Extending the Network Calculus Algorithmic Toolbox for Ultimately Pseudo-Periodic Functions: Pseudo-Inverse and Composition

Abstract

Network Calculus (NC) is an algebraic theory that represents traffic and service guarantees as curves in a Cartesian plane, in order to compute performance guarantees for flows traversing a network. NC uses transformation operations, e.g., min-plus convolution of two curves, to model how the traffic profile changes with the traversal of network nodes. Such operations, while mathematically well-defined, can quickly become unmanageable to compute using simple pen and paper for any nontrivial case, hence the need for algorithmic descriptions. Previous work identified the class of piecewise affine functions which are ultimately pseudo-periodic (UPP) as being closed under the main NC operations and able to be described finitely. Algorithms that embody NC operations taking as operands UPP curves have been defined and proved correct, thus enabling software implementations of these operations. However, recent advancements in NC make use of operations, namely the lower pseudo-inverse, upper pseudo-inverse, and composition, that are well defined from an algebraic standpoint, but whose algorithmic aspects

Nancy: An efficient parallel Network Calculus library

“…1], for instance, checks if f (0) = g(0) = 0, f (t) ≤ g(t) ∀ t, and f is 2 This operation is used, for instance, in [19]. To the best of our knowledge, it has been first formally described in the context of UPP curves in [20].…”