A Guide to the Stochastic Network Calculus

TLDR

Several models with subtle yet important differences have been explored to achieve the objectives of stochastic network calculus. The paper aims to comprehend statistical multiplexing and scheduling of non‑trivial traffic sources in a framework for end‑to‑end analysis of multi‑node networks and to provide an intuitive approach that yields fundamental results more easily. It achieves this by using moment‑generating functions, drawn from effective bandwidth theory, to characterize traffic arrivals and network service in an intuitive framework. The authors derive affine envelope functions with exponentially decaying overflow profiles that enable computation of statistical end‑to‑end backlog and delay bounds for networks.

Abstract

The aim of the stochastic network calculus is to comprehend statistical multiplexing and scheduling of non-trivial traffic sources in a framework for end-to-end analysis of multi-node networks. To date, several models, some of them with subtle yet important differences, have been explored to achieve these objectives. Capitalizing on previous works, this paper contributes an intuitive approach to the stochastic network calculus, where we seek to obtain its fundamental results in the possibly easiest way. In detail, the method that is assembled in this work uses moment generating functions, known from the theory of effective bandwidths, to characterize traffic arrivals and network service. Thereof, affine envelope functions with an exponentially decaying overflow profile are derived to compute statistical end-to-end backlog and delay bounds for networks.