1. 1 Statistical Multiplexing: Basic Principles Carey Williamson University of Calgary

2. 2 Introduction l Statistical multiplexing is one of the fundamental principles on which ATM networking is based l Everyone understands the basic concept of stat mux, but figuring out how to do it right is still a hard problem l LOTS of papers on it, but probably as many “answers” as authors!

3. 3 Agenda l This presentation: one sample paper l Woodruff and Kositpaiboon, “Multimedia Traffic Management Principles for Guaranteed ATM Network Performance” l IEEE JSAC, Vol. 8, No. 3, April 1990

4. 4 Overview of Paper l Identifies several high-level general principles regarding statistical multiplexing, traffic management, and call admission control l Presents simulation results to illustrate quantitatively the regions where statistical multiplexing makes good sense and where it does not

5. 5 Main Principles l Reasonable bandwidth utilization l Robustness to traffic uncertainties l Simplicity l Node architecture independence

6. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0

7. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 Deterministic Multiplexing for Peak/Mean = 2 0.5

8. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 Deterministic Multiplexing for Peak/Mean = 20

9. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 Deterministic Multiplexing for Peak/Mean = 2 0.5 Deterministic Multiplexing for Peak/Mean = 20

10. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5

11. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 Statistical Multiplexing for Peak/Mean = 2 when average burst B = 10

12. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 Statistical Multiplexing for Peak/Mean = 2 when average burst B = 100

13. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 B = 10 B = 100 Peak/Mean = 2

14. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 Statistical Multiplexing for Peak/Mean = 20 when average burst B = 10

15. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 Statistical Multiplexing for Peak/Mean = 20 when average burst B = 100

16. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 B = 10 B = 100 Peak/Mean = 20

17. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 B = 10 B = 100 Peak/Mean = 20 B = 10 B = 100 Peak/Mean = 2

18. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Maximum Link Utilization 0.0 1.0 0.5 B = 10 B = 100 Peak/Mean = 20 B = 10 B = 100 Peak/Mean = 2 Best region for statistical multiplexing

19. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Buffer Requirements

20. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Buffer Requirements Utilization = 10%

21. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Buffer Requirements Utilization = 50%

22. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Buffer Requirements Utilization = 90%

23. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution Deterministic Utilization = 10%

24. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution Geometric Utilization = 10%

25. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution Utilization = 50% Deterministic

26. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution Utilization = 50% Geometric

27. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution Utilization = 90% Deterministic

28. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution Utilization = 90% Geometric

29. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution G G G G G D D D U = 90% U = 50%

30. Granularity of Source (Peak rate/Link rate) 0.0 1.0 Buffer Size/Avg Burst Length 0 30 Effect of Burst Size Distribution G G G G G D D D U = 90% U = 50% Best region for statistical multiplexing

31. 31 Summary l A nice paper describing the general principles to follow in call admission control, statistical multiplexing, and traffic management l Quantitative illustration of performance effects, and illustration of when statistical multiplexing works and when it does not

32. 32 Summary (Cont’d) l General traffic management principles: –Reasonable bandwidth utilization –Robustness –Simplicity –Node architecture independence

33. 33 Summary (Cont’d) l Simulation observations: l Easier to multiplex “small” things than “big” things (peak to link ratio) l The burstier the traffic sources (peak to mean ratio), the greater the potential gains of statistical multiplexing, but the harder it is to multiplex traffic safely and still guarantee performance

34. 34 Summary (Cont’d) l Easier to multiplex homogeneous traffic than it is for heterogeneous traffic l The larger the average burst length, the harder it is to multiplex the traffic l The larger the average burst length, and the greater the variation in burst size, the more buffers you will need in your system in order to multiplex effectively