When Are On-Off Sources SIS? Conditions and Applications
Abstract
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 M|G|infinity input model are each supermodular greater than their respective independent version. Similar but weaker SIS conditions also are obtained for renewal on-off processes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2002
- Accession Number
- ADA445875
Entities
People
- Armand M. Makowski
- Sarut Vanichpun
Organizations
- University of Maryland