Probabilistic analysis of self-stabilizing systems: A case study on a mutual exclusion algorithm

The heterogeneity in cyber-physical systems (CPS) and the diverse situations that they may face with, along with the environmental hazards raise the need to self-stabilization. The uncertain nature of CPS necessitates a probabilistic view for analyzing the system stabilization-time that is a highly critical metric in distributed/time-sensitive applications. Calculating the worst-case expected stabilization-time and possible improvements help to have safer designs of CPS applications. In this paper, a mutual exclusion algorithm based on PIF (Propagation of Information with Feedback) self-stabilizing algorithm is selected in synchronous environment as a case study. Using probabilistic analysis, we present a set of guidelines for utilizing this algorithm in time-sensitive applications. We have also utilized an approximation method for improving the scalability of our probabilistic analysis and did a set of experiments to show how this analysis could be used in the design of topologies with the goal of having an optimal worst-case expected stabilization-time. Our results show that using this approach, we can significantly improve the worst-case expected stabilization-time.