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Burstiness Model and Disturbance Load in Telecommunications

Learn about burstiness modeling and disturbance load generation in telecommunications networks. Understand load probability density function (PDF) using simple generators such as CBR and Gamma. Explore examples and mathematical definitions to depict bursty load behavior.

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Burstiness Model and Disturbance Load in Telecommunications

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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

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