1. Self-Similarity of Network Traffic Presented by Wei Lu Supervised by Niclas Meier 05/06 2004

2. 2 Table of Content Network Traffic Study –Motivation –Measurement –Modeling Classic Model, Poisson or Markovian Self-Similar Model –What’s Self-Similarity –Definition of Self-Similarity –Explanation of Self-Similarity –Impact on network performance –Adapting to Self-Similarity

3. 3 Understanding network traffic behavior is essential for all aspects of network design and operation –Component design –Protocol design –Provisioning –Management –Modeling and simulation Motivation for Network Traffic Study

4. 4 Network Traffic Measurement Collect data or packet traces showing packet activity on the network for different network applications Purpose –Understand the traffic characteristics of existing networks –Develop models of traffic for future networks –Useful for simulations, planning studies

5. 5 Traffic modeling in the world of telephony was the basis for initial network models –Assumed Poisson arrival process –Assumed Exponential call duration –Well established queuing literature based on these assumptions –Enabled very successful engineering of telephone networks Network Traffic Modeling In the past…

6. 6 Classic Model Poisson Process Markov Chain ON-OFF model Interrupted Poisson Process 01  ON Fixed rate arrival OFF   Active Poisson arrival Idle   2 

7. 7 The Story Begins with Measurement In 1989, Leland and Wilson begin taking high resolution traffic traces at Bellcore –Ethernet traffic from a large research lab –Mostly IP traffic (a little NFS) –Four data sets over three year period

8. 8 Actual Network Traffic v.s. Poisson [Chun Zhang 2003] Network Traffic Measurement Poisson Traffic Model 5,8,2 mean 5

9. 9 What’s Self-Similarity Self-similarity describes the phenomenon where a certain property of an object is preserved with respect to scaling in space and/or time. (also called fractals) If an object is self-similar, its parts, when magnified, resemble the shape of the whole.

10. 10 Definition of Self-Similarity Self-similar long-range dependenceSelf-similar processes are the simplest way to model processes with long-range dependence The autocorrelation function  k of a process with long-range dependence is not summable: –   k  . e.g.  k  k -  as k  . for 0 <  < 1 Autocorrelation function follows a power law Slower decay than exponential process –If   k < . Long Range Dependence Short Range Dependence

11. 11 Self-Similarity contd. Zero-mean stationary time series X = (X t ;t = 1,2,3,…), m- aggregated series X (m) = (X k (m) ;k = 1,2,3,…) by summing X over blocks of size m. X is H-self-similar (distributional self-similarity), if for all positive m, X (m) has the same distribution as X rescaled by m H. –PDF{X at }=PDF{ m H {X t } }. X is Second-order-self-similar, if  (m) (k) of the series X (m) for all m. – Var(X (m) ) =  2 m -β, and –  (m) (k) =  (k), k  0 [Asymptotically:  (m) (k)   (k), m  Degree of self-similarity is expressed as the speed of decay of series autocorrelation function using the Hurst parameter

12. 12  =1,H=0.5 SRD  =0.6,H=0.7 LRD Log( Var(X (m) ) ) = log(  2 m -β ) =2log  - βlog m Y X Graphic Tests, e.g. Variance-time plots The variance of X (m) is plotted v.s. m on log-log plot Slope (-  > –1 indicates of SS H = 1 -  /2 –LRD, ½ < H < 1 –Degree of SS\LRD increases as H  1 H increases, more bursty

13. 13 Modeling Self-Similarity Superposition of High Variability ON-OFF Sources –Extension to traditional ON-OFF models by allowing the ON and OFF periods to have infinite variance (high variability or Noah Effect) X 1 (t)offon X 2 (t)on X 3 (t)off S 3 (t) 3 0 222 111 time

14. 14 Explanation of Self-Similarity Consider a set of processes which are either ON or OFF –The distribution of ON time is heavy tailed (wide range of different values, including large values with non-negligible probability) The size of files on a server are heavy-tail The transfer times also have the same type of characteristics. –The distribution of OFF time is heavy tailed Since some source model phenomena that are triggered by humans (e.g. HTTP sessions) have extremely long period of latency.

15. 15 Impact on Network Performance Self-similar burstiness can lead to the amplification of packet loss. The burstiness cannot be smoothed. Limited effectiveness of buffering –queue length distribution decays slower than exponentially v.s. the exponential decay associated with Markovian input

16. 16 [Kihong Park, Walter Willinger] Mean queue length v.s. buffer capacity at a bottleneck router when fed with self-similar input with varying degrees of LRD but equal traffic intensity   2 : weak Long Range Correlation, buffer capacity of about 60kB suffices to contain the input’s variability, the average buffer occupancy remains below 5kB   1:strong LRC, increase in buffer capacity accompanied by increase in buffer occupancy Impact, contd.

17. 17 Adapt to self-similarity Flexible resource allocation –Increase bandwidth to accommodate periods of “ burstiness ”. Could be wasteful in times of low traffic intensity  adaptive adjustment can be effective counter measure. –Increase the buffer size to absorb periods of “ burstiness ”. –Tradeoff, increase both appropriately.

18. 18 Current Status Many people (vendors) chose to ignore self- similarity People want to blame the protocols for observed behavior Multi-resolution analysis may provide a means for better models Lots of opportunity!!

19. 19 Questions?