2006/12/28 by Annie Druault-Vicard, Druault-Vicard, Annie, Christian Tanguy +1
Business, Management and Accounting · Computer Science · Engineering · #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #Performance (cs.PF) #Reliability and Maintenance Optimization #Software Reliability and Analysis Research #cs.PF
paper · pdf · doi:10.48550/arxiv.cs/0612141
arxiv created 2006/12/28 · openalex publication_date 2006/12/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to k-out-of-n:G and linear consecutive k-out-of-n:F systems, and to a simple ladder network in which each edge and node may fail. We also give the associated generating functions when the components have identical availabilities and failure rates. For large systems, the failure rate of the whole system is asymptotically proportional to its size. This paves the way to ready-to-use formulae for various architectures, as well as proof that the differential operator approach to failure frequency calculations is very useful and straightforward.