The Network Calculus Book
The Network Calculus book by Jean-Yves Le Boudec and Patrick Thiran is
available for free download:
Have a look at the Table of Contents.
The book is also available as Springer-Verlag Lecture Notes
on Computer Science number 2050. We are very grateful to Springer-Verlag for
this generous arrangement.
Part I A First
Course in Network Calculus
1 Network Calculus
1.1 Models for Data
Flows
1.2 Arrival Curves
1.3 Service Curves
1.4 Network Calculus
Basics
1.5 Greedy Shapers
1.6 Maximum Service Curve, Variable and Fixed
Delay
1.7 Handling Variable Length Packets
1.8 Lossless Effective
Bandwidth and Equivalent Capacity
1.9 Proof of Theorem\nobreakspace {
1.10 Bibliographic Notes
1.11 Exercises
2 Application of Network
Calculus to the Internet
2.1 GPS and Guaranteed Rate Schedulers
2.2 The
Integrated Services Model of the IETF
2.3 Schedulability
2.4 Application
to Differentiated Services
2.5 Exercises
Part II Mathematical
Background
3 Basic Min-plus and Max-plus Calculus
3.1 Min-Plus
Calculus
3.2 Max-Plus Calculus
3.3 Exercises
4 Min-plus and
Max-Plus System Theory
4.1 Min-Plus and Max-Plus Operators
4.2 Closure
of an Operator
4.3 Fixed Point Equation (Space Method)
4.4 Fixed Point
Equation (Time Method)
4.5 Conclusion
Part III A Second Course in
Network Calculus
5 Optimal Multimedia Smoothing
5.1 Problem Setting
5.2 Constraints Imposed by Lossless Smoothing
5.3 Minimal Requirements
on Delays and Playback Buffer
5.4 Optimal Smoothing Strategies
5.5
Optimal Constant Rate Smoothing
5.6 Optimal Smoothing versus Greedy Shaping
5.7 Comparison with Delay Equalization
5.8 Lossless Smoothing over Two
Networks
5.9 Bibliographic Notes
6 FIFO Systems and Aggregate
Scheduling
6.1 Introduction
6.2 General Bounds for Aggregate Scheduling
6.3 Stability of a Network with Aggregate Scheduling
6.4 Bounds for a
FIFO Service Curve Element
6.5 Bounds for a Network of FIFO CBR Servers
6.6 Bibliographic Notes
6.7 Exercises
7 Adaptive and Packet
Scale Rate Guarantees
7.1 Introduction
7.2 Adaptive Guarantee
7.3
Application to the Internet: Packet Scale Rate Guarantee
7.4 Bibliographic
Notes
7.5 Exercises
8 Time Varying Shapers
8.1 Introduction
8.2 Time Varying Shapers
8.3 Time Invariant Shaper with Non-zero Initial
Conditions
8.4 Time Varying Leaky-Bucket Shaper
8.5 Bibliographic Notes
9 Systems with Losses
9.1 A Representation Formula for Losses
9.2 Application 1: Bound on Loss Rate
9.3 Application 2: Bound on Losses
in Complex Systems
9.4 Solution to Skohorkhod's Reflection Problem with Two
Boundaries
9.5 Bibliographic Notes
Bibliography
Index
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