Comparison of different classes of service curves in Network Calculus

In envelope-based models for worst-case performance evaluation like Network Calculus or Real-Time Calculus, several types of service curves have been introduced to quantify some deterministic service guarantees. This paper studies the expressiveness of those different definitions of service curves. We revisit the hierarchy ranging from the most restrictive definition linked to variable capacity nodes to the most general definition of simple service curves. We state the conditions when the different definitions overlap and discuss the existence of canonical descriptions for systems specified through those definitions.