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Self-Similarity in Network Traffic

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Self-Similarity in Network Traffic

Kevin Henkener

5/29/2002

- 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.

- 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.

- 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.

- 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

- 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

- 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

- low, medium, and high traffic hours
- as traffic increases, the Hurst parameter increases
- i.e., traffic becomes more self-similar

- 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

- 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

- 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

- Two formal mathematical models that yield elegant representations of self-similarity
- fractional Gaussian noise
- fractional autoregressive integrated moving-average processes

- 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

- 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

- 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.

- 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.

- Dynamic Control of Traffic Flow
- Structural resource allocation

- 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

- 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

- increase level of redundancy when traffic is high

- Two types:
- bandwidth
- buffer size

- Bandwidth
- increase bandwidth to accommodate periods of “burstiness”
- could be wasteful in times of low traffic intensity

- 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