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网络演算 全文 英文 原版 I AFirstCourseinNetworkCalculus 1 NetworkCalculus 2 ApplicationtotheInternet II MathematicalBackground 3 BasicMin-plusandMax-plusCalculus 4 Min-plusandMax-PlusSystemTheory III ASecondCourseinNetworkCalculus 5 OptimalMultimediaSmoothing 6 AggregateScheduling 7 AdaptiveandPacketScaleRateGuarantees 8 TimeVaryingShaper 9 SystemswithLosses
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NETWORK CALCULUS
A Theory of Deterministic Queuing Systems for the Internet
JEAN-YVES LE BOUDEC
PATRICK THIRAN
Online Version of the Book Springer Verlag - LNCS 2050
Version May 10, 2004
2
A Annelies
A Joana, Ma
¨
elle, Audraine et Elias
Amam
`
ere
—- JL
A mes parents
—- PT
Pour
´
eviter les grumeaux
Qui encombrent les r
´
eseaux
Il fallait, c’est compliqu
´
e,
Ma
ˆ
ıtriser les seaux perc
´
es
Branle-bas dans les campus
On pourra dor
´
enavant
Calculer plus simplement
Gr
ˆ
ace
`
a l’alg
`
ebre Min-Plus
Foin des obscures astuces
Pour estimer les d
´
elais
Et la gigue des paquets
Place
`
a “Network Calculus”
—- JL
vi
Summary of Changes
2002 Jan 14, JL Chapter 2: added a better coverage of GR nodes, in particular equivalence with service
curve. Fixed bug in Proposition 1.4.1
2002 Jan 16, JL Chapter 6: M. Andrews brought convincing proof that conjecture 6.3.1 is wrong. Re-
designed Chapter 6 to account for this. Removed redundancy between Section 2.4 and Chapter 6.
Added SETF to Section 2.4
2002 Feb 28, JL Bug fixes in Chapter 9
2002 July 5, JL Bug fixes in Chapter 6; changed format for a better printout on most usual printers.
2003 June 13, JL Added concatenation properties of non-FIFO GR nodes to Chapter 2. Major upgrade of
Chapter 7. Reorganized Chapter 7. Added new developments in Diff Serv. Added properties of PSRG
for non-FIFO nodes.
2003 June 25, PT Bug fixes in chapters 4 and 5.
2003 Sept 16, JL Fixed bug in proof of theorem 1.7.1, proposition 3. The bug was discovered and brought
to our attention by Franc¸ois Larochelle.
2004 Jan 7, JL Bug fix in Proposition 2.4.1 (ν>
1
h−1
instead of ν<
1
h−1
)
2004, May 10, JL Typo fixed in Definition 1.2.4 (thanks to Richard Bradford)
Contents
Introduction xiii
I A First Course in Network Calculus 1
1 Network Calculus 3
1.1 Models for Data Flows . . ................................... 3
1.1.1 Cumulative Functions, Discrete Time versus Continuous Time Models ........ 3
1.1.2 Backlog and Virtual Delay ............................... 5
1.1.3 Example: The Playout Buffer ............................. 6
1.2 Arrival Curves .......................................... 7
1.2.1 Definition of an Arrival Curve . ............................ 7
1.2.2 Leaky Bucket and Generic Cell Rate Algorithm .................... 10
1.2.3 Sub-additivity and Arrival Curves ........................... 14
1.2.4 Minimum Arrival Curve . . .............................. 16
1.3 Service Curves ......................................... 18
1.3.1 Definition of Service Curve .............................. 18
1.3.2 Classical Service Curve Examples . . . . . ...................... 20
1.4 Network Calculus Basics . ................................... 22
1.4.1 Three Bounds . . . . . . ................................ 22
1.4.2 Are the Bounds Tight ? ................................. 27
1.4.3 Concatenation . . . . . ................................ 28
1.4.4 Improvement of Backlog Bounds ........................... 29
1.5 Greedy Shapers . . . . . . . . . ................................ 30
1.5.1 Definitions ....................................... 30
1.5.2 Input-Output Characterization of Greedy Shapers ................... 31
1.5.3 Properties of Greedy Shapers . ............................. 33
1.6 Maximum Service Curve, Variable and Fixed Delay . . . ................... 34
1.6.1 Maximum Service Curves . .............................. 34
1.6.2 Delay from Backlog .................................. 38
1.6.3 Variable versus Fixed Delay .............................. 39
vii
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