A Simple Proof of Linear Scaling of End-to-End Probabilistic Bounds using Network Calculus

TL;DR

This paper provides a straightforward proof demonstrating that end-to-end probabilistic performance bounds in network calculus scale linearly with the number of nodes, simplifying previous complex proofs.

Contribution

The paper introduces a simple, general proof showing linear scaling of probabilistic bounds in network calculus, improving understanding of end-to-end performance analysis.

Findings

End-to-end probabilistic bounds grow linearly with network nodes.

Simplifies previous complex proofs of linear scaling.

Enhances the theoretical foundation of statistical network calculus.

Abstract

Statistical network calculus is the probabilistic extension of network calculus, which uses a simple envelope approach to describe arrival traffic and service available for the arrival traffic in a node. One of the key features of network calculus is the possibility to describe the service available in a network using a network service envelope constructed from the service envelopes of the individual nodes constituting the network. It have been shown that the end-to-end worst case performance measures computed using the network service envelope is bounded by $ {\cal O} (H) $, where $H$ is the number of nodes traversed by a flow. There have been many attempts to achieve a similar linear scaling for end-to-end probabilistic performance measures but with limited success. In this paper, we present a simple general proof of computing end-to-end probabilistic performance measures using network calculus that grow linearly in the number of nodes ($H$).