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Deterministic Network Calculus

Deterministic Network Calculus. DNC history. Queueing Theory, Agner Krarup Erlang, 1909 Queueing Networks, James R. Jackson, 1957 Scheduling Theory, Liu & Layland, 1972 Network Calculus, Rene Cruz, 1991 , J. Y. Le Boudec. DNC motivation.

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Deterministic Network Calculus

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  1. Deterministic Network Calculus

  2. DNC history • Queueing Theory, Agner Krarup Erlang, 1909 • Queueing Networks, James R. Jackson, 1957 • Scheduling Theory, Liu & Layland, 1972 • Network Calculus, Rene Cruz, 1991 • , J. Y. Le Boudec

  3. DNC motivation • Queueing Networks predict backlogs and waiting in networks of servers and buffers (production, computer networks, traffic) • QN theory is probabilistic – not suited for real time analysis • Scheduling theory gives worst case (non-deterministic) results for single queues under restricting assumptions • Deterministic Network Calculus extends scheduling theory to a non deterministic theory for networks.

  4. Cirquit analysis

  5. Concatenation of Network Elements

  6. Converging Flows

  7. Feedback

  8. Definition and Range Spaces

  9. Definition and Range Spaces

  10. The Playout Buffer

  11. The Playout Buffer

  12. Arrival Curves

  13. Arrival Curves

  14. Spacing and Staircases

  15. Left Continuity

  16. An Equivalence

  17. The Leaky Bucket in Words

  18. Leaky Bucket in Graphics

  19. Nice to know about Leaky Buckets

  20. Some DN-Calculus in Play Henrik should prove this on the blackboard

  21. The Generic Cell Rate Algorithm

  22. GCRA facts

  23. Leaky Buckets and GCRAs

  24. Good Functions

  25. Subadditivity

  26. Sufficiency of Subadditive Arrivals

  27. Minimum Arrival Curves

  28. Minimum Arrival Curves (example)

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