Efficient Chernoff-Based Resource Assessment Techniques in Multi-Service Networks

In this paper two main performance measures are discussed for stream traffic flows multiplexed on a communication link: the saturation probability, that is the probability of resource overload, and the equivalent capacity of aggregate traffic, which is the necessary bandwidth for a link to carry the traffic with a given overflow probability. The investigations have been made in the context of rate envelope (bufferless) multiplexing by the aid of the well-known Chernoff bounding method. After showing fundamental relations between the aforementioned measures, we shed considerable light on some important properties. Finally, some newly developed estimates are presented.     

Compact policy routing

The main concern in this paper is to generalize compact routing to arbitrary routing policies that favor a broader set of path attributes beyond path length. Using the formalism of routing algebras we identify the algebraic requirements for a routing policy to be realizable with sublinear size routing tables, and we show that a wealth of practical policies can be classified by our results. By generalizing the notion of stretch, we also discover the algebraic validity of compact routing schemes considered so far and we show that there are routing policies for which one cannot expect sublinear scaling even if permitting arbitrary constant stretch. Finally, we apply our methodology to the routing policies used in Internet inter-domain routing, and we show that our algebraic approach readily generalizes to this setting as well.     

Hyperbolic trees for efficient routing computation

Complex system theory is increasingly applied to develop control protocols for distributed computational and networking resources. The paper deals with the important subproblem of finding complex connected structures having excellent navigability properties using limited computational resources. Recently, the two-dimensional hyperbolic space turned out to be an efficient geometry for generative models of complex networks. The networks generated using the hyperbolic metric space share their basic structural properties (like small diameter or scale-free degree distribution) with several real networks. In the paper, a new model is proposed for generating navigation trees for complex networks embedded in the two-dimensional hyperbolic plane. The generative model is not based on known hyperbolic network models: the trees are not inferred from the existing links of any network; they are generated from scratch instead and based purely on the hyperbolic coordinates of nodes. We show that these hyperbolic trees have scale-free degree distributions and are present to a large extent both in synthetic hyperbolic complex networks and real ones (Internet autonomous system topology, US flight network) embedded in the hyperbolic plane. As the main result, we show that routing on the generated hyperbolic trees is optimal in terms of total memory usage of forwarding tables.