An Approach using Demisubmartingales for the Stochastic Analysis of Networks

TL;DR

This paper introduces demisubmartingale inequalities to derive improved probabilistic bounds for end-to-end delays in stochastic network calculus, enhancing accuracy for tandem queue networks.

Contribution

It presents a novel approach using demisubmartingales to improve probabilistic bounds in network calculus, specifically for tandem GI/GI/1 queues.

Findings

New bounds outperform existing ones in tandem networks

Demisubmartingale inequalities provide more accurate delay estimates

Validated results with M/M/1 queue comparisons

Abstract

Stochastic network calculus is the probabilistic version of the network calculus, which uses envelopes to perform probabilistic analysis of queueing networks. The accuracy of probabilistic end-to-end delay or backlog bounds computed using network calculus has always been a concern. In this paper, we propose novel end-to-end probabilistic bounds based on demisubmartingale inequalities which improve the existing bounds for the tandem networks of GI/GI/1 queues. In particular, we show that reasonably accurate bounds are achieved by comparing the new bounds with the existing results for a network of M/M/1 queues.