On expressing networks with flow transformations in convolution-form

Abstract

Convolution-form networks have the property that the end-to-end service of network flows can be expressed in terms of a (min, +)-convolution of the per-node services. This property is instrumental for deriving end-to-end queueing results which fundamentally improve upon alternative results derived by a node-by-node analysis. This paper extends the class of convolution-form networks with stochastic settings to scenarios with flow transformations, e.g., by loss, dynamic routing or retransmissions. In these networks, it is shown that by using the tools developed in this paper end-to-end delays grow as O(n) in the number of nodes n; in contrast, by using the alternative node-by-node analysis, end-to-end delays grow as O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ).