Traffic Modeling

1. Traffic Modeling Nelson L. S. da Fonseca Institute of Computing State University of Campinas Campinas, Brazil

2. Network Workload: “Traffic” • Telecom networks built to transport traffic • Flow of bytes or packets or messages

3. Multimedia Networks

4. Quality of Services • “Perception of the quality of the transfer of information expressed by quantitative metrics”

5. 33011 bytes (33) 25239 bytes (30) 17179 bytes (27) 9265 bytes (24) 7042 bytes (21) 4819 bytes (18) 2617 bytes (15) 2006 bytes (12) 1393 bytes (9) 793 bytes (6) 447 bytes (3) 227 bytes (1) Quality of Service 1393 bytes (9) 793 bytes (6) 447 bytes (3) 227 bytes (1)

6. Why Traffic Models Matter?Queuing in Multimedia Networks

7. Why is Traffic Modeling Important? • Need for performance evaluation and capacity planning • Understand the nature of traffic generated by applications and their transformation along the network • Conception of effective traffic control mechanisms: congestion control, flow control, routing …

8. Why is Traffic Modeling Important? • Accurate performance prediction requires realistic traffic models • Can use in analysis or testing (“synthetic traffic”) • Synthetic traffic matches real traces, is more efficient to use

9. An Example • Traffic: 5 synchronous streams of 299,040 cells/sec • Buffer size B, line rate 312,500 cells/sec • An ATM cell 53 bytes

10. An Example • G/D/1/B or nD/D/1 r = 0.957 • E(W) = 2.7 msec • W < Wmax = 4 x 3.2 = 12.8 msec • No losses for B=4 or bigger • If Poisson: M/D/1, already big difference • E(W) = r m / 2(1- r) = r 3.2 /2(1- r) = 35.6 msec! • Need B = 249 for cell loss 10-9! • Conclusion: Mean is not enough; smoothness or burstiness affects a lot

11. Our Goal • To understand relevance of traffic characteristics with respect to network performance and QoS • Identify and familiarize with common traffic models

12. Mean and Variance

13. Mean and Variance Mean amount of work arrived at each slot = 4 Variance =

14. Mean and Variance Mean amount of work arrived= 4.0 Variance of the amount of work arrived =

15. Mean and Variance • Both processes have the same mean and variance. But what is their impact on queuing?

16. Mean and Variance • Consider a queue with a server, service rate of two cells per time unit and buffer space of two cells. 2/1

17. Mean and Variance When the first stream Feeds the queue No loss! Service = 2/1

18. Mean and Variance But when the second flow feeds the queue then 1/5 pkts are lost! 2/1

19. Correlation Low Correlation High Correlation

20. Variance v=Autocovariance Integral -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 Autocovariance

21. LRD versus SRD

22. Origins of Correlations… • Superposition of weakly correlated sources • Size of files • User behavior • Protocol dynamics • etc ….

23. Video • MPEG

24. Video • 500x500 pixels por frame = 250.000 pixels por frame, generating 2 Mbits/frame for an 8-bit gray scale at a rate of 30 frames/sec 60 Mbits/seg. If three colors are used, the transmission rate is 180 Mbits/sec Compression Variable Bit Rate

25. Video

26. Variable Bit Rate

27. Burstiness • Variable with time scales

28. Traffic Bursts and Scales • Hierarchical view • Call • Burst • Packet • How to characterize: Mean? Peak? Variance? Autocorrelation?

29. Burstiness • Most traffic types in high-speed networks are bursty • Burstiness is mainly due to autocorrelation • Renewal models assume autocorrelation away for tractability • Performance prediction non-realistic without burstiness

30. Taxonomy of Models • Renewal and IID: no dependence • Short Range Dependent (SRD) • Markov modulated, Interrupted Poisson Process etc. • Semi Markov • MAP • Fluid: useful for analysis and also for simulation • Regression models – classical statistics • Long range Dependent (LRD) • Monofractal (self-similar) • Multifractal

31. SRD Models

32. Voice Source • Human voice bursts of 0.4 a 1.2 sec durations and periods of silence of 0.6 a 1.8 sec (exponentially distributed); • Sampling at 125 mseg intervals with 8 bits coding 170 cells (53 bytes) ATM/sec ON OFF

33. Superposition of Voice Sources

34. Superposition of Voice Sources

35. Superposition of Voice Sources

36. Superposition of Voice Sources

37. Fluid-Flow Equations • x– buffer occupancy; • Each voice source generates V cells/sec during talk spurt with duration of 1/a sec; • A channel with capacity VCcells/sec has aC units of information per second; • N sources; • Fi(t,x) – system state, at time t there are isources in state on and the buffer occupancy is x;

38. Fluid-Flow Equations

39. Fluid-Flow Equations • Fj(x) = Prob. [j sources on, buffer occupancy≤x]

40. Markov Modulated Process • Arrival rate depends on understanding Markov chain 1 2 n l1 l2 ln

41. Superposition of Voice Sources 1 2 l1 l2

42. Superposition of Voice Sources

43. Superposition of Voice Sources

44. Superposition of Voice Source2-states MMPP

45. Markov Modulated Process • M/G/1 – type • Efficient algorithms

46. M/M/1

47. Markov Modulated Process

48. Markov Modulated Process single Arrivals batch discrete Time continuous

49. Markov Modulated Process • Markov Modulated Poisson Process – MMPP (continuous time, single arrival) • Batch Markovian arrival process – BMAP (continuous time, batch arrival)

50. Markov Modulated Process • Discrete Time Batch Markovian Arrival Process – D-BMAP (discrete time, batch arrivals) • Discrete Time Markovian Arrival Process (D-MAP)