Reliability Analysis of [Formula Omitted]-for-[Formula Omitted] Shared Protection Systems With General Repair-Time Distributions

• Published in: IEEE transactions on reliability 2011-09, Vol.60 (3), p.647
• Main Authors: Ozaki, Hirokazu, Kara, Atsushi
• Format: Article
• Language: English
• Subjects: Cloud computing; Failure; Mathematical models; Studies
• ISSN: 0018-9529; 1558-1721
• DOI: 10.1109/TR.2011.2160669

In this paper, we investigate the user perceived reliability of [Formula Omitted]-for-[Formula Omitted] shared protection systems. The [Formula Omitted]-for-[Formula Omitted] shared protection system is a general type of the fault-tolerant configuration with shared backup units. We assume that there are [Formula Omitted] working units each serving a single group of users and [Formula Omitted] shared protection (spare) units in the system. We also assume that the time to failure of the unit is subject to an exponential distribution, and the time to repair it is subject to a general distribution. Under these assumptions, we derive the Laplace transform of the reliability function (The cdf of the failure time, i.e. the cumulative distribution function of the time beyond which the system will survive) for each user, as well as the user-perceived Mean Time to First Failure (MTTFF) by combining the state transition analysis and the supplementary variable method. We also show the effect of the repair time distribution of the units through the case study of the cloud computing systems in which [Formula Omitted] service-independent servers share [Formula Omitted] spares for backup purpose. The analysis reveals that there exist optimal values for [Formula Omitted] and [Formula Omitted] in terms of the reliability and the cost for the given conditions of failures and repairs.