Deterministic Network Calculus

10 Modular Analysis: Computing with Curves

In the previous part, the concepts to compute the performance bounds in one server have been introduced. The aim of this part is to use them to study more complex communication networks. The general problem of computing performance bounds in networks has received much attention, and many techniques have been used, depending on the hypothesis on the arrival and departure processes.

This part is divided into three chapters. The first two chapters focus on the general methods to compute performance bounds in feed-forward networks (i.e. there is no cyclic dependence between the flows circulating in the network). Feed-forward networks are a general class of networks for which the stability condition (i.e. the condition under which the amount of data in the network remains bounded) is known. As a result, the only problem that is focused on here is the problem of computing performance bounds that approach as much as possible the exact worst-case performance bound. The third chapter will be devoted to cyclic networks, where no general result is known for the stability of large classes of networks.

As far as acyclic networks are concerned, there are two main approaches:

1. 1) the first uses the contracts (arrival and service curves) to compute worst-case delay bounds. As we will see, the tightness of the performance bounds we had in the single server case is lost, but the methods developed are very algorithmically efficient. The key tool is the ...