draft-ietf-ippm-spatial-composition-15.txt   draft-ietf-ippm-spatial-composition-16.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: January 3, 2011 France Telecom Division R&D Expires: February 14, 2011 France Telecom Division R&D
July 2, 2010 August 13, 2010
Spatial Composition of Metrics Spatial Composition of Metrics
draft-ietf-ippm-spatial-composition-15 draft-ietf-ippm-spatial-composition-16
Abstract Abstract
This memo utilizes IP Performance Metrics that are applicable to both This memo utilizes IP Performance 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 complete path metric from the sub-path metrics with some accuracy
w.r.t. the actual metrics. This is called Spatial Composition in RFC w.r.t. the actual metrics. This is called Spatial Composition in RFC
2330. The memo refers to the Framework for Metric Composition, and 2330. The memo refers to the Framework for Metric Composition, and
provides background and motivation for combining metrics to derive provides background and motivation for combining metrics to derive
others. The descriptions of several composed metrics and statistics others. The descriptions of several composed metrics and statistics
skipping to change at page 1, line 47 skipping to change at page 1, line 47
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time. It is inappropriate to use Internet-Drafts as reference time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress." material or to cite them other than as "work in progress."
This Internet-Draft will expire on January 3, 2011. This Internet-Draft will expire on February 14, 2011.
Copyright Notice Copyright Notice
Copyright (c) 2010 IETF Trust and the persons identified as the Copyright (c) 2010 IETF Trust and the persons identified as the
document authors. All rights reserved. document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal This document is subject to BCP 78 and the IETF Trust's Legal
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skipping to change at page 3, line 26 skipping to change at page 3, line 26
3.1.2. Definition and Metric Units . . . . . . . . . . . . . 9 3.1.2. Definition and Metric Units . . . . . . . . . . . . . 9
3.1.3. Discussion and other details . . . . . . . . . . . . . 9 3.1.3. Discussion and other details . . . . . . . . . . . . . 9
3.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9 3.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9
3.1.5. Composition Function . . . . . . . . . . . . . . . . . 9 3.1.5. Composition Function . . . . . . . . . . . . . . . . . 9
3.1.6. Statement of Conjecture and Assumptions . . . . . . . 9 3.1.6. Statement of Conjecture and Assumptions . . . . . . . 9
3.1.7. Justification of the Composition Function . . . . . . 9 3.1.7. Justification of the Composition Function . . . . . . 9
3.1.8. Sources of Deviation from the Ground Truth . . . . . . 10 3.1.8. Sources of Deviation from the Ground Truth . . . . . . 10
3.1.9. Specific cases where the conjecture might fail . . . . 11 3.1.9. Specific cases where the conjecture might fail . . . . 11
3.1.10. Application of Measurement Methodology . . . . . . . . 11 3.1.10. Application of Measurement Methodology . . . . . . . . 11
4. One-way Delay Composed Metrics and Statistics . . . . . . . . 12 4. One-way Delay Composed Metrics and Statistics . . . . . . . . 12
4.1. Name: 4.1. Name: Type-P-Finite-One-way-Delay-<Sample>-Stream . . . . 12
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 12
4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12 4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12
4.1.2. Definition and Metric Units . . . . . . . . . . . . . 12 4.1.2. Definition and Metric Units . . . . . . . . . . . . . 12
4.1.3. Discussion and other details . . . . . . . . . . . . . 12 4.1.3. Discussion and other details . . . . . . . . . . . . . 12
4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13 4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13
4.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 13 4.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 13
4.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13 4.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13
4.2.2. Definition and Metric Units of the Mean Statistic . . 13 4.2.2. Definition and Metric Units of the Mean Statistic . . 13
4.2.3. Discussion and other details . . . . . . . . . . . . . 13 4.2.3. Discussion and other details . . . . . . . . . . . . . 14
4.2.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13 4.2.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 14
4.2.5. Composition Function: Sum of Means . . . . . . . . . . 13 4.2.5. Composition Function: Sum of Means . . . . . . . . . . 14
4.2.6. Statement of Conjecture and Assumptions . . . . . . . 14 4.2.6. Statement of Conjecture and Assumptions . . . . . . . 14
4.2.7. Justification of the Composition Function . . . . . . 14 4.2.7. Justification of the Composition Function . . . . . . 14
4.2.8. Sources of Deviation from the Ground Truth . . . . . . 14 4.2.8. Sources of Deviation from the Ground Truth . . . . . . 14
4.2.9. Specific cases where the conjecture might fail . . . . 14 4.2.9. Specific cases where the conjecture might fail . . . . 15
4.2.10. Application of Measurement Methodology . . . . . . . . 15 4.2.10. Application of Measurement Methodology . . . . . . . . 15
4.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 15 4.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 15
4.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 15 4.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 15
4.3.2. Definition and Metric Units of the Minimum 4.3.2. Definition and Metric Units of the Minimum
Statistic . . . . . . . . . . . . . . . . . . . . . . 15 Statistic . . . . . . . . . . . . . . . . . . . . . . 15
4.3.3. Discussion and other details . . . . . . . . . . . . . 15 4.3.3. Discussion and other details . . . . . . . . . . . . . 16
4.3.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 15 4.3.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 16
4.3.5. Composition Function: Sum of Minima . . . . . . . . . 15 4.3.5. Composition Function: Sum of Minima . . . . . . . . . 16
4.3.6. Statement of Conjecture and Assumptions . . . . . . . 16 4.3.6. Statement of Conjecture and Assumptions . . . . . . . 16
4.3.7. Justification of the Composition Function . . . . . . 16 4.3.7. Justification of the Composition Function . . . . . . 16
4.3.8. Sources of Deviation from the Ground Truth . . . . . . 16 4.3.8. Sources of Deviation from the Ground Truth . . . . . . 16
4.3.9. Specific cases where the conjecture might fail . . . . 16 4.3.9. Specific cases where the conjecture might fail . . . . 17
4.3.10. Application of Measurement Methodology . . . . . . . . 16 4.3.10. Application of Measurement Methodology . . . . . . . . 17
5. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 16 5. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 17
5.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 16 5.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 17
5.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 17 5.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 17
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 17 5.1.2. Definition and Metric Units . . . . . . . . . . . . . 17
5.1.3. Discussion and other details . . . . . . . . . . . . . 17 5.1.3. Discussion and other details . . . . . . . . . . . . . 17
5.1.4. Statistic: 5.1.4. Statistic:
Type-P-One-way-Packet-Loss-Empirical-Probability . . . 17 Type-P-One-way-Packet-Loss-Empirical-Probability . . . 17
5.1.5. Composition Function: Composition of Empirical 5.1.5. Composition Function: Composition of Empirical
Probabilities . . . . . . . . . . . . . . . . . . . . 17 Probabilities . . . . . . . . . . . . . . . . . . . . 18
5.1.6. Statement of Conjecture and Assumptions . . . . . . . 18 5.1.6. Statement of Conjecture and Assumptions . . . . . . . 18
5.1.7. Justification of the Composition Function . . . . . . 18 5.1.7. Justification of the Composition Function . . . . . . 18
5.1.8. Sources of Deviation from the Ground Truth . . . . . . 18 5.1.8. Sources of Deviation from the Ground Truth . . . . . . 18
5.1.9. Specific cases where the conjecture might fail . . . . 18 5.1.9. Specific cases where the conjecture might fail . . . . 18
5.1.10. Application of Measurement Methodology . . . . . . . . 18 5.1.10. Application of Measurement Methodology . . . . . . . . 19
6. Delay Variation Metrics and Statistics . . . . . . . . . . . . 18 6. Delay Variation Metrics and Statistics . . . . . . . . . . . . 19
6.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 18 6.1. Name: Type-P-One-way-pdv-refmin-<Sample>-Stream . . . . . 19
6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 19 6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 19
6.1.2. Definition and Metric Units . . . . . . . . . . . . . 19 6.1.2. Definition and Metric Units . . . . . . . . . . . . . 20
6.1.3. Discussion and other details . . . . . . . . . . . . . 20 6.1.3. Discussion and other details . . . . . . . . . . . . . 20
6.1.4. Statistics: Mean, Variance, Skewness, Quantile . . . . 20 6.1.4. Statistics: Mean, Variance, Skewness, Quantile . . . . 20
6.1.5. Composition Functions: . . . . . . . . . . . . . . . . 21 6.1.5. Composition Functions: . . . . . . . . . . . . . . . . 21
6.1.6. Statement of Conjecture and Assumptions . . . . . . . 22 6.1.6. Statement of Conjecture and Assumptions . . . . . . . 22
6.1.7. Justification of the Composition Function . . . . . . 22 6.1.7. Justification of the Composition Function . . . . . . 23
6.1.8. Sources of Deviation from the Ground Truth . . . . . . 22 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 23
6.1.9. Specific cases where the conjecture might fail . . . . 22 6.1.9. Specific cases where the conjecture might fail . . . . 23
6.1.10. Application of Measurement Methodology . . . . . . . . 23 6.1.10. Application of Measurement Methodology . . . . . . . . 23
7. Security Considerations . . . . . . . . . . . . . . . . . . . 23 7. Security Considerations . . . . . . . . . . . . . . . . . . . 23
7.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 23 7.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 23
7.2. User Data Confidentiality . . . . . . . . . . . . . . . . 23 7.2. User Data Confidentiality . . . . . . . . . . . . . . . . 24
7.3. Interference with the metrics . . . . . . . . . . . . . . 23 7.3. Interference with the metrics . . . . . . . . . . . . . . 24
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24 8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24
9. Contributors and Acknowledgements . . . . . . . . . . . . . . 27 9. Contributors and Acknowledgements . . . . . . . . . . . . . . 27
10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 27 10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 28
10.1. Normative References . . . . . . . . . . . . . . . . . . . 27 10.1. Normative References . . . . . . . . . . . . . . . . . . . 28
10.2. Informative References . . . . . . . . . . . . . . . . . . 28 10.2. Informative References . . . . . . . . . . . . . . . . . . 29
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 29 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 29
1. Introduction 1. Introduction
The IP Performance Metrics (IPPM) framework [RFC2330] describes two The IP Performance Metrics (IPPM) framework [RFC2330] describes two
forms of metric composition, spatial and temporal. The composition forms of metric composition, spatial and temporal. The composition
framework [RFC5835] expands and further qualifies these original framework [RFC5835] expands and further qualifies these original
forms into three categories. This memo describes Spatial forms into three categories. This memo describes Spatial
Composition, one of the categories of metrics under the umbrella of Composition, one of the categories of metrics under the umbrella of
the composition framework. the composition framework.
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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
operator's domain, or is applicable to Inter-domain composition. operator's domain, or is applicable to Inter-domain composition.
Requires synchronized measurement time intervals in all sub-paths, or Requires synchronized measurement start and stop times in all sub-
largely overlapping, or no timing requirements. paths, or largely overlapping, or no timing requirements.
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.
2.3. Incomplete Information 2.3. 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),
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o M, the total number of packets sent between T0 and Tf o M, the total number of packets sent between T0 and Tf
o N, the total number of packets received at Dst (sent between T0 o N, the total number of packets received at Dst (sent between T0
and Tf) and Tf)
o S, the number of sub-paths involved in the complete Src-Dst path o S, the number of sub-paths involved in the complete Src-Dst path
o Type-P, as defined in [RFC2330], which includes any field that may o Type-P, as defined in [RFC2330], which includes any field that may
affect a packet's treatment as it traverses the network affect a packet's treatment as it traverses the network
In metric names, the term <Sample> is intended to be replaced by the
name of the method used to define a sample of values of parameter
TstampSrc. This can be done in several ways, including:
1. Poisson: a pseudo-random Poisson process of rate lambda, whose
values fall between T and Tf. The time interval between
successive values of TstampSrc will then average 1/lambda, as per
[RFC2330].
2. Periodic: a periodic stream process with pseudo-random start time
T0 between T and dT, and nominal inter-packet interval incT, as
per [RFC3432].
3.1.2. Definition and Metric Units 3.1.2. Definition and Metric Units
This section is unique for every metric. This section is unique for every metric.
3.1.3. Discussion and other details 3.1.3. Discussion and other details
This section is unique for every metric. This section is unique for every metric.
3.1.4. Statistic: 3.1.4. Statistic:
This section is unique for every metric. This section is unique for every metric.
3.1.5. Composition Function 3.1.5. Composition Function
This section is unique for every metric. This section is unique for every metric.
3.1.6. Statement of Conjecture and Assumptions 3.1.6. Statement of Conjecture and Assumptions
This section is unique for each metric. This section is unique for each metric. The term "ground truth"
frequently used in these sections and it is defined in section 4.7 of
[RFC5835].
3.1.7. Justification of the Composition Function 3.1.7. 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. Since the full mesh of N measurement points every Src-Dst pair. Since the full mesh of N measurement points
grows as N x N, the scope of measurement may be limited by testing grows as N x N, the scope of measurement may be limited by testing
resources. resources.
There may be varying limitations on active testing in different parts There may be varying limitations on active testing in different parts
of the network. For example, it may not be possible to collect the of the network. For example, it may not be possible to collect the
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next sub-path are injected just after the same exchange point. next sub-path are injected just after the same exchange point.
Clearly, the set of sub-path measurements SHOULD cover all critical Clearly, the set of sub-path measurements SHOULD cover all critical
network elements in the complete path. network elements in the complete path.
3.1.8.4. Absence of route 3.1.8.4. Absence of route
At a specific point in time, no viable route exists between the At a specific point in time, no viable route exists between the
complete path source and destination. The routes selected for one or complete path source and destination. The routes selected for one or
more sub-paths therefore differs from the complete path. more sub-paths therefore differs from the complete path.
Consequently, spatial composition may produce finite estimation of a Consequently, spatial composition may produce finite estimation of a
ground truth metric between a source and a destination, even when the ground truth metric (see section 4.7 of [RFC5835]) between a source
route between them is undefined. and a destination, even when the route between them is undefined.
3.1.9. Specific cases where the conjecture might fail 3.1.9. Specific cases where the conjecture might fail
This section is unique for most metrics (see the metric-specific This section is unique for most metrics (see the metric-specific
sections). sections).
For delay-related metrics, One-way delay always depends on packet For delay-related metrics, One-way delay always depends on packet
size and link capacity, since it is measured in [RFC2679] from first size and link capacity, since it is measured in [RFC2679] from first
bit to last bit. If the size of an IP packet changes on route (due bit to last bit. If the size of an IP packet changes on route (due
to encapsulation), this can influence delay performance. However, to encapsulation), this can influence delay performance. However,
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Applies 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.
Assumption of sub-path independence w.r.t. the metric being defined/ Assumption of sub-path independence w.r.t. the metric being defined/
composed is REQUIRED. composed is REQUIRED.
4. One-way Delay Composed Metrics and Statistics 4. One-way Delay Composed Metrics and Statistics
4.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream 4.1. Name: Type-P-Finite-One-way-Delay-<Sample>-Stream
This metric is a necessary element of Delay Composition metrics, and This metric is a necessary element of Delay Composition metrics, and
its definition does not formally exist elsewhere in IPPM literature. its definition does not formally exist elsewhere in IPPM literature.
4.1.1. Metric Parameters 4.1.1. Metric Parameters
See the common parameters section above. See the common parameters section above.
4.1.2. Definition and Metric Units 4.1.2. 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-
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-<Sample>-Stream[i] =
FiniteDelay[i] = TstampDst - TstampSrc FiniteDelay[i] = TstampDst - TstampSrc
The units of measure for this metric are time in seconds, expressed The units of measure for this metric are time in seconds, expressed
in sufficiently low resolution to convey meaningful quantitative in sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually information. For example, resolution of microseconds is usually
sufficient. sufficient.
4.1.3. Discussion and other details 4.1.3. Discussion and other details
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4.1.4. Statistic: 4.1.4. Statistic:
All statistics defined in [RFC2679] are applicable to the finite one- All statistics defined in [RFC2679] are applicable to the finite one-
way delay,and additional metrics are possible, such as the mean (see way delay,and additional metrics are possible, such as the mean (see
below). below).
4.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean 4.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean
This section describes a statistic based on the Type-P-Finite-One- This section describes a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric. way-Delay-<Sample>-Stream metric.
4.2.1. Metric Parameters 4.2.1. Metric Parameters
See the common parameters section above. See the common parameters section above.
4.2.2. Definition and Metric Units of the Mean Statistic 4.2.2. 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 \
MeanDelay = - * > (FiniteDelay [n]) = MeanDelay = - * > (FiniteDelay [n])
N / N /
--- ---
n = 1 n = 1
where all packets n= 1 through N have finite singleton delays. where all packets n= 1 through N have finite singleton delays.
The units of measure for this metric are time in seconds, expressed The units of measure for this metric are time in seconds, expressed
in sufficiently fine resolution to convey meaningful quantitative in sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually information. For example, resolution of microseconds is usually
sufficient. sufficient.
4.2.3. Discussion and other details 4.2.3. Discussion and other details
The Type-P-Finite-One-way-Delay-Mean metric requires the conditional The Type-P-Finite-One-way-Delay-Mean metric requires the conditional
delay distribution described in section 5.1. delay distribution described in section 5.1.
4.2.4. Statistic: 4.2.4. Statistic:
This metric, a mean, does not require additional statistics. This metric, a mean, does not require additional statistics.
4.2.5. Composition Function: Sum of Means 4.2.5. Composition Function: Sum of Means
The Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay, The Type-P-Finite-Composite-One-way-Delay-Mean, or CompMeanDelay, for
for the complete Source to Destination path can be calculated from the complete Source to Destination path can be calculated from sum of
sum of the Mean Delays of all its S constituent sub-paths. the Mean Delays of all its S constituent sub-paths.
Then the Then the
Type-P-Finite-Composite-One-way-Delay-Mean = Type-P-Finite-Composite-One-way-Delay-Mean =
S S
--- ---
\ \
CompMeanDelay = > (MeanDelay [s]) = CompMeanDelay = > (MeanDelay [s])
/ /
--- ---
s = 1 s = 1
where sub-paths s = 1 to S are involved in the complete path. where sub-paths s = 1 to S are involved in the complete path.
4.2.6. Statement of Conjecture and Assumptions 4.2.6. Statement of Conjecture and Assumptions
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
ground truth mean of the delay distribution (and the distributions ground truth mean of the delay distribution (and the distributions
themselves are sufficiently independent), such that the means may be themselves are sufficiently independent), such that the means may be
added to produce an estimate of the complete path mean delay. added to produce an estimate of the complete path mean delay.
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If a link contributing non-negligible delay is erroneously included If a link contributing non-negligible delay is erroneously included
or excluded, the composition will be in error. or excluded, the composition will be in error.
4.2.10. Application of Measurement Methodology 4.2.10. Application of Measurement Methodology
The requirements of the common section apply here as well. The requirements of the common section apply here as well.
4.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum 4.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum
This section describes is a statistic based on the Type-P-Finite-One- This section describes is a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric, and the composed metric way-Delay-<Sample>-Stream metric, and the composed metric based on
based on that statistic. that statistic.
4.3.1. Metric Parameters 4.3.1. Metric Parameters
See the common parameters section above. See the common parameters section above.
4.3.2. Definition and Metric Units of the Minimum Statistic 4.3.2. Definition and Metric Units of the Minimum Statistic
We define We define
Type-P-Finite-One-way-Delay-Minimum = Type-P-Finite-One-way-Delay-Minimum =
skipping to change at page 15, line 47 skipping to change at page 16, line 16
The Type-P-Finite-One-way-Delay-Minimum metric requires the The Type-P-Finite-One-way-Delay-Minimum metric requires the
conditional delay distribution described in section 5.1.3. conditional delay distribution described in section 5.1.3.
4.3.4. Statistic: 4.3.4. Statistic:
This metric, a minimum, does not require additional statistics. This metric, a minimum, does not require additional statistics.
4.3.5. Composition Function: Sum of Minima 4.3.5. Composition Function: Sum of Minima
The Type-P-Finite--Composite-One-way-Delay-Minimum, or CompMinDelay, The Type-P-Finite-Composite-One-way-Delay-Minimum, or CompMinDelay,
for the complete Source to Destination path can be calculated from for the complete Source to Destination path can be calculated from
sum of the Minimum Delays of all its S constituent sub-paths. sum of the Minimum Delays of all its S constituent sub-paths.
Then the Then the
Type-P-Finite-Composite-One-way-Delay-Minimum = Type-P-Finite-Composite-One-way-Delay-Minimum =
S S
--- ---
\ \
CompMinDelay = > (MinDelay [s]) = CompMinDelay = > (MinDelay [s])
/ /
--- ---
s = 1 s = 1
4.3.6. Statement of Conjecture and Assumptions 4.3.6. Statement of Conjecture and Assumptions
The minimum of a sufficiently large stream of packets measured on The minimum of a sufficiently large stream of packets measured on
each sub-path during the interval [T, Tf] will be representative of each sub-path during the interval [T, Tf] will be representative of
the ground truth minimum of the delay distribution (and the the ground truth minimum of the delay distribution (and the
distributions themselves are sufficiently independent), such that the distributions themselves are sufficiently independent), such that the
minima may be added to produce an estimate of the complete path minima may be added to produce an estimate of the complete path
minimum delay. minimum delay.
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We obtain a sequence of pairs with elements as follows: We obtain a sequence of pairs with elements as follows:
o TstampSrc, as above o TstampSrc, as above
o L, either zero or one, where L=1 indicates loss and L=0 indicates o L, either zero or one, where L=1 indicates loss and L=0 indicates
arrival at the destination within TstampSrc + Tmax. arrival at the destination within TstampSrc + Tmax.
5.1.3. Discussion and other details 5.1.3. Discussion and other details
None.
5.1.4. Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability 5.1.4. Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability
Given the stream parameter M, the number of packets sent, we can Given the stream parameter M, the number of packets sent, we can
define the Empirical Probability of Loss Statistic (Ep), consistent define the Empirical Probability of Loss Statistic (Ep), consistent
with Average Loss in [RFC2680], as follows: with Average Loss in [RFC2680], as follows:
Type-P-One-way-Packet-Loss-Empirical-Probability = Type-P-One-way-Packet-Loss-Empirical-Probability =
M M
--- ---
1 \ 1 \
Ep = - * > (L[m]) = Ep = - * > (L[m])
M / M /
--- ---
m = 1 m = 1
where all packets m = 1 through M have a value for L. where all packets m = 1 through M have a value for L.
5.1.5. Composition Function: Composition of Empirical Probabilities 5.1.5. 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-Composite-One-way-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 - EpS)} = CompEp = 1 - {(1 - Ep1) x (1 - Ep2) x (1 - Ep3) x ... x (1 - EpS)}
If any Eps is undefined in a particular measurement interval, If any Eps 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 s for that measurement interval is any CompEp that uses sub-path s for that measurement interval is
undefined. undefined.
5.1.6. Statement of Conjecture and Assumptions 5.1.6. Statement of Conjecture and Assumptions
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,
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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-
borne worm, loss due to queue overflow in one network may help borne worm, loss due to queue overflow in one network may help
another network to carry its traffic without loss. another network to carry its traffic without loss.
5.1.10. Application of Measurement Methodology 5.1.10. Application of Measurement Methodology
See the common section. See the common section.
6. Delay Variation Metrics and Statistics 6. Delay Variation Metrics and Statistics
6.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream 6.1. Name: Type-P-One-way-pdv-refmin-<Sample>-Stream
This packet delay variation (PDV) metric is a necessary element of This packet delay variation (PDV) metric is a necessary element of
Composed Delay Variation metrics, and its definition does not Composed Delay Variation metrics, and its definition does not
formally exist elsewhere in IPPM literature. formally exist elsewhere in IPPM literature (with the exception of
[RFC5481] .
6.1.1. Metric Parameters: 6.1.1. 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) (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.
skipping to change at page 19, line 39 skipping to change at page 20, line 15
o MinDelay, the Type-P-Finite-One-way-Delay value for F(min_delay o MinDelay, the Type-P-Finite-One-way-Delay value for F(min_delay
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(current packet) criteria. F(current packet) criteria.
6.1.2. Definition and Metric Units 6.1.2. Definition and Metric Units
Using the definition above in section 5.1.2, 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[n], the singleton Type-P-Finite-One-way-Delay-<Sample>-Stream[n], the singleton for
for each packet[i] in the stream (a.k.a. FiniteDelay[i]). each packet[i] in the stream (a.k.a. FiniteDelay[i]).
For each packet[n] that meets the F(first packet) criteria given For each packet[n] that meets the F(first packet) criteria given
above: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream[n] = above: Type-P-One-way-pdv-refmin-<Sample>-Stream[n] =
PDV[n] = FiniteDelay[n] - MinDelay PDV[n] = FiniteDelay[n] - MinDelay
where PDV[i] is in units of time in seconds, expressed in where PDV[i] is in units of time in seconds, expressed in
sufficiently fine resolution to convey meaningful quantitative sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually information. For example, resolution of microseconds is usually
sufficient. sufficient.
6.1.3. Discussion and other details 6.1.3. Discussion and other details
skipping to change at page 21, line 18 skipping to change at page 21, line 40
\ / \ \ / \
> | PDV[n]- MeanPDV | > | PDV[n]- MeanPDV |
/ \ / / \ /
--- ---
n = 1 n = 1
----------------------------------- -----------------------------------
/ \ / \
| ( 3/2 ) | | ( 3/2 ) |
\ (N - 1) * VarPDV / \ (N - 1) * VarPDV /
(see Appendix X of [Y.1541] for additional background information).
We define the Quantile of the PDVRefMin sample as the value where the We define the Quantile of the PDVRefMin sample as the value where the
specified fraction of singletons is less than the given value. specified fraction of singletons is less than the given value.
6.1.5. Composition Functions: 6.1.5. 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.
6.1.5.1. Approximate Convolution 6.1.5.1. Approximate Convolution
The Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream samples from The Type-P-Finite-One-way-Delay-<Sample>-Stream samples from each
each sub-path are summarized as a histogram with 1 ms bins sub-path are summarized as a histogram with 1 ms bins representing
representing the one-way delay distribution. the one-way delay distribution.
From [Stats], the distribution of the sum of independent random From [Stats], the distribution of the sum of independent random
variables can be derived using the relation: variables can be derived using the relation:
Type-P-Composite-One-way-pdv-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
Note that dy and dz indicate partial integration above, and that y
and z are the integration variables. Also, the probablility of an
outcome is indicated by the symbol P(outcome).
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 (in variation distributions of the sub-paths of the complete path (in
this case, there are three sub-paths), and a is the quantile of this case, there are three sub-paths), and a is the quantile of
interest. Note dy and dz indicate partial integration here.This interest.
relation can be used to compose a quantile of interest for the
This relation can be used to compose a quantile of interest for the
complete path from the sub-path delay distributions. The histograms complete path from the sub-path delay distributions. The histograms
with 1 ms bins are discrete approximations of the delay with 1 ms bins are discrete approximations of the delay
distributions. distributions.
6.1.5.2. Normal Power Approximation 6.1.5.2. Normal Power Approximation
Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to
Destination path can be calculated by combining statistics of all the Destination path can be calculated by combining statistics of all the
constituent sub-paths in the process described in [Y.1541] clause 8 constituent sub-paths in the process described in [Y.1541] clause 8
and Appendix X. and Appendix X.
skipping to change at page 23, line 29 skipping to change at page 24, line 10
should establish bilateral or multi-lateral agreements regarding the should establish bilateral or multi-lateral agreements regarding the
timing, size, and frequency of collection of sample metrics. Use of timing, size, and frequency of collection of sample metrics. Use of
this method in excess of the terms agreed between the participants this method in excess of the terms agreed between the participants
may be cause for immediate rejection or discard of packets or other may be cause for immediate rejection or discard of packets or other
escalation procedures defined between the affected parties. escalation procedures defined between the affected parties.
7.2. User Data Confidentiality 7.2. User Data Confidentiality
Active use of this method generates packets for a sample, rather than Active use of this method generates packets for a sample, rather than
taking samples based on user data, and does not threaten user data taking samples based on user data, and does not threaten user data
confidentiality. Passive measurement must restrict attention to the confidentiality. Passive measurement MUST restrict attention to the
headers of interest. Since user payloads may be temporarily stored headers of interest. Since user payloads may be temporarily stored
for length analysis, suitable precautions MUST be taken to keep this for length analysis, suitable precautions MUST be taken to keep this
information safe and confidential. In most cases, a hashing function information safe and confidential. In most cases, a hashing function
will produce a value suitable for payload comparisons. will produce a value suitable for payload comparisons.
7.3. Interference with the metrics 7.3. Interference with the metrics
It may be possible to identify that a certain packet or stream of It may be possible to identify that a certain packet or stream of
packets is part of a sample. With that knowledge at the destination packets is part of a sample. With that knowledge at the destination
and/or the intervening networks, it is possible to change the and/or the intervening networks, it is possible to change the
skipping to change at page 24, line 19 skipping to change at page 24, line 44
[RFC4148]. [RFC4148].
IANA is asked to register the following metrics in the IANA-IPPM- IANA is asked to register the following metrics in the IANA-IPPM-
METRICS-REGISTRY-MIB: METRICS-REGISTRY-MIB:
ietfFiniteOneWayDelayStream OBJECT-IDENTITY ietfFiniteOneWayDelayStream OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Finite-One-way-Delay-Stream" "Type-P-Finite-One-way-Delay-Stream"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 5.1." "Reference "RFCyyyy, section 4.1."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfFiniteOneWayDelayMean OBJECT-IDENTITY ietfFiniteOneWayDelayMean OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Finite-One-way-Delay-Mean" "Type-P-Finite-One-way-Delay-Mean"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 5.2." "Reference "RFCyyyy, section 4.2."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfCompositeOneWayDelayMean OBJECT-IDENTITY ietfCompositeOneWayDelayMean OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Finite-Composite-One-way-Delay-Mean" "Type-P-Finite-Composite-One-way-Delay-Mean"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 5.2.5." "Reference "RFCyyyy, section 4.2.5."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfFiniteOneWayDelayMinimum OBJECT-IDENTITY ietfFiniteOneWayDelayMinimum OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Finite-One-way-Delay-Minimum" "Type-P-Finite-One-way-Delay-Minimum"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 5.3.2." "Reference "RFCyyyy, section 4.3.2."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfCompositeOneWayDelayMinimum OBJECT-IDENTITY ietfCompositeOneWayDelayMinimum OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Finite-Composite-One-way-Delay-Minimum" "Type-P-Finite-Composite-One-way-Delay-Minimum"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 5.3.5." "Reference "RFCyyyy, section 4.3."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfOneWayPktLossEmpiricProb OBJECT-IDENTITY ietfOneWayPktLossEmpiricProb OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-One-way-Packet-Loss-Empirical-Probability" "Type-P-One-way-Packet-Loss-Empirical-Probability"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 6.1.4." "Reference "RFCyyyy, section 5.1.4"
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfCompositeOneWayPktLossEmpiricProb OBJECT-IDENTITY ietfCompositeOneWayPktLossEmpiricProb OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Composite-One-way-Packet-Loss-Empirical-Probability" "Type-P-Composite-One-way-Packet-Loss-Empirical-Probability"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 6.1.5." "Reference "RFCyyyy, section 5.1."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfOneWayPdvRefminStream OBJECT-IDENTITY ietfOneWayPdvRefminStream OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-One-way-pdv-refmin-Stream" "Type-P-One-way-pdv-refmin-Stream"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 7.1." "Reference "RFCyyyy, section 6.1."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfOneWayPdvRefminMean OBJECT-IDENTITY ietfOneWayPdvRefminMean OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-One-way-pdv-refmin-Mean" "Type-P-One-way-pdv-refmin-Mean"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 7.1.4." "Reference "RFCyyyy, section 6.1.4."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfOneWayPdvRefminVariance OBJECT-IDENTITY ietfOneWayPdvRefminVariance OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-One-way-pdv-refmin-Variance" "Type-P-One-way-pdv-refmin-Variance"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 7.1.4." "Reference "RFCyyyy, section 6.1.4."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfOneWayPdvRefminSkewness OBJECT-IDENTITY ietfOneWayPdvRefminSkewness OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-One-way-pdv-refmin-Skewness" "Type-P-One-way-pdv-refmin-Skewness"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 7.1.4." "Reference "RFCyyyy, section 6.1.4."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfCompositeOneWayPdvRefminQtil OBJECT-IDENTITY ietfCompositeOneWayPdvRefminQtil OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-Composite-One-way-pdv-refmin-quantile-a" "Type-P-Composite-One-way-pdv-refmin-quantile-a"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 7.1.5.1." "Reference "RFCyyyy, section 6.1.5.1."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
ietfCompositeOneWayPdvRefminNPA OBJECT-IDENTITY ietfCompositeOneWayPdvRefminNPA OBJECT-IDENTITY
STATUS current STATUS current
DESCRIPTION DESCRIPTION
"Type-P-One-way-Composite-pdv-refmin-NPA" "Type-P-One-way-Composite-pdv-refmin-NPA"
REFERENCE REFERENCE
"Reference "RFCyyyy, section 7.1.5.2." "Reference "RFCyyyy, section 6.1.5.2."
-- RFC Ed.: replace yyyy with actual RFC number & remove this -- RFC Ed.: replace yyyy with actual RFC number & remove this
note note
::= { ianaIppmMetrics nn } -- IANA assigns nn ::= { ianaIppmMetrics nn } -- IANA assigns nn
9. Contributors and Acknowledgements 9. Contributors and Acknowledgements
The following people have contributed useful ideas, suggestions, or The following people have contributed useful ideas, suggestions, or
the text of sections that have been incorporated into this memo: the text of sections that have been incorporated into this memo:
- Phil Chimento <vze275m9@verizon.net> - Phil Chimento <vze275m9@verizon.net>
skipping to change at page 28, line 35 skipping to change at page 29, line 14
[RFC5835] Morton, A. and S. Van den Berghe, "Framework for Metric [RFC5835] Morton, A. and S. Van den Berghe, "Framework for Metric
Composition", RFC 5835, April 2010. Composition", RFC 5835, April 2010.
10.2. Informative References 10.2. Informative References
[RFC5474] Duffield, N., Chiou, D., Claise, B., Greenberg, A., [RFC5474] Duffield, N., Chiou, D., Claise, B., Greenberg, A.,
Grossglauser, M., and J. Rexford, "A Framework for Packet Grossglauser, M., and J. Rexford, "A Framework for Packet
Selection and Reporting", RFC 5474, March 2009. Selection and Reporting", RFC 5474, March 2009.
[RFC5644] Stephan, E., Liang, L., and A. Morton, "IP Performance [RFC5481] Morton, A. and B. Claise, "Packet Delay Variation
Metrics (IPPM): Spatial and Multicast", RFC 5644, Applicability Statement", RFC 5481, March 2009.
October 2009.
[Stats] McGraw-Hill NY NY, "Introduction to the Theory of [Stats] McGraw-Hill NY NY, "Introduction to the Theory of
Statistics, 3rd Edition,", 1974. Statistics, 3rd Edition,", 1974.
[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", November 2007. availability performance parameters", November 2007.
[Y.1541] ITU-T Recommendation Y.1541, "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.
 End of changes. 58 change blocks. 
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