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