2008/07/03 by Christian Tanguy, Tanguy, Christian
Business, Management and Accounting · Computer Science · #Advanced Queuing Theory Analysis #Distributed systems and fault tolerance #FOS: Computer and information sciences #Performance (cs.PF) #Petri Nets in System Modeling #cs.PF
paper · pdf · doi:10.48550/arxiv.0807.0626
arxiv created 2008/07/03 · openalex publication_date 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with asymptotic expressions of the Mean Time To Failure (MTTF) and higher moments for large, recursive, and non-repairable systems in the context of two-terminal reliability. Our aim is to extend the well-known results of the series and parallel cases. We first consider several exactly solvable configurations of identical components with exponential failure-time distribution functions to illustrate different (logarithmic or power-law) behaviors as the size of the system, indexed by an integer n, increases. The general case is then addressed: it provides a simple interpretation of the origin of the power-law exponent and an efficient asymptotic expression for the total reliability of large, recursive systems. Finally, we assess the influence of the non-exponential character of the component reliability on the n-dependence of the MTTF.