Unleashing the Power of Paying Multiplexing Only Once in Stochastic Network Calculus

TL;DR

This paper introduces an innovative application of the pay multiplexing only once principle in stochastic network calculus, significantly improving probabilistic performance bounds and computational efficiency in network analysis.

Contribution

It extends the PMOO principle to stochastic network calculus, enabling more accurate bounds with less dependency consideration, especially in tree-reducible and certain general networks.

Findings

Reduces the gap between simulation and SNC calculations.

Favors accuracy and computational efficiency over existing methods.

Extends analysis to partially dependent flow scenarios.

Abstract

The stochastic network calculus (SNC) holds promise as a versatile and uniform framework to calculate probabilistic performance bounds in networks of queues. A great challenge to accurate bounds and efficient calculations are stochastic dependencies between flows due to resource sharing inside the network. However, by carefully utilizing the basic SNC concepts in the network analysis the necessity of taking these dependencies into account can be minimized. To that end, we unleash the power of the pay multiplexing only once principle (PMOO, known from the deterministic network calculus) in the SNC analysis. We choose an analytic combinatorics presentation of the results in order to ease complex calculations. In tree-reducible networks, a subclass of general feedforward networks, we obtain an effective analysis in terms of avoiding the need to take internal flow dependencies into account. In a comprehensive numerical evaluation, we demonstrate how this unleashed PMOO analysis can reduce the known gap between simulations and SNC calculations significantly, and how it favourably compares to state-of-the art SNC calculations in terms of accuracy and computational effort. Motivated by these promising results, we also consider general feedforward networks, when some flow dependencies have to be taken into account. To that end, the unleashed PMOO analysis is extended to the partially dependent case and a case study of a canonical example topology, known as the diamond network, is provided, again displaying favourable results over the state of the art.