ordered in the increasing convex (icx) ordering.
A
sufficient condition for the aforementioned sm comparison is the
stochastic increasingness in sequence (SIS) property of the input
traffic. In this article, we provide conditions for the stationary
on–off source to be SIS. We then use this result to find
conditions under which the superposition of independent on–off
sources and the M|G|∞ input model
are each sm greater than their respective independent version. Similar
but weaker SIS conditions are also obtained for renewal on–off
processes.