When Are On-Off Sources SIS? Conditions and Applications
Technical research rept.
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
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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 supermodular comparison is the stochastic increasingness in sequence SIS property of the input traffic. In this paper, the authors provide conditions for the stationary on-off source to be SIS. They then use this result to find conditions under which the superposition of independent on-off sources and the MGinfinity input model are each supermodular greater than their respective independent version. Similar but weaker SIS conditions also are obtained for renewal on-off processes.
- Statistics and Probability
- Operations Research
- Non-Radio Communications