draft-ietf-ippm-spatial-composition-03.txt   draft-ietf-ippm-spatial-composition-04.txt 
Network Working Group A. Morton Network Working Group A. Morton
Internet-Draft AT&T Labs Internet-Draft AT&T Labs
Intended status: Standards Track E. Stephan Intended status: Standards Track E. Stephan
Expires: September 16, 2007 France Telecom Division R&D Expires: January 8, 2008 France Telecom Division R&D
March 15, 2007 July 7, 2007
Spatial Composition of Metrics Spatial Composition of Metrics
draft-ietf-ippm-spatial-composition-03 draft-ietf-ippm-spatial-composition-04
Status of this Memo Status of this Memo
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Copyright Notice Copyright Notice
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Abstract Abstract
This memo utilizes IPPM metrics that are applicable to both complete This memo utilizes IPPM metrics that are applicable to both complete
paths and sub-paths, and defines relationships to compose a complete paths and sub-paths, and defines relationships to compose a complete
path metric from the sub-path metrics with some accuracy w.r.t. the path metric from the sub-path metrics with some accuracy w.r.t. the
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equal to" and ">=" as "greater than or equal to". equal to" and ">=" as "greater than or equal to".
Table of Contents Table of Contents
1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Scope and Application . . . . . . . . . . . . . . . . . . . . 5 3. Scope and Application . . . . . . . . . . . . . . . . . . . . 5
3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 6 3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 6
3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 6 3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 6
3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 7 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 6
4. Common Specifications for Composed Metrics . . . . . . . . . . 7 4. Common Specifications for Composed Metrics . . . . . . . . . . 7
4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 7 4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 7
4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 7 4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 7
4.1.2. Definition and Metric Units . . . . . . . . . . . . . 8 4.1.2. Definition and Metric Units . . . . . . . . . . . . . 8
4.1.3. Discussion and other details . . . . . . . . . . . . . 8 4.1.3. Discussion and other details . . . . . . . . . . . . . 8
4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 8 4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 8
4.1.5. Composition Function: Sum of Means . . . . . . . . . . 8 4.1.5. Composition Function . . . . . . . . . . . . . . . . . 8
4.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 8 4.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 8
4.1.7. Justification of the Composition Function . . . . . . 8 4.1.7. Justification of the Composition Function . . . . . . 8
4.1.8. Sources of Deviation from the Ground Truth . . . . . . 9 4.1.8. Sources of Deviation from the Ground Truth . . . . . . 9
4.1.9. Specific cases where the conjecture might fail . . . . 9 4.1.9. Specific cases where the conjecture might fail . . . . 9
4.1.10. Application of Measurement Methodology . . . . . . . . 9 4.1.10. Application of Measurement Methodology . . . . . . . . 9
5. One-way Delay Composed Metrics and Statistics . . . . . . . . 9 5. One-way Delay Composed Metrics and Statistics . . . . . . . . 10
5.1. Name: 5.1. Name:
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 10 Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 10
5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 10 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 10
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 10 5.1.2. Definition and Metric Units . . . . . . . . . . . . . 10
5.1.3. Discussion and other details . . . . . . . . . . . . . 10 5.1.3. Discussion and other details . . . . . . . . . . . . . 10
5.1.4. Mean Statistic . . . . . . . . . . . . . . . . . . . . 10 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 11
5.1.5. Composition Function: Sum of Means . . . . . . . . . . 11 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 11
5.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 11 5.2.2. Definition and Metric Units of the Mean Statistic . . 11
5.1.7. Justification of the Composition Function . . . . . . 11 5.2.3. Discussion and other details . . . . . . . . . . . . . 11
5.1.8. Sources of Deviation from the Ground Truth . . . . . . 11 5.2.4. Composition Function: Sum of Means . . . . . . . . . . 11
5.1.9. Specific cases where the conjecture might fail . . . . 11 5.2.5. Statement of Conjecture . . . . . . . . . . . . . . . 12
5.1.10. Application of Measurement Methodology . . . . . . . . 12 5.2.6. Justification of the Composition Function . . . . . . 12
6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 12 5.2.7. Sources of Deviation from the Ground Truth . . . . . . 12
6.1. Name: 5.2.8. Specific cases where the conjecture might fail . . . . 12
Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream . . . . 12 5.2.9. Application of Measurement Methodology . . . . . . . . 12
6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 12 5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 12
6.1.2. Definition and Metric Units . . . . . . . . . . . . . 12 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13
6.1.3. Discussion and other details . . . . . . . . . . . . . 12 5.3.2. Definition and Metric Units of the Mean Statistic . . 13
5.3.3. Discussion and other details . . . . . . . . . . . . . 13
5.3.4. Composition Function: Sum of Means . . . . . . . . . . 13
5.3.5. Statement of Conjecture . . . . . . . . . . . . . . . 13
5.3.6. Justification of the Composition Function . . . . . . 14
5.3.7. Sources of Deviation from the Ground Truth . . . . . . 14
5.3.8. Specific cases where the conjecture might fail . . . . 14
5.3.9. Application of Measurement Methodology . . . . . . . . 14
6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 14
6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 14
6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 14
6.1.2. Definition and Metric Units . . . . . . . . . . . . . 14
6.1.3. Discussion and other details . . . . . . . . . . . . . 15
6.1.4. Statistic: 6.1.4. Statistic:
Type-P-One-way-Packet-Loss-Empirical-Probability . . . 12 Type-P-One-way-Packet-Loss-Empirical-Probability . . . 15
6.1.5. Composition Function: Composition of Empirical 6.1.5. Composition Function: Composition of Empirical
Probabilities . . . . . . . . . . . . . . . . . . . . 13 Probabilities . . . . . . . . . . . . . . . . . . . . 15
6.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 13 6.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 15
6.1.7. Justification of the Composition Function . . . . . . 13 6.1.7. Justification of the Composition Function . . . . . . 15
6.1.8. Sources of Deviation from the Ground Truth . . . . . . 13 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 16
6.1.9. Specific cases where the conjecture might fail . . . . 13 6.1.9. Specific cases where the conjecture might fail . . . . 16
6.1.10. Application of Measurement Methodology . . . . . . . . 14 6.1.10. Application of Measurement Methodology . . . . . . . . 16
7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 14 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 16
7.1. Name: 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 16
Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream . . . . 14 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 16
7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 14 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 17
7.1.2. Definition and Metric Units . . . . . . . . . . . . . 15 7.1.3. Discussion and other details . . . . . . . . . . . . . 17
7.1.3. Discussion and other details . . . . . . . . . . . . . 15 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 17
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 15 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 18
7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 16 7.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 19
7.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 17 7.1.7. Justification of the Composition Function . . . . . . 19
7.1.7. Justification of the Composition Function . . . . . . 17 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 19
7.1.8. Sources of Deviation from the Ground Truth . . . . . . 17 7.1.9. Specific cases where the conjecture might fail . . . . 20
7.1.9. Specific cases where the conjecture might fail . . . . 18 7.1.10. Application of Measurement Methodology . . . . . . . . 20
7.1.10. Application of Measurement Methodology . . . . . . . . 18 8. Security Considerations . . . . . . . . . . . . . . . . . . . 20
8. Security Considerations . . . . . . . . . . . . . . . . . . . 18 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 20
8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 18 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 20
8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 18 8.3. Interference with the metrics . . . . . . . . . . . . . . 21
8.3. Interference with the metrics . . . . . . . . . . . . . . 18 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 21
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19 10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 21
10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 19 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 22
11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 20 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 22
12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 20 12.1. Normative References . . . . . . . . . . . . . . . . . . . 22
12.1. Normative References . . . . . . . . . . . . . . . . . . . 20 12.2. Informative References . . . . . . . . . . . . . . . . . . 23
12.2. Informative References . . . . . . . . . . . . . . . . . . 21 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 23
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 21 Intellectual Property and Copyright Statements . . . . . . . . . . 25
Intellectual Property and Copyright Statements . . . . . . . . . . 23
1. Contributors 1. Contributors
Thus far, the following people have contributed useful ideas, Thus far, the following people have contributed useful ideas,
suggestions, or the text of sections that have been incorporated into suggestions, or the text of sections that have been incorporated into
this memo: this memo:
- Phil Chimento <vze275m9@verizon.net> - Phil Chimento <vze275m9@verizon.net>
- Reza Fardid <RFardid@Covad.COM> - Reza Fardid <RFardid@Covad.COM>
- Roman Krzanowski <roman.krzanowski@verizon.com> - Roman Krzanowski <roman.krzanowski@verizon.com>
- Maurizio Molina <maurizio.molina@dante.org.uk> - Maurizio Molina <maurizio.molina@dante.org.uk>
- Al Morton <acmorton@att.com> - Al Morton <acmorton@att.com>
- Emile Stephan <emile.stephan@francetelecom.com> - Emile Stephan <emile.stephan@orange-ftgroup.com>
- Lei Liang <L.Liang@surrey.ac.uk> - Lei Liang <L.Liang@surrey.ac.uk>
- Dave Hoeflin <dhoeflin@att.com> - Dave Hoeflin <dhoeflin@att.com>
2. Introduction 2. Introduction
The IPPM framework [RFC2330] describes two forms of metric The IPPM framework [RFC2330] describes two forms of metric
composition, spatial and temporal. The new composition framework composition, spatial and temporal. The new composition framework
[I-D.ietf-ippm-framework-compagg] expands and further qualifies these [I-D.ietf-ippm-framework-compagg] expands and further qualifies these
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metric; metric;
o different measurement techniques like active and passive o different measurement techniques like active and passive
(recognizing that PSAMP WG will define capabilities to sample (recognizing that PSAMP WG will define capabilities to sample
packets to support measurement). packets to support measurement).
3.2. Application 3.2. Application
The new composition framework [I-D.ietf-ippm-framework-compagg] The new composition framework [I-D.ietf-ippm-framework-compagg]
requires the specification of the applicable circumstances for each requires the specification of the applicable circumstances for each
metric. In particular, the application of Spatial Composition metric. In particular, each section addresses whether the metric:
metrics are addressed as to whether the metric:
Requires the same test packets to traverse all sub-paths, or may use Requires the same test packets to traverse all sub-paths, or may use
similar packets sent and collected separately in each sub-path. similar packets sent and collected separately in each sub-path.
Requires homogeneity of measurement methodologies, or can allow a Requires homogeneity of measurement methodologies, or can allow a
degree of flexibility (e.g., active or passive methods produce the degree of flexibility (e.g., active or passive methods produce the
"same" metric). Also, the applicable sending streams will be "same" metric). Also, the applicable sending streams will be
specified, such as Poisson, Periodic, or both. specified, such as Poisson, Periodic, or both.
Needs information or access that will only be available within an Needs information or access that will only be available within an
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Requires assumption of sub-path independence w.r.t. the metric being Requires assumption of sub-path independence w.r.t. the metric being
defined/composed, or other assumptions. defined/composed, or other assumptions.
Has known sources of inaccuracy/error, and identifies the sources. Has known sources of inaccuracy/error, and identifies the sources.
3.3. Incomplete Information 3.3. Incomplete Information
In practice, when measurements cannot be initiated on a sub-path (and In practice, when measurements cannot be initiated on a sub-path (and
perhaps the measurement system gives up during the test interval), perhaps the measurement system gives up during the test interval),
then there will not be a value for the sub-path reported, and the then there will not be a value for the sub-path reported, and the
result SHOULD be recorded as "undefined". This case should be entire test result SHOULD be recorded as "undefined". This case
distinguished from the case where the measurement system continued to should be distinguished from the case where the measurement system
send packets throughout the test interval, but all were declared continued to send packets throughout the test interval, but all were
lost. declared lost.
When a composed metric requires measurements from sub paths A, B, and When a composed metric requires measurements from sub paths A, B, and
C, and one or more of the sub-path results are undefined, then the C, and one or more of the sub-path results are undefined, then the
composed metric SHOULD also be recorded as undefined. composed metric SHOULD also be recorded as undefined.
4. Common Specifications for Composed Metrics 4. Common Specifications for Composed Metrics
To reduce the redundant information presented in the detailed metrics To reduce the redundant information presented in the detailed metrics
sections that follow, this section presents the specifications that sections that follow, this section presents the specifications that
are common to two or more metrics. The section is organized using are common to two or more metrics. The section is organized using
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This section is unique for every metric. This section is unique for every metric.
4.1.3. Discussion and other details 4.1.3. Discussion and other details
This section is unique for every metric. This section is unique for every metric.
4.1.4. Statistic: 4.1.4. Statistic:
This section is unique for every metric. This section is unique for every metric.
4.1.5. Composition Function: Sum of Means 4.1.5. Composition Function
This section is unique for every metric. This section is unique for every metric.
4.1.6. Statement of Conjecture 4.1.6. Statement of Conjecture
This section is unique for each metric. This section is unique for each metric.
4.1.7. Justification of the Composition Function 4.1.7. Justification of the Composition Function
It is sometimes impractical to conduct active measurements between It is sometimes impractical to conduct active measurements between
every Src-Dst pair. For example, it may not be possible to collect every Src-Dst pair. Since the full mesh of N measurement points
the desired sample size in each test interval when access link speed grows as N x N, the scope of measurement may be limited by testing
is limited, because of the potential for measurement traffic to resources.
degrade the user traffic performance. The conditions on a low-speed
access link may be understood well-enough to permit use of a small There may be varying limitations on active testing in different parts
sample size/rate, while a larger sample size/rate may be used on of the network. For example, it may not be possible to collect the
other sub-paths. desired sample size in each test interval when access link speed is
limited, because of the potential for measurement traffic to degrade
the user traffic performance. The conditions on a low-speed access
link may be understood well-enough to permit use of a small sample
size/rate, while a larger sample size/rate may be used on other sub-
paths.
Also, since measurement operations have a real monetary cost, there Also, since measurement operations have a real monetary cost, there
is value in re-using measurements where they are applicable, rather is value in re-using measurements where they are applicable, rather
than launching new measurements for every possible source-destination than launching new measurements for every possible source-destination
pair. pair.
4.1.8. Sources of Deviation from the Ground Truth 4.1.8. Sources of Deviation from the Ground Truth
The measurement packets, each having source and destination addresses The measurement packets, each having source and destination addresses
intended for collection at edges of the sub-path, may take a intended for collection at edges of the sub-path, may take a
different specific path through the network equipment and parallel different specific path through the network equipment and parallel
exchanges than packets with the source and destination addresses of links when compared to packets with the source and destination
the complete path. Therefore, the sub-path measurements may differ addresses of the complete path. Therefore, the composition of sub-
from the performance experienced by packets on the complete path. path measurements may differ from the performance experienced by
Multiple measurements employing sufficient sub-path address pairs packets on the complete path. Multiple measurements employing
might produce bounds on the extent of this error. sufficient sub-path address pairs might produce bounds on the extent
of this error.
others... Related to the case of an alternate path described above is the case
where elements in the measured path are unique to measurement system
connectivity. For example, a measurement system may use a dedicated
link to a LAN switch, and packets on the complete path do not
traverse that link. The performance of such a dedicated link would
be measured continuously, and its contribution to the sub-path
metrics SHOULD be minimized as a source of error.
others???
4.1.9. Specific cases where the conjecture might fail 4.1.9. Specific cases where the conjecture might fail
This section is unique for each metric. This section is unique for each metric.
4.1.10. Application of Measurement Methodology 4.1.10. Application of Measurement Methodology
The methodology: The methodology:
SHOULD use similar packets sent and collected separately in each sub- SHOULD use similar packets sent and collected separately in each sub-
path. path.
Allows a degree of flexibility (e.g., active or passive methods can Allows a degree of flexibility (e.g., active or passive methods can
produce the "same" metric, but timing and correlation of passive produce the "same" metric, but timing and correlation of passive
measurements is much more challenging). measurements is much more challenging).
Poisson and/or Periodic streams are RECOMMENDED. Poisson and/or Periodic streams are RECOMMENDED.
Applicable to both Inter-domain and Intra-domain composition. Applies to both Inter-domain and Intra-domain composition.
SHOULD have synchronized measurement time intervals in all sub-paths, SHOULD have synchronized measurement time intervals in all sub-paths,
but largely overlapping intervals MAY suffice. but largely overlapping intervals MAY suffice.
REQUIRES assumption of sub-path independence w.r.t. the metric being REQUIRES assumption of sub-path independence w.r.t. the metric being
defined/composed. defined/composed.
5. One-way Delay Composed Metrics and Statistics 5. One-way Delay Composed Metrics and Statistics
5.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream 5.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream
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Using the parameters above, we obtain the value of Type-P-One-way- Using the parameters above, we obtain the value of Type-P-One-way-
Delay singleton as per [RFC2679]. Delay singleton as per [RFC2679].
For each packet [i] that has a finite One-way Delay (in other words, For each packet [i] that has a finite One-way Delay (in other words,
excluding packets which have undefined one-way delay): excluding packets which have undefined one-way delay):
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] = Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] =
FiniteDelay[i] = TstampDst - TstampSrc FiniteDelay[i] = TstampDst - TstampSrc
The units of measure for this metric are time in seconds, expressed
in sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
5.1.3. Discussion and other details 5.1.3. Discussion and other details
The "Type-P-Finite-One-way-Delay" metric permits calculation of the The "Type-P-Finite-One-way-Delay" metric permits calculation of the
sample mean statistic. This resolves the problem of including lost sample mean statistic. This resolves the problem of including lost
packets in the sample (whose delay is undefined), and the issue with packets in the sample (whose delay is undefined), and the issue with
the informal assignment of infinite delay to lost packets (practical the informal assignment of infinite delay to lost packets (practical
systems can only assign some very large value). systems can only assign some very large value).
The Finite-One-way-Delay approach handles the problem of lost packets The Finite-One-way-Delay approach handles the problem of lost packets
by reducing the event space. We consider conditional statistics, and by reducing the event space. We consider conditional statistics, and
estimate the mean one-way delay conditioned on the event that all estimate the mean one-way delay conditioned on the event that all
packets in the sample arrive at the destination (within the specified packets in the sample arrive at the destination (within the specified
waiting time, Tmax). This offers a way to make some valid statements waiting time, Tmax). This offers a way to make some valid statements
about one-way delay, and at the same time avoiding events with about one-way delay, and at the same time avoiding events with
undefined outcomes. This approach is derived from the treatment of undefined outcomes. This approach is derived from the treatment of
lost packets in [RFC3393], and is similar to [Y.1540] . lost packets in [RFC3393], and is similar to [Y.1540] .
5.1.4. Mean Statistic 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean
This section describes a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric.
5.2.1. Metric Parameters
See the common parameters section above.
5.2.2. Definition and Metric Units of the Mean Statistic
We define We define
Type-P-Finite-One-way-Delay-Mean = Type-P-Finite-One-way-Delay-Mean =
N N
--- ---
1 \ 1 \
- * > (FiniteDelay [i]) MeanDelay = - * > (FiniteDelay [i])
N / N /
--- ---
i = 1 i = 1
where all packets i= 1 through N have finite singleton delays. where all packets i= 1 through N have finite singleton delays.
5.1.5. Composition Function: Sum of Means The units of measure for this metric are time in seconds, expressed
in sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
The Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay for 5.2.3. Discussion and other details
the complete Source to Destination path can be calculated from sum of
the Mean Delays of all its S constituent sub-paths.
Then the The Type-P-Finite-One-way-Delay-Mean metric requires the conditional
delay distribution described in section 5.1.
5.2.4. Composition Function: Sum of Means
The Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay,
for the complete Source to Destination path can be calculated from
sum of the Mean Delays of all its S constituent sub-paths.
Then the
Type-P-Finite-Composite-One-way-Delay-Mean = Type-P-Finite-Composite-One-way-Delay-Mean =
S S
--- ---
\ \
CompMeanDelay = > (MeanDelay [i]) CompMeanDelay = > (MeanDelay [i])
/ /
--- ---
i = 1 i = 1
5.1.6. Statement of Conjecture 5.2.5. Statement of Conjecture
The mean of a sufficiently large stream of packets measured on each The mean of a sufficiently large stream of packets measured on each
sub-path during the interval [T, Tf] will be representative of the sub-path during the interval [T, Tf] will be representative of the
true mean of the delay distribution (and the distributions themselves true mean of the delay distribution (and the distributions themselves
are sufficiently independent), such that the means may be added to are sufficiently independent), such that the means may be added to
produce an estimate of the complete path mean delay. produce an estimate of the complete path mean delay.
5.1.7. Justification of the Composition Function 5.2.6. Justification of the Composition Function
See the common section. See the common section.
5.1.8. Sources of Deviation from the Ground Truth 5.2.7. Sources of Deviation from the Ground Truth
See the common section. See the common section.
5.1.9. Specific cases where the conjecture might fail 5.2.8. Specific cases where the conjecture might fail
If any of the sub-path distributions are bimodal, then the measured If any of the sub-path distributions are bimodal, then the measured
means may not be stable, and in this case the mean will not be a means may not be stable, and in this case the mean will not be a
particularly useful statistic when describing the delay distribution particularly useful statistic when describing the delay distribution
of the complete path. of the complete path.
The mean may not be sufficiently robust statistic to produce a The mean may not be sufficiently robust statistic to produce a
reliable estimate, or to be useful even if it can be measured. reliable estimate, or to be useful even if it can be measured.
others... others...
5.1.10. Application of Measurement Methodology 5.2.9. Application of Measurement Methodology
The requirements of the common section apply here as well.
5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum
This section describes is a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric, and the composed metric
based on that statistic.
5.3.1. Metric Parameters
See the common parameters section above.
5.3.2. Definition and Metric Units of the Mean Statistic
We define
Type-P-Finite-One-way-Delay-Minimum =
= MinDelay = (FiniteDelay [j])
such that for some index, j, where 1<= j <= N
FiniteDelay[j] <= FiniteDelay[i] for all i
where all packets i= 1 through N have finite singleton delays.
The units of measure for this metric are time in seconds, expressed
in sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
5.3.3. Discussion and other details
The Type-P-Finite-One-way-Delay-Minimum metric requires the
conditional delay distribution described in section 5.1.3.
5.3.4. Composition Function: Sum of Means
The Type-P-Finite--Composite-One-way-Delay-Minimum, or CompMinDelay,
for the complete Source to Destination path can be calculated from
sum of the Minimum Delays of all its S constituent sub-paths.
Then the
Type-P-Finite-Composite-One-way-Delay-Minimum =
S
---
\
CompMinDelay = > (MinDelay [i])
/
---
i = 1
5.3.5. Statement of Conjecture
The minimum of a sufficiently large stream of packets measured on
each sub-path during the interval [T, Tf] will be representative of
the true minimum of the delay distribution (and the distributions
themselves are sufficiently independent), such that the minima may be
added to produce an estimate of the complete path minimum delay.
5.3.6. Justification of the Composition Function
See the common section.
5.3.7. Sources of Deviation from the Ground Truth
See the common section.
5.3.8. Specific cases where the conjecture might fail
If the routing on any of the sub-paths is not stable, then the
measured minimum may not be stable. In this case the composite
minimum would tend to produce an estimate for the complete path that
may be too low for the current path.
others???
5.3.9. Application of Measurement Methodology
The requirements of the common section apply here as well. The requirements of the common section apply here as well.
6. Loss Metrics and Statistics 6. Loss Metrics and Statistics
6.1. Name: Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream 6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability
6.1.1. Metric Parameters: 6.1.1. Metric Parameters:
Same as section 4.1.1. Same as section 4.1.1.
6.1.2. Definition and Metric Units 6.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of Type-P-One-way- Using the parameters above, we obtain the value of Type-P-One-way-
Packet-Loss singleton and stream as per [RFC2680]. Packet-Loss singleton and stream as per [RFC2680].
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where all packets i= 1 through M have a value for L. where all packets i= 1 through M have a value for L.
6.1.5. Composition Function: Composition of Empirical Probabilities 6.1.5. Composition Function: Composition of Empirical Probabilities
The Type-P-One-way-Composite-Packet-Loss-Empirical-Probability, or The Type-P-One-way-Composite-Packet-Loss-Empirical-Probability, or
CompEp for the complete Source to Destination path can be calculated CompEp for the complete Source to Destination path can be calculated
by combining Ep of all its constituent sub-paths (Ep1, Ep2, Ep3, ... by combining Ep of all its constituent sub-paths (Ep1, Ep2, Ep3, ...
Epn) as Epn) as
Type-P-One-way-Composite-Packet-Loss-Empirical-Probability = Type-P-Composite-One-way-Packet-Loss-Empirical-Probability =
CompEp = 1 ? {(1 - Ep1) x (1 ? Ep2) x (1 ? Ep3) x ... x (1 ? Epn)} CompEp = 1 - {(1 - Ep1) x (1 - Ep2) x (1 - Ep3) x ... x (1 - Epn)}
If any EpN is undefined in a particular measurement interval, If any Epn is undefined in a particular measurement interval,
possibly because a measurement system failed to report a value, then possibly because a measurement system failed to report a value, then
any CompEp that uses sub-path N for that measurement interval is any CompEp that uses sub-path n for that measurement interval is
undefined. undefined.
6.1.6. Statement of Conjecture 6.1.6. Statement of Conjecture
The empirical probability of loss calculated on a sufficiently large The empirical probability of loss calculated on a sufficiently large
stream of packets measured on each sub-path during the interval [T, stream of packets measured on each sub-path during the interval [T,
Tf] will be representative of the true loss probability (and the Tf] will be representative of the true loss probability (and the
probabilities themselves are sufficiently independent), such that the probabilities themselves are sufficiently independent), such that the
sub-path probabilities may be combined to produce an estimate of the sub-path probabilities may be combined to produce an estimate of the
complete path loss probability. complete path loss probability.
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6.1.8. Sources of Deviation from the Ground Truth 6.1.8. Sources of Deviation from the Ground Truth
See the common section. See the common section.
6.1.9. Specific cases where the conjecture might fail 6.1.9. Specific cases where the conjecture might fail
A concern for loss measurements combined in this way is that root A concern for loss measurements combined in this way is that root
causes may be correlated to some degree. causes may be correlated to some degree.
For example, if the links of different networks follow the same For example, if the links of different networks follow the same
physical route, then a single event like a tunnel fire could cause an physical route, then a single catastrophic event like a fire in a
outage or congestion on remaining paths in multiple networks. Here tunnel could cause an outage or congestion on remaining paths in
it is important to ensure that measurements before the event and multiple networks. Here it is important to ensure that measurements
after the event are not combined to estimate the composite before the event and after the event are not combined to estimate the
performance. composite performance.
Or, when traffic volumes rise due to the rapid spread of an email- Or, when traffic volumes rise due to the rapid spread of an email-
born worm, loss due to queue overflow in one network may help another born worm, loss due to queue overflow in one network may help another
network to carry its traffic without loss. network to carry its traffic without loss.
others... others...
6.1.10. Application of Measurement Methodology 6.1.10. Application of Measurement Methodology
See the common section. See the common section.
7. Delay Variation Metrics and Statistics 7. Delay Variation Metrics and Statistics
7.1. Name: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream
This metric is a necessary element of Composed Delay Variation This packet delay variation (PDV) metric is a necessary element of
metrics, and its definition does not formally exist elsewhere in IPPM Composed Delay Variation metrics, and its definition does not
literature. formally exist elsewhere in IPPM literature.
7.1.1. Metric Parameters: 7.1.1. Metric Parameters:
In addition to the parameters of section 4.1.1: In addition to the parameters of section 4.1.1:
o TstampSrc[i], the wire time of packet[i] as measured at MP(Src) o TstampSrc[i], the wire time of packet[i] as measured at MP(Src)
(measurement point at the source)
o TstampDst[i], the wire time of packet[i] as measured at MP(Dst), o TstampDst[i], the wire time of packet[i] as measured at MP(Dst),
assigned to packets that arrive within a "reasonable" time. assigned to packets that arrive within a "reasonable" time.
o B, a packet length in bits o B, a packet length in bits
o F, a selection function unambiguously defining the packets from o F, a selection function unambiguously defining the packets from
the stream that are selected for the packet-pair computation of the stream that are selected for the packet-pair computation of
this metric. F(first packet), the first packet of the pair, MUST this metric. F(first packet), the first packet of the pair, MUST
have a valid Type-P-Finite-One-way-Delay less than Tmax (in other have a valid Type-P-Finite-One-way-Delay less than Tmax (in other
words, excluding packets which have undefined, or infinite one-way words, excluding packets which have undefined one-way delay) and
delay) and MUST have been transmitted during the interval T, Tf. MUST have been transmitted during the interval T, Tf. The second
The second packet in the pair MUST be the packet with the minimum packet in the pair, F(second packet) MUST be the packet with the
valid value of Type-P-Finite-One-way-Delay for the stream, in minimum valid value of Type-P-Finite-One-way-Delay for the stream,
addition to the criteria for F(first packet). If multiple packets in addition to the criteria for F(first packet). If multiple
have equal minimum Type-P-Finite-One-way-Delay values, then the packets have equal minimum Type-P-Finite-One-way-Delay values,
value for the earliest arriving packet SHOULD be used. then the value for the earliest arriving packet SHOULD be used.
o MinDelay, the Type-P-Finite-One-way-Delay value for F(second o MinDelay, the Type-P-Finite-One-way-Delay value for F(second
packet) given above. packet) given above.
o N, the number of packets received at the Destination meeting the o N, the number of packets received at the Destination meeting the
F(first packet) criteria. F(first packet) criteria.
7.1.2. Definition and Metric Units 7.1.2. Definition and Metric Units
Using the definition above in section 4.1.2, we obtain the value of Using the definition above in section 5.1.2, we obtain the value of
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i], the singleton Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i], the singleton
for each packet[i] in the stream (a.k.a. FiniteDelay[i]). for each packet[i] in the stream (a.k.a. FiniteDelay[i]).
For each packet[i] that meets the F(first packet) criteria given For each packet[i] that meets the F(first packet) criteria given
above: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream[i] = above: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream[i] =
IPDVRefMin[i] = FiniteDelay[i] - MinDelay PDV[i] = FiniteDelay[i] - MinDelay
where IPDVRefMin[i] is in units of time (seconds, milliseconds). where PDV[i] is in units of time in seconds, expressed in
sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
7.1.3. Discussion and other details 7.1.3. Discussion and other details
This metric produces a sample of delay variation normalized to the This metric produces a sample of delay variation normalized to the
minimum delay of the sample. The resulting delay variation minimum delay of the sample. The resulting delay variation
distribution is independent of the sending sequence (although distribution is independent of the sending sequence (although
specific FiniteDelay values within the distribution may be specific FiniteDelay values within the distribution may be
correlated, depending on various stream parameters such as packet correlated, depending on various stream parameters such as packet
spacing). This metric is equivalent to the IP Packet Delay Variation spacing). This metric is equivalent to the IP Packet Delay Variation
parameter defined in [Y.1540]. parameter defined in [Y.1540].
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle
We define the mean IPDVRefMin as follows (where all packets i= 1 We define the mean PDV as follows (where all packets i= 1 through N
through N have a value for IPDVRefMin): have a value for PDV[i]):
Type-P-One-way-ipdv-refmin-Mean = MeanIPDVRefMin = Type-P-One-way-pdv-refmin-Mean = MeanPDV =
N N
--- ---
1 \ 1 \
- * > (IPDVRefMin [i]) - * > (PDV[i])
N / N /
--- ---
i = 1 i = 1
We define the variance of IPDVRefMin as follows: We define the variance of PDV as follows:
Type-P-One-way-ipdv-refmin-Variance = VarIPDVRefMin = Type-P-One-way-pdv-refmin-Variance = VarPDV =
N N
--- ---
1 \ 2 1 \ 2
------- > (IPDVRefMin [i] - MeanIPDVRefMin) ------- > (PDV[i] - MeanPDV)
(N - 1) / (N - 1) /
--- ---
i = 1 i = 1
We define the skewness of IPDVRefMin as follows: We define the skewness of PDV as follows:
Type-P-One-way-ipdv-refmin-Skewness = SkewIPDVRefMin = Type-P-One-way-pdv-refmin-Skewness = SkewPDV =
N N
--- 3 --- 3
\ / \ \ / \
> | IPDVRefMin[i]- MeanIPDVRefMin | > | PDV[i]- MeanPDV |
/ \ / / \ /
--- ---
i = 1 i = 1
------------------------------------------- -----------------------------------
/ \ / \
| ( 3/2 ) | | ( 3/2 ) |
\ (N - 1) * VarIPDVRefMin / \ (N - 1) * VarPDV /
We define the Quantile of the IPDVRefMin sample as the value where We define the Quantile of the IPDVRefMin sample as the value where
the specified fraction of points is less than the given value. the specified fraction of singletons is less than the given value.
7.1.5. Composition Functions: 7.1.5. Composition Functions:
This section gives two alternative composition functions. The This section gives two alternative composition functions. The
objective is to estimate a quantile of the complete path delay objective is to estimate a quantile of the complete path delay
variation distribution. The composed quantile will be estimated variation distribution. The composed quantile will be estimated
using information from the sub-path delay variation distributions. using information from the sub-path delay variation distributions.
7.1.5.1. Approximate Convolution 7.1.5.1. Approximate Convolution
The Type-P-One-way-Delay-Poisson/Periodic-Stream samples from each The Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream samples from
sub-path are summarized as a histogram with 1 ms bins representing each sub-path are summarized as a histogram with 1 ms bins
the one-way delay distribution. representing the one-way delay distribution.
From [TBP], the distribution of the sum of independent random From [TBP], the distribution of the sum of independent random
variables can be derived using the relation: variables can be derived using the relation:
Type-P-One-way-Composite-ipdv-refmin-quantile-a = Type-P-Composite-One-way-pdv-refmin-quantile-a =
/ / / /
P(X + Y + Z <= a) = | | P(X <= a-y-z) * P(Y = y) * P(Z = z) dy dz P(X + Y + Z <= a) = | | P(X <= a-y-z) * P(Y = y) * P(Z = z) dy dz
/ / / /
z y z y
where X, Y, and Z are random variables representing the delay where X, Y, and Z are random variables representing the delay
variation distributions of the sub-paths of the complete path, and a variation distributions of the sub-paths of the complete path (in
is the quantile of interest. Note dy and dz indicate partial this case, there are three sub-paths), and a is the quantile of
integration here.This relation can be used to compose a quantile of interest. Note dy and dz indicate partial integration here.This
interest for the complete path from the sub-path delay distributions. relation can be used to compose a quantile of interest for the
The histograms with 1 ms bins are discrete approximations of the complete path from the sub-path delay distributions. The histograms
delay distributions. with 1 ms bins are discrete approximations of the delay
distributions.
7.1.5.2. new section 7.1.5.2. Normal Power Approximation
Type-P-One-way-Composite-ipdv-refmin-<something> for the complete Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to
Source to Destination path can be calculated by combining statistics Destination path can be calculated by combining statistics of all the
of all the constituent sub-paths in the following process: constituent sub-paths in the following process:
< see [Y.1541] section 8 > < see [Y.1541] clause 8 and Appendix X >
7.1.6. Statement of Conjecture 7.1.6. Statement of Conjecture
The delay distribution of a sufficiently large stream of packets The delay distribution of a sufficiently large stream of packets
measured on each sub-path during the interval [T, Tf] will be measured on each sub-path during the interval [T, Tf] will be
sufficiently stationary and the sub-path distributions themselves are sufficiently stationary and the sub-path distributions themselves are
sufficiently independent, so that summary information describing the sufficiently independent, so that summary information describing the
sub-path distributions can be combined to estimate the delay sub-path distributions can be combined to estimate the delay
distribution of complete path. distribution of complete path.
7.1.7. Justification of the Composition Function 7.1.7. Justification of the Composition Function
See the common section. See the common section.
7.1.8. Sources of Deviation from the Ground Truth 7.1.8. Sources of Deviation from the Ground Truth
In addition to the common deviations, the a few additional sources In addition to the common deviations, a few additional sources exist
exist here. For one, very tight distributions with range on the here. For one, very tight distributions with range on the order of a
order of a few milliseconds are not accurately represented by a few milliseconds are not accurately represented by a histogram with 1
histogram with 1 ms bins. This size was chosen assuming an implicit ms bins. This size was chosen assuming an implicit requirement on
requirement on accuracy: errors of a few milliseconds are acceptable accuracy: errors of a few milliseconds are acceptable when assessing
when assessing a composed distribution quantile. a composed distribution quantile.
Also, summary statistics cannot describe the subtleties of an Also, summary statistics cannot describe the subtleties of an
empirical distribution exactly, especially when the distribution is empirical distribution exactly, especially when the distribution is
very different from a classical form. Any procedure that uses these very different from a classical form. Any procedure that uses these
statistics alone may incur error. statistics alone may incur error.
7.1.9. Specific cases where the conjecture might fail 7.1.9. Specific cases where the conjecture might fail
If the delay distributions of the sub-paths are somehow correlated, If the delay distributions of the sub-paths are somehow correlated,
then neither of these composition functions will be reliable then neither of these composition functions will be reliable
skipping to change at page 21, line 16 skipping to change at page 23, line 26
[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network [RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network
performance measurement with periodic streams", RFC 3432, performance measurement with periodic streams", RFC 3432,
November 2002. November 2002.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics [RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005. Registry", BCP 108, RFC 4148, August 2005.
12.2. Informative References 12.2. Informative References
[I-D.stephan-ippm-multimetrics] [I-D.ietf-ippm-multimetrics]
Stephan, E., "IP Performance Metrics (IPPM) for spatial Stephan, E., "IP Performance Metrics (IPPM) for spatial
and multicast", draft-stephan-ippm-multimetrics-02 (work and multicast", draft-ietf-ippm-multimetrics-04 (work in
in progress), October 2005. progress), July 2007.
[Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data [Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data
communication service - IP packet transfer and communication service - IP packet transfer and
availability performance parameters", December 2002. availability performance parameters", December 2002.
[Y.1541] ITU-T Recommendation Y.1540, "Network Performance [Y.1541] ITU-T Recommendation Y.1541, "Network Performance
Objectives for IP-based Services", February 2006. Objectives for IP-based Services", February 2006.
Authors' Addresses Authors' Addresses
Al Morton Al Morton
AT&T Labs AT&T Labs
200 Laurel Avenue South 200 Laurel Avenue South
Middletown,, NJ 07748 Middletown,, NJ 07748
USA USA
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