Stochastic Network Calculus with Localized Application of Martingales

TL;DR

This paper enhances stochastic network calculus by integrating martingale analysis with recent probabilistic bounds, leading to tighter performance estimates for network delays.

Contribution

It introduces a novel combination of martingale techniques with stochastic network calculus, improving the accuracy of performance bounds in network analysis.

Findings

Tighter bounds compared to traditional methods.

Applicable to a non-trivial class of networks.

Validated through comparison with simulations.

Abstract

Stochastic Network Calculus is a probabilistic method to compute performance bounds in networks, such as end-to-end delays. It relies on the analysis of stochastic processes using formalism of (Deterministic) Network Calculus. However, unlike the deterministic theory, the computed bounds are usually very loose compared to the simulation. This is mainly due to the intensive use of the Boole's inequality. On the other hand, analyses based on martingales can achieve tight bounds, but until now, they have not been applied to sequences of servers. In this paper, we improve the accuracy of Stochastic Network Calculus by combining this martingale analysis with a recent Stochastic Network Calculus results based on the Pay-Multiplexing-Only-Once property, well-known from the Deterministic Network calculus. We exhibit a non-trivial class of networks that can benefit from this analysis and compare our bounds with simulation.