×

zbMATH — the first resource for mathematics

Time-dependent behavior of redundant systems with deterministic repair. (English) Zbl 0862.60075
Stewart, William J. (ed.), Computations with Markov chains. Proceedings of the 2nd international workshop on the numerical solution of Markov chains, Raleigh, NC, USA, January 16–18, 1995. Boston, MA: Kluwer Academic Publishers. 135-150 (1995).
Summary: We consider various redundant systems attended by a single repairperson that services components in a first come first served order. Failure times are taken to be exponentially distributed random variables, while repair times are deterministic. As a result, the underlying stochastic process is not Markovian or semi-Markovian. However, the underlying stochastic process is Markov regenerative and as such we are able to write and solve equations for the process. We compute various dependability measures, such as reliability function, mean time to failure, time-dependent and steady-state availability.
For the entire collection see [Zbl 0940.00042].

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
PDF BibTeX XML Cite