Self-Similarity in Network Traffic

1. Self-Similarity in Network Traffic Kevin Henkener 5/29/2002

2. What is 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. • If an object is self-similar, its parts, when magnified, resemble the shape of the whole.

3. Pictorial View of Self-Similarity

4. The Famous Data • Leland and Wilson collected hundreds of millions of Ethernet packets without loss and with recorded time-stamps accurate to within 100µs. • Data collected from several Ethernet LAN’s at the Bellcore Morristown Research and Engineering Center at different times over the course of approximately 4 years.

6. Why is Self-Similarity Important? • Recently, network packet traffic has been identified as being self-similar. • Current network traffic modeling using Poisson distributing (etc.) does not take into account the self-similar nature of traffic. • This leads to inaccurate modeling which, when applied to a huge network like the Internet, can lead to huge financial losses.

7. Problems with Current Models • Current modeling shows that as the number of sources (Ethernet users) increases, the traffic becomes smoother and smoother • Analysis shows that the traffic tends to become less smooth and more bursty as the number of active sources increases

8. Problems with Current Models Cont.’d • Were traffic to follow a Poisson or Markovian arrival process, it would have a characteristic burst length which would tend to be smoothed by averaging over a long enough time scale. Rather, measurements of real traffic indicate that significant traffic variance (burstiness) is present on a wide range of time scales

9. Pictorial View of Current Modeling

10. Side-by-side View

11. Definitions and Properties • Long-range Dependence • covariance decays slowly • Hurst Parameter • Developed by Harold Hurst (1965) • H is a measure of “burstiness” • also considered a measure of self-similarity • 0 < H < 1 • H increases as traffic increases

12. Definitions and Properties Cont.’d • low, medium, and high traffic hours • as traffic increases, the Hurst parameter increases • i.e., traffic becomes more self-similar

13. Self-Similar Measures • Background • Let time series: X = (Xt : t = 0, 1, 2, ….) be a covariance stationary stochastic process • autocorrelation function: r(k), k ≥ 0 • assume r(k) ~ k-βL(t), as k∞where 0 < β < 1 • limt∞ L(tx) / L(t) = 1, for all x > 0

14. Second-order Self-Similar • Exactly • A process X is called (exactly) self-similar with self-similarity parameter H = 1 – β/2 if • for all m = 1, 2, …. var(X(m)) = σ2m-β • r(m)(k) = r(k), k ≥ 0 • Asymptotically • r(m)(k) = r(k), as m∞ • aggregated processes are the same • Current model shows aggregated processes tending to pure noise

15. Measuring Self-Similarity • time-domain analysis based on R/S statistic • analysis of the variance of the aggregated processes X(m) • periodogram-based analysis in the frequency domain

16. Methods of Modeling Self-Similar Traffic • Two formal mathematical models that yield elegant representations of self-similarity • fractional Gaussian noise • fractional autoregressive integrated moving-average processes

17. Results • Ethernet traffic is self-similar irrespective of time • Ethernet traffic is self-similar irrespective of where it is collected • The degree of self-similarity measured in terms of the Hurst parameter h is typically a function of the overall utilization of the Ethernet and can be used for measuring the “burstiness” of the traffic • Current traffic models are not capable of capturing the self-similarity property

18. Results Cont.’d • There exists the presence of concentrated periods of congestion at a wide range of time scales • This implies the existence of concentrated periods of light network load • These two features cannot be easily controlled by traffic control. • i.e., burstiness cannot be smoothed

19. Results Cont.’d • These two implications make it difficult to allocated services such that QOS and network utilization are maximized. • Self-similar burstiness can lead to the amplification of packet loss.

20. Problems with Packet Loss • Effects in TCP • TCP guarantees that packets will be delivered and will be delivered in order • When packets are lost in TCP, the lost packets must be retransmitted • This wastes valuable resources • Effects in UDP • UDP sends packets as quickly as possible with no promise of delivery • When packets are lost, they are not retransmitted • Repercussions for packet loss in UDP include “jitter” in streaming audio/video etc.

21. Possible Methods for Dealing with the Self-Similar Property of Traffic • Dynamic Control of Traffic Flow • Structural resource allocation

22. Dynamic Control of Traffic Flow • Predictive feedback control • identify the on-set of concentrated periods of either high or low traffic activity • adjust the mode of congestion control appropriately from conservative to aggressive

23. Dynamic Control of Traffic Flow Cont.’d • Adaptive forward error correction • retransmission of lost information is not viable because of time-constraints (real-time) • adjust the degree of redundancy based on the network state • increase level of redundancy when traffic is high • could backfire as too much of an increase will only further aggrevate congestion • decrease level of redundancy when traffic is low

24. Structural Resource Allocation • Two types: • bandwidth • buffer size • Bandwidth • increase bandwidth to accommodate periods of “burstiness” • could be wasteful in times of low traffic intensity

25. Structural Resource Allocation Cont.’d • buffer size • increase the buffer size in routers (et. al.) such that they can absorb periods of “burstiness” • still possible to fill a given router’s buffer and create a bottleneck • tradeoff • increase both until they complement each other and begin curtailing the effects of self-similarity