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| Introduction I A First Course in Network Calculus 1 Network Calculus 1.1 Models for Data Flows 1.1.1 Cumulative Functions, Discrete Time versus Continuous Time Medels 1.1.2 Backlog and Virtual Delay 1.1.3 Example: The Playout Buffer 1.2 Arrival Curves 1.2.1 Definition cf an Arrival Curve 1.2.2 Leaky Bucket and Generic Cell Rate Algorithm 1.2.3 Sub-additivity and Arrival Curves 1.2.4 Minimum Arrival Curve 1.3 Service Curves 1.3.1 Definition of Service Curve 1.3.2 Classical Service Curve Examples 1.4 Network Calculus Basics 1.4.1 Three Bounds 1.4.2 Are the Bounds Tight ? 1.4.3 Concatenation 1.4.4 Improvement of Backlog Bounds 1.5 Greedy Shapers 1.5.1 Definiticns 1.5.2 Input-Output Characterization of Greedy Shapers 1.5.3 Properties of Greedy Shapers 1.6 Maximum Service Curve, Variable and Fixed Delay 1.6.1 Maximum Service Curves 1.6.2 Delay from Backlog 1.6.3 Variable versus Fixed Delay 1.7 Handling Variable Length Packets 1.7.1 An Example of Irregularity Introduced by Variable Length Packets 1.7.2 The Packetizer 1.7.3 A Relation between Greedy Shaper and Packetizer 1.7.4 Packetized Greedy Shaper 1.8 Lossless Effective Bandwidth and Equivalent Capacity 1.8.1 Effective Bandwidth of a Flow 1.8.2 Equivalent Capacity 1.8.3 Example: Acceptance Region for a FIFO Multiplexer 1.9 Proof of Theorem 1.4.5 1.10 Bibliographic Notes 1.11 Exercises 2 Application of Network Calculus to the Internet 2.1 GPS and Guaranteed Rate Schedulers 2.1.1 Packet Scheduling 2.1.2 GPS and a Practical Implementation (PGPS) 2.1.3 Guaranteed Rate Schedulers 2.2 The Integrated Services Model of the IETF 2.2.1 The Guaranteed Service 2.2.2 The Integrated Services Model for Internet Routers 2.2.3 Reservation Setup with RSVP 2.2.4 A Flow Setup Algorithm 2.2.5 Multicast Flows 2.2.6 Flow Setup with ATM 2.3 Schedulability 2.3.1 EDF Schedulers 2.3.2 SCED Schedulers [65] 2.3.3 Buffer Requirements 2.4 Application to Differentiated Services 2.4.1 Differentiated Services 2.4.2 A Bounding Method for Aggregate Scheduling 2.4.3 An Explicit Delay Bound for Differentiated Services Networks 2.4.4 Bounds for Aggregate Scheduling with Dampers 2.5 Exercises II Mathematical Background 3 Basic Min-plus and Max-plus Calculus 3.1 Min-plus Calculus 3.1.1 Infimum and Minimum …… III A Second Course in Network Calculus Bibliogrphy Index |
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