Computing Scores of Forwarding Schemes in Switched Networks with Probabilistic Faults

TL;DR

This paper introduces a method to compute the probability that a forwarding scheme in a switched network with probabilistic faults ensures timely delivery of messages, addressing reliability in real-time systems.

Contribution

It models fault handling in switched networks using probabilistic failures, reduces the scoring problem to #SAT, and analyzes its computational complexity as #P-complete.

Findings

The scoring problem can be reduced to a reachability problem on a structured Markov chain.

The problem is #P-complete, indicating high computational complexity.

The proposed methods can estimate the reliability scores effectively.

Abstract

Time-triggered switched networks are a deterministic communication infrastructure used by real-time distributed embedded systems. Due to the criticality of the applications running over them, developers need to ensure that end-to-end communication is dependable and predictable. Traditional approaches assume static networks that are not flexible to changes caused by reconfigurations or, more importantly, faults, which are dealt with in the application using redundancy. We adopt the concept of handling faults in the switches from non-real-time networks while maintaining the required predictability. We study a class of forwarding schemes that can handle various types of failures. We consider probabilistic failures. For a given network with a forwarding scheme and a constant $\ell$, we compute the {\em score} of the scheme, namely the probability (induced by faults) that at least $\ell$ messages arrive on time. We reduce the scoring problem to a reachability problem on a Markov chain with a "product-like" structure. Its special structure allows us to reason about it symbolically, and reduce the scoring problem to #SAT. Our solution is generic and can be adapted to different networks and other contexts. Also, we show the computational complexity of the scoring problem is #P-complete, and we study methods to estimate the score. We evaluate the effectiveness of our techniques with an implementation.