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- W2087021013 abstract "The distribution of the maximum of the virtual waiting time during a cycle C is studied for a variety of queueing models. For the M/M/1 queue, the idea is a generalization of the ladder height representation of the steady-state limit V( ∞), and the results are explicit in terms of the failure rate r(u) and the density. For queues with a general Markovian arrival process and phase-type service times, the basic idea is to represent the distribution of (C) by means of a multivariate version r(u) of the failure rate which again is related to generalized ladder heights. The fundamental step in the evaluation of r(u) is the determination of a set of first passage probabilities, which can be done either by solving a set of linear equations, or by deriving a matrix Ricatti differential equation having an explicit matrix-exponential solution; both approaches require the steady-state characteristics. For extreme value theory in the form of studying the asymptotic behaviour of as t → ∞, essentially only the tail cha..." @default.
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- W2087021013 date "1992-01-01" @default.
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- W2087021013 title "On cycle maxima, first passage problems and extreme value theory for queues" @default.
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