The impact of autocorrelation on queuing systems
Management Science
Supermodular stochastic orders and positive dependence of random vectors
Journal of Multivariate Analysis
Some remarks on the supermodular order
Journal of Multivariate Analysis
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
Queueing Systems: Theory and Applications
On a reduced load equivalence for fluid queues under subexponentiality
Queueing Systems: Theory and Applications
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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.