Bernoulli Trials: Examples

Abstract

The following examples illustrate ideas in Chapter 5. Our running queueing example is continued in the second, following the setup in the first. The third and fourth examples, independent of the first two, show how the transitions of a continuous-state Markov chain can be structured so that our RQMC techniques for Bernoulli trials apply. Section 10.3 shows, in greater generality than we have seen previously, how extreme skewness arises naturally when applying change of measure and/or Russian roulette at the successive states visited of a Markov chain. It also gives the first modern treatment of filtering when splitting and Russian roulette are used as well as change of measure. Example 10.3.1 in that section deals with weight windows, which depend on filtering and attentuate skewness. Except for the subsubsection on tailoring weight windows for RQMC, Section 10.3 can be read independently of the rest of this book. The sixth (and last) example treats network reliability; there is no reference to it elsewhere in this book, so it can be skimmed at first reading.