Boundary Problems for Sequences with Independent Increments and Factorization Identities
We have already seen that the study of the basic characteristics of queueing systems (and of many other service systems as well; see Chapters 5–8) leads to certain functional of the trajectories generated by the governing sequences. It is natural to call these boundary functionals, since all of them are connected with attainment by these trajectories of certain boundaries. In this regard, it seems fitting to present here the basic methods of investigation and the corresponding results relating to the problem of finding the distributions of the most important and (for us) interesting boundary functionals (we will call these boundary problems). We will consider functionals of the sequences Y n ;n≥ 0 formed by sums of i.i.d. variables (see also §§ 5, 9).
KeywordsJoint Distribution Boundary Problem Factorization Identity Lower Characteristic Independent Increment
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