Fractal Analysis of Intraflow Unidirectional Delay over W-LAN and W-WAN WAN Environments

Transcription

1 Fractal Analysis of Intraflow Unidirectional Delay over W-LAN and W-WAN WAN Environments Dimitrios Pezaros with Manolis Sifalakis and Laurent Mathy Computing Department Lancaster University

2 Outline Motivation Experimental measurement environment In-line measurement Fractal analysis of unidirectional delay Process calibration and tuning Long-range dependence estimation Measurement results Conclusion

3 Motivation Self-similarity and Long Range Dependence (LRD) widely studied on aggregate (LA)Network traffic Traffic arrival process; single observation point; linked to heavytailed phenomena Limited LRD examination on intraflow performance Few studies concentrated on periodic poll flows Different metrics; Different influencing factors; different mechanisms to control per-flow performance This study: unidirectional delay as input signal Wireless networks reported to exhibit large and variable delays W-LAN: fluctuating radio quality W-WAN: link-layer (reliability) mechanisms

4 Experimental Wireless Environment Mixed wired-wireless configuration IEEE b/g campus-wide LAN Orange, UK, GPRS/GSM wireless WAN Nokia D211 combo PCMCIA b/GPRS adapter

5 In-line measurement for IPv6 traffic Instrumentation mechanism complementing active and passive measurements Overcome existing limitations; e.g. Heisenberg effects, scalability of untargeted monitoring, etc. Targeted measurement on the actual network traffic Employ native IPv6 features to directly implement a set of performance metrics Destination options header; selective processing only at adequately engineered/provisioned nodes The triggers involving the measurement activity and minimal measurement data are carried in-line, within the actual user packets Flexibility to incrementally develop new options Network layer ubiquity: potentially applicable to any type of traffic E2E One-Way Delay (OWD) implementation Linux (2.4.x) kernel-level prototype implementation Kernel timestamps computed at network layer entry/exit functions OWD P = T AP -T D P

6 In-line measurement (e2e) operation

7 Fractals, Self-Similarity Similarity (SS) and Long-Range Dependence (LRD) Fractal analyses focus on the spatiotemporal evolution properties of data series and their correlation structure Self-similar processes: statistical properties of segments within the corresponding time series are similar irrespective of the time scale of observation Manifestations of self-similar processes Slowly decaying variances; non-summable spectral density for frequencies close to the origin; long-range dependence Long memory or Long-Range Dependence (LRD) Current state of the process has significant influence on subsequent states far into the future High variability is preserved over multiple time scales

8 SS and LRD Notations A stochastic process Y(t), is self-similar with selfsimilarity (Hurst) parameter 0 < H < 1, if for α >0, t 0 H Yt () = d a Y( αt). The autocorrelation function of the increment process X(t)=Y(t) Y(t-1) at lag k is given by For 0.5 < H < 1, X(t) is Long-Range Dependent, i.e. β ( ) t 1 ρ k = k+ k + k k 2 2H 2 ρ( k) H(2H 1) k, k 2H 2H 2H ( ) (( 1) 2 ( 1) ), 1. lim ρ k /[ ck ] = 1, 0 < β < 1, c > 0, β = 2 2H k k = 1 ρ( k) =.

9 Stochastic self-similarity similarity in OWD data: TCPoWLAN Unidirectional Delay (ms) Unidirectional Delay (ms) Unidirectional Delay (ms) Unidirectional Delay (ms) Normalised Time (Slots of 1 sec) Normalised Time (Slots of 0.5 sec) Normalised Time (Slots of 1 sec) Normalised Time (Slots of 0.5 sec) Unidirectional Delay (ms) Unidirectional Delay (ms) Unidirectional Delay (ms) Unidirectional Delay (ms) Normalised Time (Slots of 0.1 sec) Normalised Time (Slots of 0.05 sec) Normalised Time (Slots of 0.1 sec) Normalised Time (Slots of 0.05 sec)

10 Tuning the OWD analysis process NTP Synchronisation Examine traces against negative delays and linear alterations (trends) Convert measurement traces into time series data Discretise delay observations into equally-sized bins based on packet arrival time; average OWD within each bin Inevitably smooths out short-term variations Time series length Series sufficiently long for unbiased Hurst Exponent estimates OWD series length N ~ 2 12 Inspection for non-stationarities Intuitive approach: visually examine trace against long plateaus of very high delays; still, sometimes impossible to tell Systematic approach: classify signal as noise or motion using the slope of the power spectral density plot

11 Tuning the LRD estimation process Randomised buckets: independently control amount of correlation at different timescales Internal randomisation: remove short-term correlations; preserve long-memory Simultaneous employment of diverse LRD estimators LRD estimators exhibit different characteristics, e.g. detection vs. accuracy No single estimator can reliably quantify the presence (or otherwise) of LRD Oversampling Alleviate statistical inaccuracies at high aggregation levels Expand the series by D-times duplicate insertion in round-robin fashion and smooth out using a digital low-pass filter

12 Time-domain (heuristic) estimators Investigate the evolution of a statistical property of the time series at different time-aggregation levels Aggregated Variance method For LRD processes the variance of the m-aggregated series decays more slowly than the reciprocal of the sample size On a log-log plot of sample variance vs. sample size a least squares line assumes slope -1 < β < 0; H = 1 β/2 R/S Statistic The rescaled adjusted range statistic of a LRD time series grows according to a power law with exponent H as a function of the number of points (n) included E[R(n)/S(n)] ~ cn H, n On a log-log plot of R/S versus n, the slope of a least squares fit is a direct estimate of ½ < H < 1

13 Frequency-domain estimators Examine the power spectral density of the series based on the periodogram obtained by the Fast Fourier Transform algorithm Periodogram n 1 I( λ) = X je 2 π n j= 1 On a log-log plot of the periodogram versus frequency, the regression of a LRD series should give a slope of 1-2H Whittle Non-graphical method based on the periodogram; the estimator is the value of η that minimises the following function ( λη ; ) Allows the calculation of confidence intervals; assumes data is consistent with fgn ijλ π I( λ) Q( η): = dλ, π f 2

14 Graphical estimation methods: WLAN flows Aggregated Variance Method H = R/S Method H = Periodogram Method H = log10(variances) log10(r/s) log10(periodogram) log10(m) Aggregated Variance Method H = log10(d) R/S Method H = log10(frequency) Periodogram Method H = log10(variances) log10(r/s) log10(periodogram) log10(m) Aggregated Variance Method H = log10(d) R/S Method H = log10(frequency) Periodogram Method H = log10(variances) log10(r/s) log10(periodogram) log10(m) 3.0 log10(d) log10(frequency)

15 Graphical estimation methods: WWAN flows Aggregated Variance Method H = R/S Method H = Periodogram Method H = log10(variances) log10(r/s) log10(periodogram) log10(m) Aggregated Variance Method H = log10(d) R/S Method H = log10(frequency) Periodogram Method H = log10(variances) log10(r/s) log10(periodogram) log10(m) Aggregated Variance Method H = log10(d) R/S Method H = log10(frequency) Periodogram Method H = log10(variances) log10(r/s) log10(periodogram) log10(m) log10(d) log10(frequency)

16 LRD intensity estimation results Microflow Aggregated Variance Normal / Oversampling R/S Normal / Oversampling Periodogram Whittle [95% C.I.] TCP data path [W-LAN] / / [ ] TCP data path [W-WAN] / / [ ] TCP reverse path [W-LAN] / / [ ] TCP reverse path [W-WAN] / / [ ] CBR [W-LAN] / / [ ] CBR [W-WAN] / / [ ]

17 Non-trivial correlations TCPoWLAN TCPoWWAN Autocorrelation Function Internal Randomisation Autocorrelation Function Internal Randomisation Autocorrelation Function Internal Randomisation Autocorrelation Function Internal Randomisation ACF Bucket size 1 Bucket size 20 Bucket size 50 Bucket size 100 ACF Bucket size 1 Bucket size 20 Bucket size 50 Bucket size 100 ACF Bucket size 1 Bucket size 20 Bucket size 50 Bucket size 100 ACF Bucket size 1 Bucket size 20 Bucket size 50 Bucket size Lag Lag Lag Lag Autocorrelation Function Internal Randomisation Autocorrelation Function Internal Randomisation UDPoWLAN ACF Bucket size 1 Bucket size 20 Bucket size 50 Bucket size 100 UDPoWWAN ACF Bucket size 1 Bucket size 20 Bucket size 50 Bucket size Lag Lag

18 Conclusions and future work Intraflow unidirectional delay exhibits fractal-like behaviour over W- LAN and W-WAN environments Existence of non-trivial correlations at large lags LRD estimators vary; whittle estimates seem to agree most with ACFs; LRD cannot be safely assumed when the majority of estimators report small Hurst values (<0.65) Correlation between OWD, packet size, and packetisation mechanisms is probable Similar behaviour is expected for IPv4 traffic Further work Experimentation with very long-lived flows (elephants) Comparison between end-to-end unidirectional delays experienced over wireless and wired infrastructures Investigation of causal relationships: heavy-tailness in fundamental related phenomena Transport protocol engineering to account for/reduce delay variability