Abstract
In previous chapters, we were interested mainly in the limiting or pre-limiting the behaviour of the probabilities of the states of queueing models. However, there exists another class of problems associated with non-stationary behaviour. Namely, imagine that we are seeking the time of the first accessing of a queue-length Q(•) of some fixed level Q*. If we study a redundant system, we may want to know what is the first break-down time. When studying a storage problem, it is interesting to estimate the first time of zero stock or the first time of overflow. In all such situations, the first-occurrence time is actually an r.v. and the problem consists of finding either the d.f. of this r.v., or its reasonable bounds.
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© 1994 Springer Science+Business Media Dordrecht
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Kalashnikov, V.V. (1994). First-Occurrence Events. In: Mathematical Methods in Queuing Theory. Mathematics and Its Applications, vol 271. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2197-4_11
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DOI: https://doi.org/10.1007/978-94-017-2197-4_11
Publisher Name: Springer, Dordrecht
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