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1. Telecommunications Industry Association TR-30.3/08-12-022 Lake Buena Vista, FL December 8 - 9, 2008 Anue Systems, Inc. www.anuesystems.com v1.0 - 20050426

2. Overview • Recap last meeting • Define a Burstiness Model • Define the disturbance Load PDF • Simple generators (CBR, Gamma) • Bursty case • Composite case • Next presentation: Putting it all together • The Relationship between load and delay/loss • one node • multiple cascaded nodes Anue Systems, Inc. www.anuesystems.com

3. Recap: G.8261 Network model Anue Systems, Inc. www.anuesystems.com

4. Disturbanceloadgenerator Output packets Input packets LinkLatency + DisturbancePackets Recap: Node model • 10 cascaded instances of this basic element Anue Systems, Inc. www.anuesystems.com

5. Recap: Test cases Anue Systems, Inc. www.anuesystems.com

6. TM1 and TM2 • TM1 is composed of packets carrying voice and SMS messages and is specified as • 80% minimum size packets (64 bytes) • 5% medium size packets (576 bytes) • 15 % maximum size packets (1518 bytes) • TM2 is composed of larger packets representative of a more data-centric network. It is specified as • 30% minimum size packets (64 bytes) • 10% medium size packets (576 bytes) • 60 % maximum size packets (1518 bytes) • The maximum size packets for both TM1 and TM2 occur in bursts lasting between 0.1s and 3 s. • The minimum size packets for TM1 are constant bit rate (CBR). Anue Systems, Inc. www.anuesystems.com

7. A fly in the ointment • Definitions of TM1 and TM2 in G.8261 are incomplete • Burstiness is critical and not defined • I’ll define one view of burstiness later • And only max-len pkt generators are bursty. Others need to be specified as well. • Assume CBR for simplicity, but there is no loss of generality in the subsequent analysis. Anue Systems, Inc. www.anuesystems.com

8. Burstiness: Definitions • Define as an off and on process • Disturbance load generator is off or on • Definitions: • Nominal generator load is Lnom • While the generator is on, it creates a burst load Lburst • While the generator is off, it generates load of 0% • The time that the generator is on is Tburst • The time that the generator is off is Tgap Anue Systems, Inc. www.anuesystems.com

9. Burstiness: Some math • Require: Average load over a burst and immediately following gap must equal Lnom. • Therefore: • To complete the burstiness definition • Must define either Lburst or Tgap. • One way: Define Lburst as a function of Lnom. • Where LBmin and LBmax represent the minimum and maximum burst load values • Thus there is a linear relation between burst & nominal load Anue Systems, Inc. www.anuesystems.com

10. Burstiness: more math • The only remaining item is Tgap: • Can calculate burst duty cycle as well: Anue Systems, Inc. www.anuesystems.com

11. Burstiness Example #1 • LBmin=0,LBmax=200%, then: • Lburst= 2 x Lnom • Duty is always 50%. Anue Systems, Inc. www.anuesystems.com

12. Burstiness Example #2 • LBmin=LBmax= 100%, then: • Burst load is constant at 100% • Duty decreases as Lnom increases. Anue Systems, Inc. www.anuesystems.com

13. Burstiness Example #3 • LBmin= 50%, LBmax= 133% Anue Systems, Inc. www.anuesystems.com

14. Question • What happens if we take • LBmin= 0%, LBmax= 100% • ?? • Burstiness disappears entirely. Anue Systems, Inc. www.anuesystems.com

15. Burstiness: • So: Is this a good way to define burstiness? • Yes. It is a good way to set up a model. • It is flexible to model a wide variety of network conditions, while still being mathematically tractable. • We gave three examples (+1) of how the mathematical model can be used. • This shows its flexibility. Anue Systems, Inc. www.anuesystems.com

16. Load Probability Density Function (PDF) • The Load PDF represents the fraction of time that a given disturbance load generator is generating a given short-term load level. • We analyze two fairly simple cases here • CBR generator • Gamma generator • Then generalize to bursty sources using the foregoing burstiness model • And further generalize to sums of disturbance loads. Anue Systems, Inc. www.anuesystems.com

17. CBR generator • A CBR packet generator always generates the same percentage load, so it has a load PDF consisting of an impulse at the generator’s percentage load. Anue Systems, Inc. www.anuesystems.com

18. Gamma generator • A Gamma packet generator has a load PDF that is based on the Gamma probability density function. • The gamma distribution has two parameters • The shape of the distribution • The horizontal scale. • We choose k=2 and then substitute =/k=/2 so that the PDF is parameterized by its mean value . Anue Systems, Inc. www.anuesystems.com

19. Gamma Generator (cont.) Anue Systems, Inc. www.anuesystems.com

20. Load PDF for bursty generators • The PDF of a bursty generator has two parts: • An impulse at zero load, which represents the proportion of time that the generator is off. • A scaled copy of the load generator’s PDF which represents the time that the generator is on. • The relative weights of these two parts are given by the duty cycle of the bursts which we calculated earlier Anue Systems, Inc. www.anuesystems.com

21. Bursty CBR PDF: Example #1 • Take a bursty CBR generator at Lnom=50% • LBmin = 50% and LBmax= 133% • Calculate that Lburst=92% and Duty=55%. Anue Systems, Inc. www.anuesystems.com

22. Bursty CBR PDF: Example #1 (cont.) Anue Systems, Inc. www.anuesystems.com

23. Bursty Gamma PDF: Example #2 • Take a bursty Gamma generator at Lnom=50% • LBmin = 50% and LBmax= 133% • Burstiness same as before • Lburst=92% and Duty=55%. Anue Systems, Inc. www.anuesystems.com

24. Bursty Gamma PDF: Example #2 (cont.) Anue Systems, Inc. www.anuesystems.com

25. Composite Disturbance Load PDFs • A composite disturbance load is just a sum of two or more underlying disturbance loads. • Want to calculate the load PDF for such a source (e.g. TM1) • For TM1, the traffic mix is 80%/5%/15%, so a 50% nominal load has • 40% load of CBR 64 byte packets • 2.5% load of CBR 576 byte packets • 7.5% Bursty load of 1518 byte packets Anue Systems, Inc. www.anuesystems.com

26. 40% CBR64-byte 50% TM1 CBR Bursty 2.5% CBR576-byte  7.5% Bursty1518-byte Composite Disturbance Load PDFs • For max size (1518 byte) bursty generator, we use the same burst parameters as before, LBmin = 50% and LBmax= 133%, which gives Lburst=56% and Duty=13%. Anue Systems, Inc. www.anuesystems.com

27. Composite Disturbance Load PDFs • We know the load PDF for the two CBR generators • We do not know the load PDF underlying the bursty generator. It is not specified. • Therefore, analyze for both the CBR and Gamma cases • TM1 Bursty CBR • TM1 Bursty Gamma Anue Systems, Inc. www.anuesystems.com

28. Load PDF: TM1 Bursty CBR Anue Systems, Inc. www.anuesystems.com

29. Load PDF: TM1 Bursty CBR • To calculate the overall PDF, weeed to calculate the PDF of a sum of random variables. • This can be accomplished by convolution. • Use the  symbol to represent convolution Anue Systems, Inc. www.anuesystems.com

30. Load PDF: TM1 Bursty CBR Anue Systems, Inc. www.anuesystems.com

31. Load PDF: TM1 Bursty CBR Anue Systems, Inc. www.anuesystems.com

32. Load PDF: TM1 Bursty Gamma Anue Systems, Inc. www.anuesystems.com

33. Load PDF: TM1 Bursty Gamma Anue Systems, Inc. www.anuesystems.com

34. Load PDF: TM1 Bursty Gamma Anue Systems, Inc. www.anuesystems.com

35. Next steps • Analytical • Show how the disturbance load PDF is related to packet latency and loss at one node • Show how this can be generalized to two or more cascaded nodes • Show how Packet Delay Variation PDV can be predicted using an analytical model • Discuss how to modify the disturbance load model to better suit the needs of next version of TIA-921B. Anue Systems, Inc. www.anuesystems.com