Equivalent Versions of Total Flow Analysis

TL;DR

This paper demonstrates that the choice of cuts in Fixed-Point Total Flow Analysis does not influence convergence or bounds, and introduces an alternative method that avoids cuts altogether for networks with cyclic dependencies.

Contribution

It proves the independence of cut choices in Fixed-Point TFA and proposes a new cut-free algorithm applicable to cyclic dependency networks.

Findings

Cut choice does not affect convergence or bounds in Fixed-Point TFA.

A new algorithm without cuts is effective for cyclic dependency networks.

The proposed method maintains valid performance bounds without artificial cuts.

Abstract

Total Flow Analysis (TFA) is a method for conducting the worst-case analysis of time sensitive networks without cyclic dependencies. In networks with cyclic dependencies, Fixed-Point TFA introduces artificial cuts, analyses the resulting cycle-free network with TFA, and iterates. If it converges, it does provide valid performance bounds. We show that the choice of the specific cuts used by Fixed-Point TFA does not affect its convergence nor the obtained performance bounds, and that it can be replaced by an alternative algorithm that does not use any cut at all, while still applying to cyclic dependencies.