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, order to compute performance for flows traversing network. NC uses transformation operations, e.g., min-plus convolution of two curves, model how the profile changes with traversal network nodes. Such while mathematically well-defined, can quickly become unmanageable using simple pen paper any non-trivial case, hence need algorithmic descriptions. Previous work identified class piecewise affine functions which are ultimately pseudo-periodic (UPP) being closed under main operations able be described finitely. Algorithms embody taking operands UPP have been defined proved correct, thus enabling software implementations these operations. However, recent advancements make use namely lower pseudo-inverse , upper composition well-defined from standpoint, but whose aspects not addressed yet. In this paper, we introduce algorithms above when extending available toolbox NC. We discuss properties providing formal proofs correctness.