Some examples and counterexamples for (min,+) filtering operations

This paper collects a serie of examples and counterexamples encountered in the study of the algorithmics of Network Calculus operations. Network Calculus is a deterministic queuing theory which aims at providing bounds on the performances of communication networks thanks to a nice formalization in (min,+) algebra. Often presented as a (min,+) filtering theory by analogy with the (+,x) filtering of traditional system theory, it makes use a well-defined set of operations. Their algorithmic aspects have not been much addressed. For this reason, we describe and analyze in a previous report a set of algorithms implementing these Network Calculus operations for a well-chosen class of functions. During this work, we had to construct some examples and counterexamples in order to draw the limits of our results or to illustrate them. Many of them have been omitted in that report and are now presented in this companion-paper