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Rational Interpolation for Rare Event Probabilities
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gong, Wei-Bo |
| Copyright Year | 2007 |
| Abstract | We propose to use rational interpolants to tackle some com-putationally complex performance analysis problems such as rare-event probabilities in stochastic networks. Our main example is the computation of the cell loss probabilities in ATM multiplexers. The basic idea is to use the values of the performance function when the system size is small, together with the asymptotic behaviour when the size is very large, to obtain a rational interpolant which can be used for medium or large systems. This approach involves the asymptotic analysis of the rare-event probability as a function of the system size, the convergence analysis of rational inter-polants on the positive real line, and the quasi-Monte Carlo analysis of discrete event simulation. The introduction of rational interpolation for evaluating rare event probabilities in 20] was motivated by the earlier work on the application of Pad e approximants to single-server queues with renewal arrival processes 6]. To obtain the Pad e approximants of a performance function we rst need to obtain its MacLaurin series. This has been done for several systems 5, 6, 9, 21]. The basic idea is to expand the innermost part of the performance function (for example the k-fold convolution of the interarrival-time density functions) into a MacLaurin series. Then interchange the operations (integrations, expectations, and summations) so that the summation operation is in the outermost position. The interchanges of operations are usually justiiable using the dominated convergence theorem. We rst derive the MacLaurin series of the k-fold convolution of a function. Let f(t) and g(t) be deened on the real line and are 0 when t < 0: The convolution of f(t) and g(t) is denoted by (f g)(t), and the k-fold convolution of f(t) is denoted by f k (t), where f 1 (t) 4 = f(t): Assume that P 1 i=0 f (i) (0) i! t i and P 1 i=0 g (i) (0) j! t i converge at any nite t 0. The convolu |
| File Format | PDF HTM / HTML |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | ATM Turbo Computation Converge Convolution Emoticon Extreme value theory HL7PublishingSubSection |
| Content Type | Text |
| Resource Type | Article |
