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Additional info for Contributions to Simulation Speed-Up
The simulated random variable is considered in such a way that its value space is divided into importance regions which can be handled separately. In [GS96], [Gör97] and [GF98], the possibilities of the combination of RESTART and LRE are shown. 1 Motivation To investigate QoS in high-speed networks, e. , cell loss probabilities (CLP) in ATM networks in the range of 10−9 , special simulation techniques are required which are able to evaluate the statistical properties of such rare events with a sufﬁcient accuracy.
The distance between the levels Hi = G(Ii ) of neighbouring thresholds should be set as close to optimum as possible. 4) A larger number of steps leads to a higher relative error for B, provided that the steps are all simulated with the same error limit dS . 3) contributes to the total error. 5) ∗ Discussions about the optimum values Ri and Hi , the resulting number of steps and the sample size, depending on correlation and given maximum error, can be found, among others, in [SG94], [GS96], [Gör97], and [PLG02].
14) shows this as a relation of the levels Hi of the thresholds Ii : Hi|X ≥Ii−1 = Hi ∀i = 0, . . 14) The theoretical optimum is Hi|X ≥Ii−1 = e−2 as long as no unknown model dependent parameters are taken into account, see [PLG02]. If the random variable is discrete, obviously the thresholds Ii cannot always be set to the exact ∗ values corresponding to the optimum Hi . They have to be rounded to the closest value of the value space. Precisely, a threshold can also be put between two possible neighbouring values of the random variable’s value space, but not more than one.