1. Anue Systems Inc1 v1.0 - 20050426 Telecommunications Industry AssociationTR-30.3/08-12-023 Lake Buena Vista, FL December 8 - 9, 2008

2. Load, Delay and Packet Loss TIA TR 30.3 meeting December 8-9, 2008 Orlando, FL

3. TR 30.3 Meeting 12/8/2008 Goals Improve TIA-921-A Packet based Model Correctly emulates impairment with different bit rate, packet size and packet intervals. Can handle mixed traffic. Contrast with Time based model where the fixed packet size and packet interval must be specified. Cannot handle mixed traffic. Variable bit rate user data (e.g. MPEG4 video) Results depend on user packet sizes and when they arrive Bidirectional network model (asymmetric) Enforce bandwidth limits Better correspondence between high latency and lost packets Fewer “magic” numbers in the model Fewer test cases

4. TR 30.3 Meeting 12/8/2008 Goal: Understand this diagram. Disturbance load generator + Input user packets Output user packets Disturbance Packets Link Latency

5. TR 30.3 Meeting 12/8/2008 Review of our previous work Excellent proposal by Alan Clark to create a new model The model takes into account traffic characteristics Models typical TCP flow characteristics. We discussed models used for G.8261 Many similarities between TIA-921 and G.8261 But enough differences to warrant a new effort We discussed characteristics of disturbance loads Burstiness definitions Disturbance load probability density functions

6. TR 30.3 Meeting 12/8/2008 Modeling strategies Top down or bottom up Many models are hybrids. Top down models are constructed empirically Observe behavior of the system under various conditions Select parameter values that fits the observations The parameters may or may not be physical properties of the system Bottom up models are constructed analytically Analyze how an idealized network component should behave Parameters for these models are usually physical properties of the system For example: buffer size in a router or switch Test model components individually and compare the idealized results with actual measurements to verify. If there’s a discrepancy, the idealized model must be revised

7. TR 30.3 Meeting 12/8/2008 Modeling Strategies (cont.) TIA-921 and TIA-921-A A hybrid approach These models are mainly top down models today But have some bottom up characteristics Some effects (such as serialization delay) derive from actual physical characteristics of the links Other effects (such as core network behavior and link impulse probability) are empirically determined. Goal for TIA-921-B is to build on previous work Improved model should have more parts built bottom up.

8. TR 30.3 Meeting 12/8/2008 The ultimate bottom-up model We could build a discrete event simulation of every packet But it is too computationally intensive. It requires that we simulate both packets of interest (user packets) and disturbance load packets. A 24-hour simulation of a 10 hop network built out of GE switches and operating at 50% load with 1400 byte (avg) packets represents about 40 Billion packets. That’s half a petabit. If you watched HDTV for two years straight, without sleeping, it would use about that many bits. Therefore it is not possible to simulate everything. We must make some approximations.

9. TR 30.3 Meeting 12/8/2008 Strategy for simplification Create a statistical model of the disturbance load traffic Derive the delay and loss characteristics for different levels of disturbance loads. Fully simulate all of the user packets Use a statistical approximation of the disturbance load Alan indicated he had information on characterizing typical TCP flows. Last conference call, we talked about load PDFs Statistical models of the disturbance packets Result is a model that only needs to perform calculations when a user packet is received. Significant increase in performance and accuracy.

10. TR 30.3 Meeting 12/8/2008 Review: Burstiness 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 (chosen randomly) The time that the generator is off is T gap Choose a linear mapping for burst load L Bmin – Load during burst when L nom = 0 L Bmax – Load during burst when L nom = 100%

11. TR 30.3 Meeting 12/8/2008 Review: Burstiness Equations

12. TR 30.3 Meeting 12/8/2008 Review: Burstiness L Bmin = 50%, L Bmax = 133%

13. TR 30.3 Meeting 12/8/2008 Review: Composite Load PDF Two CBR disturbance load generators One bursty gamma disturbance load generator

14. TR 30.3 Meeting 12/8/2008 Idealized wire rate ethernet switch/router Disturbance load generator + Input user packets Output user packets Disturbance Packets Link Latency Store & Forward Enqueue Delay Dequeue Delay Clock Crossing Link Bit Rate R (bits/sec) Fixed Latency Buffer Size F(bits)

15. TR 30.3 Meeting 12/8/2008 Idealized wire rate ethernet switch/router Delay for idealized switch has several factors Fixed latency constant (approx 500ns) Link latency Time of flight for the signal (photons or electrons) Store and Forward delay (serialization delay) depends on user packet size (receive packet size/receive link rate) Random Clock crossing delay uncertainty (small, dozens of ns) Enqueue and Dequeue latency (small, hundreds of ns) Queuing delay Load dependent This is the hard part

16. TR 30.3 Meeting 12/8/2008 Our example load PDF

17. TR 30.3 Meeting 12/8/2008 Delay and loss from disturbance load PDF Assume that the queue starts out empty We’ll revisit this assumption later, don’t worry A user packet of size S i arrives at time t i Define: Step 1: How much disturbance load arrived between t i-1 and t i ? t i-1 titi SiSi

18. TR 30.3 Meeting 12/8/2008 Disturbance Load CDF CDF is cumulative distribution function for PDF Is piecewise continuous, monotonically increasing and invertible

19. TR 30.3 Meeting 12/8/2008 Inverse CDF function (CDF -1 ) The inverse CDF function can help It is a mapping from uniform random numbers (easy to make) to random numbers of any distribution (hard to make) This mapping can be pre-computed and saved in memory (very fast!) Uniform Random Number

20. TR 30.3 Meeting 12/8/2008 Delay and loss from disturbance load PDF A user packet of size S i arrives at time t i Step 1: How much disturbance load arrived between t i-1 and t i ? Generate by mapping a uniform random number through CDF -1 Get a load percentage for t i : L i t i-1 titi SiSi

21. TR 30.3 Meeting 12/8/2008 Divide into three simpler sub-problems Non-congested Load is between 0 and L CONGEST (100%) Congested Load is between L CONGEST (100%) and L DROP Overloaded Load is more than L DROP We’ll define L DROP in a moment

22. TR 30.3 Meeting 12/8/2008 Three simpler sub-problems

23. TR 30.3 Meeting 12/8/2008 Simplest sub-problem: Overload Easiest sub-problem: the user packet gets dropped This happens if the disturbance load percentage is so high that the queue is completely full when the user packet arrives. Define L DROP as the load threshold above which a drop must occur. If L i >= L DROP then the user packet is dropped If F =16k bytes, R =100Mbit/second, and  =1ms, then L DRO P =231%

24. TR 30.3 Meeting 12/8/2008 Next simplest problem: non-congested If 0 < L i < 100% then the queue will contain at most one disturbance load packet when the user packet arrives. The user packet is not dropped in this case. Therefore it will be serviced immediately after any in-progress packet Delay depends on the size of the disturbance packet (known), and when the user packet arrives relative to the disturbance packet (random). Assume arrival times are uncorrelated -> uniform RV. Assume that the disturbance packets are E bits, which means that the maximum amount of time it has to wait ( δ ) is So for this case, the delay is a uniform random value: [0.. δ ]

25. TR 30.3 Meeting 12/8/2008 Non-congested case: Example δ=110.4us

26. TR 30.3 Meeting 12/8/2008 Non-Congested case: 50% TM2 TM2 has 30%-64Byte, 10%-576Byte, 60%-1518Byte So a 50% TM2 load is 15%,5%,30%. This PDV histogram is often said to resemble a church or cathedral

27. TR 30.3 Meeting 12/8/2008 Non-Congested case: Lab measurements See the characteristic “cathedral” shape of the PDV? Typical measured PDV

28. TR 30.3 Meeting 12/8/2008 Congested case Disturbance load 100% < L i < L DROP Seems hard (but actually turns out to be simple) We assumed that the buffer started out empty (remember, we’ll fix this in a few more slides) Conservation: Bits added to queue during  i : L i *  i * R Bits removed from queue during  i :  i * R The difference is the buffer fullness (G) And the delay is G i /R

29. TR 30.3 Meeting 12/8/2008 Adding memory We assumed that the queue always started out empty This essentially means that the time intervals (  ) are independent It is a reasonable approximation when the buffer size is much smaller than the number of bits serviced by the queue during . It’s usually a good approximation for high speed links But not for low speed links like TIA-921 Access links So, to fix that, save the queue state as a variable G i Need an equation to calculate G i+1 Change the threshold levels for L CONGEST and L DROP

30. TR 30.3 Meeting 12/8/2008 Add memory Adjust the thresholds L CONGEST and L DROP Update equation for G i (after calculation, G i+1 is limited to be less than or equal to F)

31. TR 30.3 Meeting 12/8/2008 Conclusion Statistically modeling the disturbance load allows more accurate implementation of TIA-921-B Supports Variable bit rate user data (e.g. MPEG4 video) Results depend on user packet sizes when they arrive Bidirectional network model (assymetric) Enforces bandwidth limits Better correspondence between high latency and lost packets Fewer “magic” numbers in the model

32. TR 30.3 Meeting 12/8/2008 Next Steps TBD