Synchronized concurrent processes as a modelling pattern and their efficient solution by compositional uniformization

In: Tagungsband Vierter Workshop des GI-ITG-Fachausschusses MMB zur Leistungs-, Zuverlässigkeits- und Verlässlichkeitsbewertung von Kommunikationsnetzen und verteilten Systemen / Heidtmann, K.; Wolfinger, B. (Hrsg.)
Hamburg (2007)
Buchaufsatz / Kapitel / Fach: Informatik; Wirtschaftswissenschaften
Abstract:
The paper starts with a brief overview on performance and reliability modelling
paradigms for concurrent processes and their mapping to a Markov chain which is
composed of marginal absorbing Markov chains. We use a new technique called
compositional uniformization which allows for the evaluation of the mean time for a
complete synchronization cycle which can be expressed as the mean time to
absorption of concurrent and independent marginal Markov chains. The mean time to
absorption exhibits a compositional character in the sense that quantities belonging
to the marginal chains are combined to yield the desired cumulative measure. We
demonstrate the efficiency of the technique by means of a very large example. Finally
we discuss an extension to the field of reliability evaluation; we sketch how to
calculate the exact MTTF for heterogeneous k-of-m systems by usage of the new
technique.