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Statistical Multiplexing: Basic Principles

Statistical Multiplexing: Basic Principles. Carey Williamson. University of Calgary. Introduction . Statistical multiplexing is one of the fundamental principles on which ATM networking is based

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Statistical Multiplexing: Basic Principles

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  33. Summary (Cont’d) • Simulation observations: • Easier to multiplex “small” things than “big” things (peak to link ratio) • 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. Summary (Cont’d) • Easier to multiplex homogeneous traffic than it is for heterogeneous traffic • The larger the average burst length, the harder it is to multiplex the traffic • 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

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