# 5 Network Calculus Basics: a Server Crossed by a Single Flow

This chapter presents the basic concepts of network calculus, namely arrival and service curves and the basic results concerning performance bounds, for the simplest model: a single flow crossing a single server. These results are fundamental for the analysis of more complex systems that will be handled in the rest of the book. For example, the analysis of a sequence of servers crossed by a single flow or of a server crossed by a single flow can be, after some transformations, reduced to the analysis of such a simple system. These transformations will be respectively explained in Chapters 6 and 7.

Our simple network composed of one flow and one server is illustrated in Figure 5.1. Its *modeling* has been presented in Chapter 1, as well as the performance criteria (delay and memory usage). As the real system is usually not known at design time, the challenge is to define *abstractions*, also called *envelopes*, of the real components such that the behavior of the final system will respect the expected properties. Then, the *analysis* is based on this abstraction of the system. This abstraction can be seen as a *contract* between components, a specification, allowing us to compute bounds valid on every conform implementation. Such an abstraction can also be seen as an *approximation*, when the exact behavior is known, but too complex to model, or partially known. Whatever the interpretation is, we need a framework for this abstraction ...

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