Positive correlations and buffer occupancy: Lower bound via supermodular ordering
نویسندگان
چکیده
We use recent advances from the theory of multivariate stochastic orderings to formalize the “folk theorem” to the effect that positive correlations lead to increased buffer occupancy and larger buffer levels at a discrete-time infinite capacity multiplexer queue. Input sequences will be compared in the supermodular (sm) ordering and buffer contents in the increasing convex (icx) ordering, respectively. Three popular classes of (discrete-time) traffic models are discussed, namely the Fractional Gaussian Noise traffic model, the on-off source model and the M |G|∞ traffic model. The independent version of an input process in each of these classes of traffic models is a member of the same class. In varying degree of generality, we show that this independent version is smaller than the input sequence itself, and that the corresponding buffer content processes are similarly ordered.
منابع مشابه
Modeling strength of locality of reference via notions of positive dependence
The performance of demand-driven caching depends on the locality of reference exhibited by the stream of requests made to the cache. In spite of numerous efforts, no consensus has been reached on how to formally compare streams of requests on the basis of their locality of reference. We take on this issue by introducing the notion of Temporal Correlations (TC) ordering for comparing strength of...
متن کاملWhen 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 ...
متن کاملComparison of multivariate risks and positive dependence
In this paper we extend some recent results on the comparison of multivariate risk vectors w.r.t. supermodular and related orderings. We introduce a dependence notion called ‘weakly conditional increasing in sequence order’ that allows to conclude that ‘more dependent’ vectors in this ordering are also comparable w.r.t. the supermodular ordering. At the same time this ordering allows to compare...
متن کاملApproximating Minimum Linear Ordering Problems
This paper addresses the Minimum Linear Ordering Problem (MLOP): Given a nonnegative set function f on a finite set V , find a linear ordering on V such that the sum of the function values for all the suffixes is minimized. This problem generalizes well-known problems such as the Minimum Linear Arrangement, Min Sum Set Cover, Minimum Latency Set Cover, and Multiple Intents Ranking. Extending a ...
متن کاملCesaro Supermodular Order and Archimedean Copulas
In this paper, we introduce a new kind of order, Cesaro supermodular order, which includes supermodular order and stochastic order. For this new order, we show that it almost fulfils all desirable properties of a multivariate positive dependence order that have been proposed by Joe (1997). Also, we obtain some relations between it with other orders. Finally, we consider different issues related...
متن کامل