Non-Blocking Robustness Analysis in Discrete Event Systems

TL;DR

This paper develops a mathematical framework and algorithm to analyze and ensure non-blocking behavior in discrete event systems when transitions are deleted, improving robustness and computational efficiency.

Contribution

It introduces a formal characterization of transition-induced blocking, defines robust deviations that preserve non-blocking properties, and provides an efficient algorithm for critical transition analysis.

Findings

The framework accurately identifies blocking scenarios in case studies.

The algorithm significantly reduces computational complexity.

Case studies demonstrate improved robustness analysis in manufacturing and autonomous systems.

Abstract

This paper presents a mathematical framework for characterizing state blocking in discrete event systems (DES) under transition deletions. We introduce a path-based analysis approach that determines whether systems maintain non-blocking properties when transitions are removed. Through formal analysis and case studies, we establish three key contributions: a mathematical characterization of transition-induced blocking with necessary and sufficient conditions, a definition of robust deviations that preserve non-blocking properties, and an algorithm for identifying critical transitions and analyzing system behavior under deletions. Our algorithm reduces computational complexity by leveraging minimal blocking sets, achieving significant reduction in computational requirements. We demonstrate the framework's effectiveness through manufacturing system and autonomous vehicle case studies, showing substantial improvements in identifying critical transitions and predicting potential blocking scenarios across different application domains.