Subadditive convolutions

Two typical instances where subadditive curves occur are arrival curves (given an a.c. $\alpha$, $\overline{\alpha}$ is also an arrival curve) and the service curve for a link with window flow-control, since it involves the structure $\overline{\beta + W}$.

When these are used in studies, one may find expressions comprised of the convolution of several of these subadditive curves. In [ZS23], we identified several properties that, leveraging the subadditivity, enable significant optimizations of these convolutions.

These optimizations are implemented in Nancy transparently: the user only needs to mark the curves known to be subadditive using SubAdditiveCurve, or obtain them using SubadditiveClosure(), and the library will do the rest.

For more details, checkout the paper [ZS23] or [Zippo23], Chapter 13.