Internet Engineering Task Force R. Geib, Ed.
Internet-Draft Deutsche Telekom
Intended status: Informational A. Morton
Expires: April 29, 2010 AT&T Labs
R. Fardid
Covad Communications
October 26, 2009
IPPM standard compliance testing
draft-geib-ippm-metrictest-01
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Abstract
This document specifies tests to determine if multiple, independent,
and interoperable implementations of a metrics specification document
are at hand so that the metrics specification can be advanced to an
Internet standard. Results of different IPPM implementations can be
compared if they measure under the same underlying network
conditions. Results are compared using state of the art statistical
methods.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements Language . . . . . . . . . . . . . . . . . . 4
2. Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Verification of conformance to a metric specification . . . . 6
3.1. Tests of an individual implementation against a metric
specification . . . . . . . . . . . . . . . . . . . . . . 6
3.2. Test set up resulting in identical live network
testing conditions . . . . . . . . . . . . . . . . . . . . 7
3.3. Tests two or more different implementations against a
metric specification . . . . . . . . . . . . . . . . . . . 9
3.4. Clock synchronisation . . . . . . . . . . . . . . . . . . 10
3.5. Recommended Metric Verification Measurement Process . . . 11
4. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 13
5. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 13
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 13
7. Security Considerations . . . . . . . . . . . . . . . . . . . 14
8. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8.1. Normative References . . . . . . . . . . . . . . . . . . . 14
8.2. Informative References . . . . . . . . . . . . . . . . . . 14
Appendix A. Further ideas on statistical tests . . . . . . . . . 15
Appendix B. Verification of measurement precision by
statistical methods . . . . . . . . . . . . . . . . . 17
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 19
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1. Introduction
Draft bradner-metrictest [bradner-metrictest] states:
The Internet Standards Process RFC2026 [RFC2026] requires that for a
IETF specification to advance beyond the Proposed Standard level, at
least two genetically unrelated implementations must be shown to
interoperate correctly with all features and options. There are two
distinct reasons for this requirement.
In the case of a protocol specification, the notion of
"interoperability" is reasonably intuitive - the implementations must
successfully "talk to each other", while exercising all features and
options.
In the case of a specification for a performance metric, network
latency for example, exactly what constitutes "interoperation" is
less obvious. The IESG didn't yet decide how to judge "metric
specification interoperability" in the context of the IETF Standards
Process and this new draft suggests a methodology which (hopefully)
is suitable for IPPM metrics. General applicability of the methods
proposed in the following should however not be excluded.
A metric specification describes a method of testing and a way to
report the results of this testing. One example of such a metric
would be a way to test and report the latency that data packets would
incur while being sent from one network location to another.
Since implementations of testing metrics are by their nature stand-
alone and do not interact with each other, the level of the
interoperability called for in the IETF standards process cannot be
simply determined by seeing that the implementations interact
properly. Instead, verifying equivalence by proofing that different
implementations verifiably give statistically equivalent results
Verifiable equivalence may take the place of interoperability.
This document defines the process of verifying equivalence by using a
specified test set up to create the required separate data sets
(which may be seen as samples taken from the same underlying
distribution) and then apply state of the art statistical methods to
verify equivalence of the results. To illustrate application of the
process defined her, validating compliance with RFC2679 [RFC2679] is
picked as an example. While test set ups may vary with the metrics
to be validated, the statistical methods will not. Documents
defining test setups to validate other metrics should be created by
the IPPM WG, once the process proposed here has been agreed upon.
This document defines the process of verifying equivalence by using a
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specified test set up to create the required separate data sets
(which may be seen as samples taken from the same underlying
distribution) and then apply state of the art statistical methods to
verify equivalence of the results. To illustrate application of the
process defined her, validating compliance with RFC2679 [RFC2679] is
picked as an example. While test set ups may vary with the metrics
to be validated, the statistical methods will not. Documents
defining test setups to validate other metrics should be created by
the IPPM WG, once the process proposed here has been agreed upon.
Changes from -00 to -01 version
o Addition of a comparison of individual metric implementations
against the metric specification (trying to pick up problems and
solutions for metric advancement [morton-advance-metrics]).
o More emphasis on the requirement to carefully design and document
the measurement set up of the metric comparison.
o Proposal of testing conditions under identical WAN netwrok
conditions using IP in IP tunneling or Pseudo Wires and parallel
measurement streams.
o Proposing the requirement to document the smallest resolution at
which an ADK test was passed by 95%. As no minimum resolution is
specified, IPPM metric compliance is not linked to a particular
performance of an implementation.
o Reference to RFC 2330 and RFC 2679 for the 95% confidence interval
as preferred criterion to decide on statistical equivalence
o Reducing the proposed statistical test to ADK with 95% confidence.
1.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
2. Basic idea
The Framework for IP Performance Metrics (RFC 2330, [RFC2330])
expects that a "methodology for a metric should have the property
that it is repeatable: if the methodology is used multiple times
under identical conditions, it should result in consistent
measurements." This means, an IPPM implementation is expected to
measure a metric with high precision. The metric compliance test
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specified in the following emphasises precision over accuracy.
Further the methodology and test methods proposed by RFC 2330 are
used by this document too.
The implementation of a standard compliant metric is expected to meet
the requrirements of the related a metric specification. So before
comparing two metrice implementations, each metric implementation is
individually compared against the metric specification. As an
example, an implementation of the OWD metric must be calibrated.
Calibration results of a standard conformant metric implementation
must be published then.
Most metric specificatios leave freedom to implementors on those
aspects, which aren't fundamental for an individual metric
implementation. Calibration of individual metric implementations and
comparing different ones requires a careful design and documentation
of the metric implementation and of the testing conditions.
The IPPM framework expects repeating measurements to lead to the same
results, if the conditions under which these measurements have been
collected are identical. Small deviations are expected to lead to
small deviations in results only. To charaterise statistical
equivalence in the case of small deviations, RFC 2330 and RFC 2679
suggest to apply a 95% confidence interval. Quoting RFC 2679, "95
percent was chosen because ... a particular confidence level should
be specified so that the results of independent implementations can
be compared."
Two different IPPM implementations are expected to measure
statistically equivalent results, if they both measure a metric under
the same networking conditions. Formulating the measurement in
statistical terms: separate samples are collected (by separate metric
implementations) from the same underlying statistical process (the
same network conditions). The "statistical hypothesis" to be tested
is the expectation, that both samples do not expose statistically
different properties. This requires careful test design:
o The error induced by the sample size must be small enough to
minimize its influence on the test result. This may have to be
respected, especially if two implementations measure with
different average probing rates.
o If statistics of time series are compared, the implementation with
the lowest probing frequency determines the smallest temporal
interval for which results can be compared.
o Every comparison must be repeated several times based on different
measurement data to avoid random indications of compatibility (or
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the lack of it).
o The measurement test set up must be self-consistent to the largest
possible extent. This means, network conditions, paths and IPPM
metric implementations SHOULD be identical for the compared
implementations to the largest possible degree to minimize the
influence of the test and measurement set up on the result. This
includes e.g. aspects of the stability and non-ambiguity of routes
taken by the measurement packets. See RFC 2330 for a discussion
on self-consistency RFC 2330 [RFC2330].
As addressed by "problems and solutions for metric advancement"
[morton-advance-metrics], documentation of the metric test will
indicate which requirements and options of a metric specification are
specified clear enough for an implementation or uncover gaps in the
metric specification. The final step in advancing a metric
specification to standard is by improving unclear specifications and
by cleaning it from not supported options.
3. Verification of conformance to a metric specification
This section specifies how to verify compliance of two or more IPPM
implementations against a metric specification. This document only
proposes a general methodology. Compliance criteria to a specific
metric implementation are expected to be drafted for each individual
metric specification. The only exception is the statistical test
comparing two metric implementations which are simultaneously tested.
This test is applicable without metric specific decision criteria.
3.1. Tests of an individual implementation against a metric
specification
A metric implementation MUST support the requirements classified as
"MUST" and "REQUIRED" of the related metric specification to be
compliant to the latter.
Further, supported options of a metric implementation SHOULD be
documented in sufficient detail to validate and improve the
underlying metric specification option or remove options which saw no
implementation or which are badly specified from the metric
specification to be promoted to a standard.
RFC2330 and RFC2679 emphasise precision as an aim of IPPM metric
implementations. A single IPPM conformant implementation MUST under
otherwise identical network conditions produce precise results for
repeated measurements of the same metric.
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RFC 2330 prefers the "empirical distribution function" EDF to
describe collections of measurements. RFC 2330 determines, that
"unless otherwise stated, IPPM goodness-of-fit tests are done using
5% significance." The goodness of fit test required to determine the
preciusion of a metric implementation consists of testing, whether
two or more samples belong to the same underlying distribution (of
measured network performance events). The goodness of fit test to be
applied is the Anderson-Darling K sample test (ADK test, K stands for
the number of samples to be compared). Please note that RFC 2330 and
RFC 2679 apply an Anderson Darling goodness of fit test too.
The results of a repeated tests with a single implementation MUST
pass an ADK sample test with confidence level of 95%. The resolution
for which the ADK test has been passed with the specified confidence
level MUST be documented. To formulate different: The requirement is
to document the smalles resolution, at which the results of the
tested metric implementation pass an ADK test with a confidence level
of 95%.
As an example, a one way delay measurement may pass an ADK test with
a timestamp resultion of 1 ms. The same test may fail, if timestamps
with a resolution of 100 microseconds are eavluated. The
implementation then is then conforming to the metric specification up
to a timestamp resolution of 1 ms.
3.2. Test set up resulting in identical live network testing conditions
Two major issues complicate tests for metric compliance across live
networks under identical testing conditions. One of these is the
general posit, "metric definition implementations cannot be
conveniently examined in field measurement scenarios". The other is
more more specificcally addressing "parallelism in devices and
networks", by which mechanisms like load balancing are meant. As a
reference for the latter, [RFC 4814] is given.
This section proposes two measures how to deal with both. Tunneling
mechanisms can be used to avoid pallalel processing of different
flows in the network. Measuring by separate parallel probe flows
results in repeated collection of data. In both cases, WAN network
conditions are identical, no matter what they are in detail.
Any measurement set up MUST be made to avoid the probing traffic
itself to impede the metric measurement. The created measurement
load MUST NOT result in congestion at the access link connecting the
measurement implementation to the WAN. The created measurement load
MUST NOT overload the measurement implementation itself, eg. by
causing a high CPU load or by creating imprecisions due to internal
send/receive probe packet collisions.
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IP in IP tunnels can be used to avoid ECMP routing of different
measurement streams if they allow to carry inner IP packets from
different senders in a single tunnel with the same outer origin and
destination address as well as the same port numbers. The author is
not an expert on tunneling and appreciates guidance on the
applicability of one or more of the following protocols: IP in IP
[RFC2003], GRE [RFC2784] or L2TP [RFC2661] or [RFC3931]. RFC 4928
[RFC4928] proposes measures how to avoid ECMP treatment in MPLS
networks. Applying Pseudo-Wires for a metric implementation test is
one way to avoid MPLS based ECMP treatment. If tuneling is applied,
a single tunnel MUST carry all test traffic in one direction. If eg.
Ethernet Pseudo Wires are applied and the measurement streams are
carried in different VLANs, the Pseudo Wires MUST be set up in
physical port mode to avoid set up of Pseudo Wires per VLAN (which
may see different paths due to ECMP routing), see RFC 4448 [RFC4448].
To have statsitical significance, a test MUST be repeated 5 times at
least (see below). WAN conditions may change over time. Sequential
testing is no useful metric test option. However tests can be
carried out by applying 5 or more different parallel measuremet
flows. The author takes no position, whether such a test is carried
out by sending eg a single CBR flow and defining avery n-th (n =
1..5) packet to belong to a specific measurement flow, or whether
multiple network cards are applied to create several distinct flows
of a single implementation. In the latter case, three different
cards of one implementation at a single test site will do, if
tunneling set ups like the one proposed by GRE encapsulated multicast
probing [GU&Duffield] are applied (note that one or more remote
tunnel end points and the same number of routers are required).
Some additional rules to calculate and compare samples have to be
respected. The following rules are of importance for the IPPM metric
test:
o To compare different probes of a common underlying distribution in
terms of metrics characterising a communication network requires
to respect the temporal nature for which the assumption of common
underlying distribution may hold. Any singletons or samples to be
compared MUST be captured within the same time interval.
o Whenever statistical events like singletons or rates are used to
characterise measured metrics of a time-interval, at least 5
events of a relevant metric MUST be present to ensure a minimum
confidence into the reported value (see Wikipedia on confidence
[Rule of thumb]). Note that this criterion also is to be
respected e.g. when comparing packet loss metrics. Any packet
loss measurement interval to be compared with the results of
another implementation needs to contain at least five lost packets
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to have a minimum confidence that the observed loss rate wasn't
caused by a samll number of random packet drops.
o The minimum number of singletons or samples to be compared by an
Anderson-Darling test is 100 per tested metric implementation.
Note that the Anderson-Darling test detects small differences in
distributions fairly well and will fail for high number of
compared results (RFC2330 mentions an example with 8192
measurements to guarantee a failure of an Anderson-Darling test).
o The Anderson-Darling test is sensible against differing accuracy
or bias of different implementations. These differences result in
differing averages of compared samples. In general, differences
in averages of samples may result from differing test conditions.
An example may be different packet sizes, resulting in a constant
delay difference between compared samples. Therefore samples to
be compared by an Anderson Darling test MAY be calibrated by the
difference of the average values of the samples.
3.3. Tests two or more different implementations against a metric
specification
RFC2330 expects that a "a methodology for a given metric exhibits
continuity if, for small variations in conditions, it results in
small variations in the resulting measurements. Slightly more
precisely, for every positive epsilon, there exists a positive delta,
such that if two sets of conditions are within delta of each other,
then the resulting measurements will be within epsilon of each
other." A small variation in conditions in the context of a metric
comparison can be seen as different implementations measuring the
same metric along the same path.
RFC2679 comments that a "95 percent [confidence level for an
Anderson-Darling goodness of fit test] was chosen because....a
particular confidence level should be specified so that the results
of independent implementations can be compared." While the RFC 2679
statement refers to calibration, it expresses the expectation that
the methodology allows for comparisons between different
implementations.
IPPM metric specification however allow for implementor options to
the largest possible degree. It can't be expected that two
implementors pick identical options for the implementations.
Implementors SHOULD to the highest degree possible pick the same
configurations for their systems when comparing their implementations
by a metric test.
In some cases, a goodness of fit test may not be possible or show
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dissapointing results. To clarify the difficulties arising from
different implemenation options, the individual options picked for
every compared implementation SHOULD be documented in sufficient
detail. Based on this documentation, the underlying metric
specification should be improved before it is promoted to a standard.
The same statistical test as applicable to quantify precision of a
single metric implementation MUST be passed to compare metric
conformance of different implemenations. To document compatibility,
the smallest measurement resolution at which the compared
implementations passed the ADK sample test MUST be documented.
For different implementations of the same metric, "variations in
conditions" are reasonably expected. The ADK test comparing samples
of the different implemenations may result in a lower precision than
the test for precision of each implementation individually.
3.4. Clock synchronisation
Clock synchronization effects require special attention. Accuracy of
one-way active delay measurements for any metrics implementation
depends on clock synchronization between the source and destination
of tests. Ideally, one-way active delay measurement (RFC 2679,
[RFC2679]) test endpoints either have direct access to independent
GPS or CDMA-based time sources or indirect access to nearby NTP
primary (stratum 1) time sources, equipped with GPS receivers.
Access to these time sources may not be available at all test
locations associated with different Internet paths, for a variety of
reasons out of scope of this document.
When secondary (stratum 2 and above) time sources are used with NTP
running acrossthe same network, whose metrics are subject to
comparative implementation tests, network impairments can affect
clock synchronization, distort sample one-way values and their
interval statistics. It is RECOMMENDED to discard sample one-way
delay values for any implementation, when one of the following
reliability conditions is met:
o Delay is measured and is finite in one direction, but not the
other.
o Absolute value of the difference between the sum of one-way
measurements in both directions and round-trip measurement is
greater than X% of the latter value.
Examination of the second condition requires RTT measurement for
reference, e.g., based on TWAMP (RFC5357, RFC 5357 [RFC5357]), in
conjunction with one-way delay measurement.
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Specification of X% to strike a balance between identification of
unreliable one-way delay samples and misidentification of reliable
samples under a wide range of Internet path RTTs probably requires
further study.
An IPPM compliant metric implementation whose measurement requires
synchonized clocks is however expected to provide precise measurement
results. Any IPPM metric implementation MUST be of a precision of 1
ms (+/- 500 us) with a confidence of 95% if the metric is captured
along an Internet path which is stable and not congested during a
measurement duration of an hour or more. [Editor: this latter
definition may avoid NTP (stratum 2 or worse) synchonized IPPM
implementations from becoming IPPM compliant. However internal PC
clock synched implementations can't be rejected that way. Ideas on
criteria to deal with the latter are welcome. May drift be one, as
GPS synched implementations shouldn't have one or the same on origin
and destination, respectively].
3.5. Recommended Metric Verification Measurement Process
The proposal made by the authors of bradner-metrictest
[bradner-metrictest] is picked up and slightly enhanced:
"In order to meet their obligations under the IETF Standards Process
the IESG must be convinced that each metric specification advanced to
Draft Standard or Internet Standard status is clearly written, that
there are the required multiple verifiably equivalent
implementations, and that all options have been implemented.
"In the context of this memo, metrics are designed to measure some
characteristic of a data network. An aim of any metric definition
should be that it should be specified in a way that can reliably
measure the specific characteristic in a repeatable way."
Each metric, statistic or option of those to be validated must be
compared against a reference measurement or another implementation by
at least 5 different basic data sets, each on with sufficient size to
reach the specified level of confidence.
"In the same way, sequentially running different implementations of
software that perform the tests described in the metric document on a
stable network, or simultaneously on a network that may or may not be
stable should produce essentially the same results."
Following these assumptions any recommendation for the advancement of
a metric specification needs to be accompanied by an implementation
report, as is the case with all requests for the advancement of IETF
specifications. The implementation report needs to include a
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specific plan to test the specific metrics in the RFC in lab or real-
world networks and reports of the tests performed with two or more
implementations of the software. The test plan should cover key
parts of the specification, specify the precision reached for each
measured metric and thus define the meaning of "statistically
equivalent" for the specific metrics being tested. Ideally, the test
plan would co-evolve with the development of the metric, since that's
when people have the most context in their thinking regarding the
different subtleties that can arise.
In particular, the implementation report MUST as a minimum document:
o The metric compared and the RFC specifying it, including the
chosen options (like e.g. the implemented selection function in
the case of IPDV).
o A complete specification of the measurement stream (mean rate,
statistical distribution of packets, packet size (or mean packet
size and their distribution), DSCP and any other measurement
stream property which could result in deviating results.
Deviations in results can be caused also if chosen IP addresses
and ports of different implementations can result in different
layer 2 or layer 3 paths due to operation of Equal Cost Multi-Path
routing in an operational network
o The duration of each measurement to be used for a metric
validation, the number of measurement points collected for each
metric during each measurement interval (i.e. the probe size) and
the level of confidence derived from this probe size for each
measurement interval.
o The result of the statistical tests performed for each metric
validation.
o The measurement configuration and set up.
o A parameterization of laboratory conditions and applied traffic
and network conditions allowing reproduction of these laboratory
conditions for readers of the implementation report.
All of the tests for each set MUST be run in a test set up as
specified in the section "Test set up resulting in identical live
network testing conditions."
It is RECOMMENDED to avoid effects falsifying results of real data
networks, if validation measurements are taken over them. Obviously,
the conditions met there can't be reproduced. As the measurement
equipment compared is designed to reliable quantify real network
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performance, validating metrics under real network conditions is
desirable of course.
Data networks may forward packets differently in the case of:
o Different packet sizes chosen for different metric
implementations. A proposed countermeasure is selecting the same
packet size when validating results of two samples or a sample
against an original distribution.
o Selection of differing IP addresses and ports used by different
metric implementations during metric validation tests. If ECMP is
applied on IP or MPLS level, different paths can result (note that
it may be impossible to detect an MPLS ECMP path from an IP
endpoint). A proposed counter measure is to connect the
measurement equipment to be compared by a NAT device, or
establishing a single tunnel to transport all measurement traffic
The aim is to have the same IP addresses and port for all
measurement packets or to avoid ECMP based local routing diversion
by using a layer 2 tunnel.
o Different IP options.
o Different DSCP.
4. Acknowledgements
Gerhard Hasslinger commented a first version of this document,
suggested statistical tests and the evaluation of time series
information. Henk Uijterwaal pushed this work and Mike Hamilton
reviewed the document before publication.
5. Contributors
Scott Bradner, Vern Paxson and Allison Manking drafted bradner-
metrictest [bradner-metrictest], and major parts of it are quoted in
this document. Scott Bradner and Emile Stephan commented this draft
before publication.
6. IANA Considerations
This memo includes no request to IANA.
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7. Security Considerations
This draft does not raise any specific security issues.
8. References
8.1. Normative References
[RFC2003] Perkins, C., "IP Encapsulation within IP", RFC 2003,
October 1996.
[RFC2026] Bradner, S., "The Internet Standards Process -- Revision
3", BCP 9, RFC 2026, October 1996.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
"Framework for IP Performance Metrics", RFC 2330,
May 1998.
[RFC2661] Townsley, W., Valencia, A., Rubens, A., Pall, G., Zorn,
G., and B. Palter, "Layer Two Tunneling Protocol "L2TP"",
RFC 2661, August 1999.
[RFC2679] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
Delay Metric for IPPM", RFC 2679, September 1999.
[RFC2784] Farinacci, D., Li, T., Hanks, S., Meyer, D., and P.
Traina, "Generic Routing Encapsulation (GRE)", RFC 2784,
March 2000.
[RFC3931] Lau, J., Townsley, M., and I. Goyret, "Layer Two Tunneling
Protocol - Version 3 (L2TPv3)", RFC 3931, March 2005.
[RFC4448] Martini, L., Rosen, E., El-Aawar, N., and G. Heron,
"Encapsulation Methods for Transport of Ethernet over MPLS
Networks", RFC 4448, April 2006.
[RFC4928] Swallow, G., Bryant, S., and L. Andersson, "Avoiding Equal
Cost Multipath Treatment in MPLS Networks", BCP 128,
RFC 4928, June 2007.
8.2. Informative References
[Autocorrelation]
N., N., "Autocorrelation", December 2008.
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[Correlation]
N., N., "Correlation", June 2009.
[GU&Duffield]
Gu, Y., Duffield, N., Breslau, L., and S. Sen, "GRE
Encapsulated Multicast Probing: A Scalable Technique for
Measuring One-Way Loss", SIGMETRICS'07 San Diego,
California, USA, June 2007.
[Precision]
N., N., "Accuracy and precision", June 2009.
[RFC5357] Hedayat, K., Krzanowski, R., Morton, A., Yum, K., and J.
Babiarz, "A Two-Way Active Measurement Protocol (TWAMP)",
RFC 5357, October 2008.
[Rule of thumb]
N., N., "Confidence interval", October 2008.
[bradner-metrictest]
Bradner, S., Mankin, A., and V. Paxson, "Advancement of
metrics specifications on the IETF Standards Track",
draft -morton-ippm-advance-metrics-00, (work in progress),
July 2007.
[morton-advance-metrics]
Morton, A., "Problems and Possible Solutions for Advancing
Metrics on the Standards Track", draft -bradner-
metricstest-03, (work in progress), July 2009.
Appendix A. Further ideas on statistical tests
IPPM metrics are captured by time series. Time series can be checked
for correlation. There are two expectations on statistical time
series properties which should be met by separate measurements
probing the same underlying network performance distribution:
o The Autocorrelation indicates, whether there are any repeating
patterns within a time series. For the purpose of this document,
it does not matter whether there is autocorrelation in a
measurement. It is however expected, that two measurements expose
the same autocorrelation on identical "lag" intervals. If
calculable, the autocorrelation lies within an interval [-1;1],
(see Wikipedia on autocorrelation [Autocorrelation]).
o The correlation coefficient "indicates the strength of a linear
relationship between two random variables." The two random
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variables in the case of this document are the measurement time
series of the IPPM implementations to be compared. The
expectation is, that both are strongly correlated and the
resulting correlation coefficient is close to 1, (see Wikipedia on
correlation [Correlation]).
A metric test can derive additional statistics from time series
analysis. Further, formulation of a test hypothesis is possible for
autocorrelation and the correlation coefficient. It is however not
clear, whether an appropriate statistical test to validate the
hypothesis by 95% significance exists. Applicability of time series
analysis for a metric test requires further input from statisticians.
In the absence of any metric test on time series, any test result
SHOULD provide the autocorrelation of the compared metrics time
series by lags from 1 to 10. In addition, the value of the
correlation coefficient SHOULD be provided. Autocorrelation and
Correlation coefficient are expected to be rather close to the value
1.
As mentioned earlier, the time series analysis requires application
of identical time intervals to allow a comparison. In our delay
example, single sample delay metric values are calculated for 9
minute intervals. If 200 consecutive sample delay metrics with the
same start and end interval are available for each implementation,
autocorrelation can be calculated for different n * 9 minute lags.
The autocorrelation calculated for the time series of each
implementation should be very close to the autocorrelation of the
other implementation for the same time lag. Further, the correlation
coefficient for both time series should be close to 1.
The way to prove that two IPPM metric measurements provide compatible
results then could be performed stepwise:
o First prove that the two compared implementations have the same
precision by comparing statistics of the distribution of
singletons (or samples) of a metric by comparing the EDF of the
samples captured by the two implementations.
o Second indicate that two compared implementations produce strongly
correlated time series of which each one individually has the same
autocorrelation as the other one.
Comparing "Accuracy" of IPPM implementations based on averages and
variations may require prior checks for the absence of long range
dependency within the compared measurements. Large outliers as
typically occurring in the case of long range dependency, can have a
serious impact on mean values. The median or percentiles may be more
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robust measures on which to compare the accuracy of different IPPM
implementations. An idea may be to consider data up to a certain
percentile, calculate the mean for data up to this percentile and
then compare the means of the two implementations. This could be
repeated for different percentiles. If long range dependencies
impact is limited to large outliers, the method may work for lower
percentiles. Whether this makes sense must be confirmed by a
statistician, so this attempt requires further study.
Appendix B. Verification of measurement precision by statistical
methods
Following the definition of statistical precision [Precision], a
measurement process can be characterised by two properties:
o Accuracy, which is the degree of conformity of a measured quantity
to its actual (true) value.
o Precision, also called reproducibility or repeatability, the
degree to which repeated measurements show the same or similar
results.
Figure 1 further clarifies the difference between accuracy and
precision of a measurement.
Probability ^
Density |
| Reference value Measured Value
| | |
| |<---Accuracy---->|
| | _|_
| | / | \
| | / | \
| | / | \
| | / | \
| | / | \
| | / | \
Measured | | /<- Precision ->\
Value -|---------|-----------------|---------->
|
Measurement accuracy and precision [Precision].
Figure 1
The Framework for IP Performance Metrics (RFC 2330, [RFC2330])
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expects that a "methodology for a metric should have the property
that it is repeatable: if the methodology is used multiple times
under identical conditions, it should result in consistent
measurements." This means, an IPPM implementation is expected to
measure a metric with high precision.
A guideline for an IPPM conformant metric implementation can be taken
from these principles:
Two different implementations measuring the same IPPM metric must
produce results with a limited difference if measuring under to the
largest extent possible identical network conditions.
In a metric test, both conditions are expected to hold, meaning that
repeated tests of two implementations MUST produce precise results
for all repetition intervals.
A suitable statistical test and and a level of confidence to define
whether differences are rather limited and whether a measurement is
highly precise are specified below.
Let's assume a one way delay measurement comparison between system A,
probing with a frequency of 2 probes per second and system B probing
at a rate of 2 probes every 3 minutes. To ensure reasonable
confidence in results, sample metrics are calculated from at least 5
singletons per compared time interval. This means, sample delay
values are calculated for each system for identical 6 minute
intervals for the whole test duration. Per 6 minute interval, the
sample metric is calculated from 720 singletons for system A and from
6 singletons for system B). Note, that if outliers are not filtered,
moving averages are an option for an evaluation too. The minimum
move of an averaging interval is three minutes in our example.
The test set up for the delay measurement is chosen to minimize
errors by locating one system of each implementation at the same end
of two separate sites, between which delay is measured for the metric
test. Both measurement sites are connected by one IPSEC tunnel, so
that all measurement packets cross the Internet with the same IP
addresses. Both measurement systems measure simultaneously and the
local links are dimensioned to avoid congestion caused by the probing
traffic itself.
The measured delay values are reported with a resolution above the
measurement error and above the synchronisation error. This is done
to avoid comparing these errors between two different metric
implementations instead of comparing the IPPM metric implementation
itself.
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The overall duration of the test is chosen so that more than 1000 six
minute measurement intervals are collected. The amount of data
collected allows separate comparisons for e.g. 200 consecutive 6
minute intervals. intervals, during which routes were instable, are
discarded prior to evaluation.
The captured delays may have been captured singletons ranging from an
absolute minimum Delay Dmin to values Dmin + 5 ms. To compare
distributions, the set of singletons of a chosen evaluation interval
(e.g. the data of one of the five 1800 minute capture sequences, see
above) is sorted for the frequency of singletons per Dmin + N * 0.5
ms (n = 1, 2, ...). After that, a comparison of the two probe sets
with any of the mentioned tests may be applied.
Authors' Addresses
Ruediger Geib (editor)
Deutsche Telekom
Heinrich Hertz Str. 3-7
Darmstadt, 64295
Germany
Phone: +49 6151 628 2747
Email: Ruediger.Geib@telekom.de
Al Morton
AT&T Labs
200 Laurel Avenue South
Middletown, NJ 07748
USA
Phone: +1 732 420 1571
Fax: +1 732 368 1192
Email: acmorton@att.com
URI: http://home.comcast.net/~acmacm/
Reza Fardid
Covad Communications
2510 Zanker Road
San Jose, CA 95131
USA
Phone: +1 408 434-2042
Email: RFardid@covad.com
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