Probabilistic verification of Herman's self-stabilisation algorithm

Kwiatkowska, M., Norman, G. and Parker, D. (2012) Probabilistic verification of Herman's self-stabilisation algorithm. Formal Aspects of Computing, 24(4-6), pp. 661-670. (doi: 10.1007/s00165-012-0227-6)

Abstract

Herman's self-stabilisation algorithm provides a simple randomised solution to the problem of recovering from faults in an N-process token ring. However, a precise analysis of the algorithm's maximum execution time proves to be surprisingly difficult. McIver and Morgan have conjectured that the worst-case behaviour results from a ring configuration of three evenly spaced tokens, giving an expected time of approximately 0.15N2. However, the tightest upper bound proved to date is 0.64N2. We apply probabilistic verification techniques, using the probabilistic model checker PRISM, to analyse the conjecture, showing it to be correct for all sizes of the ring that can be exhaustively analysed. We furthermore demonstrate that the worst-case execution time of the algorithm can be reduced by using a biased coin.

• Item Type: Articles (Other)
• Additional Information: From the issue entitled "Celebrating the 60th Birthday of Carroll Morgan"
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Norman, Dr Gethin
• Authors: Kwiatkowska, M., Norman, G., and Parker, D.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Formal Aspects of Computing
• ISSN: 0934-5043
• ISSN (Online): 1433-299X