Deterministic Network Calculus

Table of contents

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