Performance analysis of Israeli‐Jalfon's algorithm using probabilistic model checking

Abstract

SummaryIsraeli‐Jalfon's self‐stabilization algorithm provides a solution to the problem of fault tolerance in distributed systems. To quantitatively evaluate the algorithm and discover the factors contributing to its performance, we used a probabilistic model checking technique to study the algorithm across different configurations. The mainstream probabilistic model checker PRISM assisted with our final assessment. We focus here on three aspects of the algorithm's performance: convergence, time complexity, and maximum execution time. Our experimental results show that time complexity is O (N^2) when N is less than 23, and we examine the factors contributing to this performance. These prove to be: the number of tokens, the number of processes, the probability of token transmission, and how tokens are spaced. Performance degrades as the number of tokens grows. For a certain number of processes, better performance can be obtained when the probability of token transmission is 0.5. Three tokens spaced evenly, meanwhile, yields the worst performance. The main contribution of this paper is its exhaustive quantitative performance analysis of Israeli‐Jalfon's algorithm and the presentation of accurate rather than approximate numerical results. Moreover, our assessment was undertaken in a reducible fashion, with stable states being set against a proper subset of the set of possible configurations rather than allowing two sets to coincide.