1. 10/24/2015Anue Systems, Inc. www.anuesystems.com 1 v1.0 - 20050426 Telecommunications Industry AssociationTR-30.3/08-12-022 Lake Buena Vista, FL December 8 - 9, 2008

2. 10/24/2015Anue Systems, Inc. www.anuesystems.com 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

3. 10/24/2015Anue Systems, Inc. www.anuesystems.com 3 Recap: G.8261 Network model

4. 10/24/2015Anue Systems, Inc. www.anuesystems.com 4 Recap: Node model 10 cascaded instances of this basic element Disturbance load generator + Input packets Output packets Disturbance Packets Link Latency

5. 10/24/2015Anue Systems, Inc. www.anuesystems.com 5 Recap: Test cases ScenarioNote G.8261MEF18 Test CaseTMDS1E1DS3E3 Static Load1TM2 Step Changes 2TM1 2TM26.1a6.1b6.1c6.1d Slow Ramp24 hr 3TM1 3TM26.2a6.2b6.2c6.2d Network Outage 10 sec 4TM1 4TM26.3a6.3b6.3c6.3d 100 sec 4TM1 4TM26.4a6.4b6.4c6.4d Congestion 10 sec 5TM1 5TM26.5a6.5b6.5c6.5d 100 sec 5TM1 5TM26.6a6.6b6.6c6.6d Route Change 1 hop 6TM1 6TM26.7a6.7b6.7c6.7d 5 hops 6TM1 6TM26.8a6.8b6.8c6.8d

6. 10/24/2015Anue 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).

7. 10/24/2015Anue 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.

8. 10/24/2015Anue 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 L nom  While the generator is on, it creates a burst load L burst  While the generator is off, it generates load of 0%  The time that the generator is on is T burst  The time that the generator is off is T gap

9. 10/24/2015Anue Systems, Inc. www.anuesystems.com 9 Burstiness: Some math Require: Average load over a burst and immediately following gap must equal L nom. Therefore: To complete the burstiness definition  Must define either L burst or T gap. One way: Define L burst as a function of L nom. Where L Bmin and L Bmax represent the minimum and maximum burst load values Thus there is a linear relation between burst & nominal load

10. 10/24/2015Anue Systems, Inc. www.anuesystems.com 10 Burstiness: more math The only remaining item is T gap : Can calculate burst duty cycle as well:

11. 10/24/2015Anue Systems, Inc. www.anuesystems.com 11 Burstiness Example #1 L Bmin =0, L Bmax =200%, then:  L burst = 2 x L nom  Duty is always 50%.

12. 10/24/2015Anue Systems, Inc. www.anuesystems.com 12 Burstiness Example #2 L Bmin = L Bmax = 100%, then:  Burst load is constant at 100%  Duty decreases as L nom increases.

13. 10/24/2015Anue Systems, Inc. www.anuesystems.com 13 Burstiness Example #3 L Bmin = 50%, L Bmax = 133%

14. 10/24/2015Anue Systems, Inc. www.anuesystems.com 14 Question What happens if we take  L Bmin = 0%, L Bmax = 100% ?? Burstiness disappears entirely.

15. 10/24/2015Anue 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.

16. 10/24/2015Anue 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.

17. 10/24/2015Anue 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.

18. 10/24/2015Anue 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 .

19. 10/24/2015Anue Systems, Inc. www.anuesystems.com 19 Gamma Generator (cont.)

20. 10/24/2015Anue 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

21. 10/24/2015Anue Systems, Inc. www.anuesystems.com 21 Bursty CBR PDF: Example #1 Take a bursty CBR generator at L nom =50%  L Bmin = 50% and L Bmax = 133% Calculate that L burst =92% and Duty=55%.

22. 10/24/2015Anue Systems, Inc. www.anuesystems.com 22 Bursty CBR PDF: Example #1 (cont.)

23. 10/24/2015Anue Systems, Inc. www.anuesystems.com 23 Bursty Gamma PDF: Example #2 Take a bursty Gamma generator at L nom =50%  L Bmin = 50% and L Bmax = 133% Burstiness same as before  L burst =92% and Duty=55%.

24. 10/24/2015Anue Systems, Inc. www.anuesystems.com 24 Bursty Gamma PDF: Example #2 (cont.)

25. 10/24/2015Anue 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

26. 10/24/2015Anue Systems, Inc. www.anuesystems.com 26 Composite Disturbance Load PDFs For max size (1518 byte) bursty generator, we use the same burst parameters as before, L Bmin = 50% and L Bmax = 133%, which gives L burst =56% and Duty=13%. 40% CBR 64-byte 2.5% CBR 576-byte 7.5% Bursty 1518-byte 50% TM1 CBR Bursty 

27. 10/24/2015Anue 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

28. 10/24/2015Anue Systems, Inc. www.anuesystems.com 28 Load PDF: TM1 Bursty CBR

29. 10/24/2015Anue 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

30. 10/24/2015Anue Systems, Inc. www.anuesystems.com 30 Load PDF: TM1 Bursty CBR

31. 10/24/2015Anue Systems, Inc. www.anuesystems.com 31 Load PDF: TM1 Bursty CBR

32. 10/24/2015Anue Systems, Inc. www.anuesystems.com 32 Load PDF: TM1 Bursty Gamma

33. 10/24/2015Anue Systems, Inc. www.anuesystems.com 33 Load PDF: TM1 Bursty Gamma

34. 10/24/2015Anue Systems, Inc. www.anuesystems.com 34 Load PDF: TM1 Bursty Gamma

35. 10/24/2015Anue 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.