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PART 3: Network Calculus: Global Analysis
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PART 3: Network Calculus: Global Analysis
by Euriell Le Corronc, Marc Boyer, Anne Bouillard
Deterministic Network Calculus
Cover
Acknowledgments
Introduction
1 Basic Model: Single Server, Single Flow
1.1. Modeling principles
1.2. Constant rate server
1.3. Flow model
1.4. Server model
1.5. Delay and memory usage models
1.6. Summary
PART 1: (min,plus) Functions and Algorithms
2 The (min,plus) Functions Semi-ring
2.1. The (min,plus)-based dioids
2.2. Sub-additive closure
2.3. Deconvolution
2.4. Link with (max,plus) dioid
2.5. Summary
3 Sub-classes of Functions
3.1. Usual functions
3.2. Non-negative and non-decreasing functions
3.3. Concave and convex functions
3.4. Summary
4 Efficient Computations for (min,plus) Operators
4.1. Classes of functions with finite representations
4.2. Piecewise linear concave/convex functions
4.3. A stable class of functions
4.4. Containers of (min,plus) functions
4.5. Implementations
PART 2: Network Calculus: Local Analysis
5 Network Calculus Basics: a Server Crossed by a Single Flow
5.1. Arrival curve
5.2. Service curves
5.3. From curves to performance guarantees
5.4. Bibliographic and historic notes
5.5. Summary
6 Single Flow Crossing Several Servers
6.1. Servers in tandem
6.2. Control design
6.3. Essential use cases
6.4. Summary
7 Multiple Flows Crossing One Server
7.1. MIMO servers and aggregation of flows
7.2. Blind or arbitrary multiplexing
7.3. Some service policies
7.4. Summary
8 Packets
8.1. Packetizer
8.2. Packet-based schedulers
8.3. Bibliographic notes
8.4. Summary
9 A Hierarchy of Service Curves
9.1. Different types of service curves
9.2. Comparison of service curves
9.3. No intermediate service curve
PART 3: Network Calculus: Global Analysis
10 Modular Analysis: Computing with Curves
10.1. Network model
10.2. Some special topologies
10.3. The pay multiplexing only once phenomenon
10.4. Per-flow analysis of networks
10.5. NP-hardness of computing tight bounds
10.6. Conclusion
11 Tight Worst-case Performances
11.1. Tandem networks under arbitrary multiplexing
11.2. Tandem networks under the FIFO policy
11.3. Bibliographic notes
12 Stability in Networks with Cyclic Dependencies
12.1. Network stability
12.2. The fix-point method: sufficient condition for global stability
12.3. Universally stable service policies
12.4. Instability of some systems
12.5. Bibliographic notes
Conclusion
Appendix
List of Symbols
References
Index
End User License Agreement
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9 A Hierarchy of Service Curves
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10 Modular Analysis: Computing with Curves
PART 3
Network Calculus: Global Analysis
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