On the Constancy of Internet Path Properties Yin Zhang, Nick Duffield AT&T Labs Vern Paxson, Scott...
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Transcript of On the Constancy of Internet Path Properties Yin Zhang, Nick Duffield AT&T Labs Vern Paxson, Scott...
On the Constancy of Internet Path Properties
Yin Zhang, Nick DuffieldAT&T Labs
Vern Paxson, Scott ShenkerACIRI
Internet Measurement Workshop 2001
Presented by Ryan
Outline
Motivation Three Notions of Constancy
Mathematical, Operational and Predictive Analysis Methodology Measurement Methodology Constancy of Internet Path Properties
Packet Loss and Throughput Conclusion
Motivation
There has been a surge of interest in network measurements Mathematical Traffic Models Operational Procedures Adaptive Algorithms
Measurements are inherently bound to the “present” state of the network
Motivation
Measurements are valuable when network properties exhibit constancy
Constancy like “stationarity” More general rather then a specific mathematical
view “Hold steady and does not change”
Notions of Constancy
Mathematical Constancy Operational Constancy Predictive Constancy
Mathematical Constancy
A dataset is mathematically steady if it can be described with a single time-invariant mathematical model
Key : To find the appropriate model Simplest Example
A single independent and identically distributed (IID) random variable
Operational Constancy
A dataset is operationally steady if the quantities of interest remain within bounds considered operationally equivalent
Key : Whether an application care about the changes
Operational Constancy
Operational but not Mathematical Loss rate remains constant at 10% for first thirty
minutes, abruptly changes to 10.1% for next thirty minutes
Mathematical but not Operational Loss process is a bimodal process with a high
degree of correlation An application will see sharp transitions from low-loss
to high-loss regimes
Predictive Constancy
A dataset is predictively steady if past measurements allow one to reasonably predict future characteristics
Key : How well changes can be tracked
Predictive Constancy
Mathematical but not Predictive IID process (no correlations in the process)
Predictive but neither Mathematical nor Operational Examples will be shown later
Analysis Methodology
Mathematical Constancy To find change-points
CP/Bootstrap CP/RankOrder
To partition a time series into change free regions (CFR)
To test for IID within each CFR Box-Ljung test (based on autocorrelation, r)
k
ii
k in
rnnQ
1
2
)2(
Analysis Methodology
Operational Constancy To define operational categories based on
requirements of real applications Predictive Constancy
To evaluate the performance of commonly used estimators Moving Average (MA) Exponentially-Weighted Moving Average (EWMA)
Measurement Methodology
Measurement Infrastructure NIMI (National Internet Measurement
Infrastructure) During Winter 1999-2000 (W1)
31 hosts, 80% located in US During Winter 2000-2001 (W2)
49 hosts, 73% located in US
Measurement Methodology
Losses Poisson packet streams
Duration – 1 hour Mean rate – 10Hz (W1) and 20Hz (W2) Payloads – 256 bytes (W1) and 64 bytes (W2)
Throughput TCP transfers
Duration – 5 hours 1 MB transfer every minute
Summary of Datasets
Dataset# NIMIsites
# packettraces
# packets# thruput
traces# transfers
W1 31 2,375 140M 58 16,900
W2 49 1,602 113M 111 31,700
W1 + W2 49 3,977 253M 169 48,600
Loss Constancy
Previous Works by Mukherjee Individual loss High correlation in packet loss for packets with a s
pacing of <= 200ms In this paper
Much of correlation from back-to-back losses rather than from “nearby” losses
Loss episode A series of consecutive packets that are lost
Loss Constancy
Individual Loss VS Loss Episode
Time scale
Traces consistent with IID
Individual Loss
Loss Episode
Up to 0.5-1 sec 27% 64%
Up to 5-10 sec 25% 55%
Loss Constancy
Poisson nature of loss episode
Loss episode inter-arrivals with exponential distributions
Loss Constancy
Mathematical Constancy All traces – more than half over the full hour Lossy traces – half less than 20 - 30 minutes
Overall loss rate exceeded 1%
Loss Constancy
Mathematical Constancy 88-92% of CFR are consistent with an absence of
lag 1 correlation 77-86% are consistent with no correlation up to
lag 100
Loss Constancy
Operational Constancy Loss rate categories (total 6)
0-0.5%, 0.5-2%, 2-5%, 5-10%, 10-20% and 20+% Short Period of Constancy Long Period of Constancy
Loss Constancy
Shorter period of Constancy (lasting 50 minutes or less) No significant difference between 10 seconds
average and 1 minutes average results
Loss Constancy
Longer period of Constancy (lasting 50 minutes or more)
Take only a single 10 sec change in loss rate is much likely than a singe 1 min change
Interval Type Prob.
1 minEpisode 71%
Loss 57%
10 secEpisode 25%
Loss 22%
Loss Constancy
Mathematical VS Operational 20 mins steady region – categorizing as “steady”
MO
OM
OM
MO
SetInterval
1 min 10 sec
6-9% 11%
6-15% 37-45%
2-5% 0.1%
74-83% 44-52%
OM OMMO MO
M : Mathematical Steady
O : Operational Steady
Loss Constancy
Predictive Constancy Mean Prediction Error
E[ | log( predicted value / actual value ) | ] Estimation Scheme and Parameters
Don’t matter
Computed over entire traces Computed over CFR
Loss Constancy
Prediction performance is the worst for the traces are Mathematical and Operational steady
Using EWMA (α = 0.25) estimator
Throughput Constancy
Mathematical Constancy Around 60%, the largest CFR is less than 2.5 hrs But only 10%, the CFR is under 20 min
Weighted average – the average length of CFR if you pick a random point in the traces E.g. 5 hrs trace 2 hrs CFR + 3hrs CFR Weighted average = 2/5 * 2 + 3/5 * 3 = 2.6hrs
Throughput Constancy
Mathematical Constancy 92% passes the independence test for autocorrel
ation up to 6 lags
Throughput Constancy
Operational Constancy The ratio between MAX and MIN throughput, ρ
Throughput Constancy
Predictive Constancy Almost all estimators perform well Estimators with long memory are worse
EWMA with α=0.01 MA with windows of 128
Conclusion
This paper raised the concepts and tools to understand three different notions of constancy Mathematical, Operational, Predictive
The degree of constancy found in the Internet path properties is under study
The relationships between three constancy are discussed
Loss Constancy
Binary loss series <Ti, Ei> Ti is the time of ith observation
Ei is an indicator, value = 1 if there is a loss
original packet loss series
(0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0)
(0, 0, 1, 1, 0, 1, 0, 0)
loss episode series
Appendix (CP Detection)
A set of n value xi, i = 1, 2, … n
Rank ri of each xi with 1 for the smallest
If there is a change point, si’ will climb to a max before decreasing to 0 at i = n
i
j ii rs1
2/)1( nisi
||' iii sss