When Are On-off Sources Sis? Conditions and Applications

Recent advances from the theory of multivariate stochastic orderings can be used to formalize the “folk theorem” to the effect that positive correlations lead to larger buffer levels at a discrete-time infinite capacity multiplexer queue. For instance, 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 paper, 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.