Deterministic Network Calculus

9 A Hierarchy of Service Curves

In section 5.2, we defined the notion of service curves. One particularity of the service curves is that they can be of different types, and we defined two of these curves, namely the min-plus service curves and the strict service curves. We also put emphasis on the differences between these two types of service curves and their respective properties.

Several other types of minimal service curves have been developed in the literature, and the topic of this chapter is to study some of these types.

We will see that some types of service curves are very similar to one another (e.g. variable capacity nodes and strict service curves are similar for a large class of functions). Some others, such as the weakly strict service curve, the sufficiently strict service curve and the adaptive service curve have been defined as compromises between min-plus and strict service curves. We will also study the service curve from the real-time calculus, a formalism that is very close to network calculus.

In this chapter, we define the different types of service curves in section 9.1, and comment on each of them. In section 9.2, we compare the different types of service curves, establish a hierarchy between them and describe the cases when two types of service curves are equivalent.

It can be considered as problematic that there are several non-equivalent types of service curves: they have different modeling power, and more importantly, the type of the service curve ...