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NETWORK CALCULUS
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Network Calculus is a set of recent developments that provide deep insights into flow problems encountered
in networking. The foundation of network calculus lies in the mathematical theory of dioids, and in particular,
the Min-Plus dioid (also called Min-Plus algebra). With network calculus, we are able to understand
some fundamental properties of integrated services networks, window flow control, scheduling and buffer
or delay dimensioning.
This book is organized in three parts. Part I (Chapters 1 and 2) is a self contained, first course on network
calculus. It can be used at the undergraduate level or as an entry course at the graduate level. The prerequisite
is a first undergraduate course on linear algebra and one on calculus. Chapter 1 provides the main set of
results for a first course: arrival curves, service curves and the powerful concatenation results are introduced,
explained and illustrated. Practical definitions such as leaky bucket and generic cell rate algorithms are cast
in their appropriate framework, and their fundamental properties are derived. The physical properties of
shapers are derived. Chapter 2 shows how the fundamental results of Chapter 1 are applied to the Internet.
We explain, for example, why the Internet integrated services internet can abstract any router by a ratelatency
service curve. We also give a theoretical foundation to some bounds used for differentiated services.
Part II contains reference material that is used in various parts of the book. Chapter 3 contains all first level
mathematical background. Concepts such as min-plus convolution and sub-additive closure are exposed in
a simple way. Part I makes a number of references to Chapter 3, but is still self-contained. The role of
Chapter 3 is to serve as a convenient reference for future use. Chapter 4 gives advanced min-plus algebraic
results, which concern fixed point equations that are not used in Part I.
JEAN-YVES LE BOUDEC and PATRICK THIRAN - Personal Name
1st Edition
NONE
Mathematics
English
2012
1-263
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