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- W2494338568 abstract "The connection between reliability theory and queueing theory has enriched both sciences. In reliability theory, investigators have used the methods and results from queueing theory; however, queueing theory has adopted new ideas and new problems from reliability theory. In studying standby systems with renewal, it is assumed that the life length is distributed according to an exponential law. Under these conditions, the operation of the system is described by a homogeneous Markov process with a finite number of states. Almost all reliability theory problems are solved under the assumption that all the distribution laws are exponential. A number of problems in queueing theory, in which some of the distribution laws are arbitrary, have been solved. Methods of solving such problems have been developed. These methods include the method of embedded Markov chains, the method of integro-differential equations, and the method using Spitzer's identity. These methods are not suitable for use in reliability theory. The reason lies not only in the fact that these methods are complicated and not easily accessible to engineers but also in the fact that the solution of such problems leads to cumbersome formulas that are unsuitable for computations." @default.
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- W2494338568 date "1969-01-01" @default.
- W2494338568 modified "2023-09-28" @default.
- W2494338568 title "Standby Redundancy without Renewal" @default.
- W2494338568 cites W1964772730 @default.
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- W2494338568 doi "https://doi.org/10.1016/b978-1-4832-3053-5.50011-9" @default.
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