 1/draftietfippmspatialcomposition08.txt 20090623 15:12:10.000000000 +0200
+++ 2/draftietfippmspatialcomposition09.txt 20090623 15:12:10.000000000 +0200
@@ 1,19 +1,19 @@
Network Working Group A. Morton
InternetDraft AT&T Labs
Intended status: Standards Track E. Stephan
Expires: September 8, 2009 France Telecom Division R&D
 March 7, 2009
+Expires: December 23, 2009 France Telecom Division R&D
+ June 21, 2009
Spatial Composition of Metrics
 draftietfippmspatialcomposition08
+ draftietfippmspatialcomposition09
Status of this Memo
This InternetDraft is submitted to IETF in full conformance with the
provisions of BCP 78 and BCP 79. This document may contain material
from IETF Documents or IETF Contributions published or made publicly
available before November 10, 2008. The person(s) controlling the
copyright in some of this material may not have granted the IETF
Trust the right to allow modifications of such material outside the
IETF Standards Process. Without obtaining an adequate license from
@@ 32,21 +32,21 @@
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use InternetDrafts as reference
material or to cite them other than as "work in progress."
The list of current InternetDrafts can be accessed at
http://www.ietf.org/ietf/1idabstracts.txt.
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http://www.ietf.org/shadow.html.
 This InternetDraft will expire on September 8, 2009.
+ This InternetDraft will expire on December 23, 2009.
Copyright Notice
Copyright (c) 2009 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Provisions Relating to IETF Documents in effect on the date of
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Please review these documents carefully, as they describe your rights
@@ 72,116 +72,117 @@
equal to" and ">=" as "greater than or equal to".
Table of Contents
1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 6
3. Scope and Application . . . . . . . . . . . . . . . . . . . . 6
3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 7
 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 7
+ 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 8
4. Common Specifications for Composed Metrics . . . . . . . . . . 8
4.1. Name: TypeP . . . . . . . . . . . . . . . . . . . . . . . 8
4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 8
4.1.2. Definition and Metric Units . . . . . . . . . . . . . 9
4.1.3. Discussion and other details . . . . . . . . . . . . . 9
4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9
4.1.5. Composition Function . . . . . . . . . . . . . . . . . 9
4.1.6. Statement of Conjecture and Assumptions . . . . . . . 9
 4.1.7. Justification of the Composition Function . . . . . . 9
+ 4.1.7. Justification of the Composition Function . . . . . . 10
4.1.8. Sources of Deviation from the Ground Truth . . . . . . 10
4.1.9. Specific cases where the conjecture might fail . . . . 11
 4.1.10. Application of Measurement Methodology . . . . . . . . 11
 5. Oneway Delay Composed Metrics and Statistics . . . . . . . . 11
+ 4.1.10. Application of Measurement Methodology . . . . . . . . 12
+ 5. Oneway Delay Composed Metrics and Statistics . . . . . . . . 12
5.1. Name:
 TypePFiniteOnewayDelayPoisson/PeriodicStream . . . 11
 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 11
+ TypePFiniteOnewayDelayPoisson/PeriodicStream . . . 12
+ 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 12
 5.1.3. Discussion and other details . . . . . . . . . . . . . 12
 5.2. Name: TypePFiniteCompositeOnewayDelayMean . . . . . 12
 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12
 5.2.2. Definition and Metric Units of the Mean Statistic . . 12
 5.2.3. Discussion and other details . . . . . . . . . . . . . 13
 5.2.4. Composition Function: Sum of Means . . . . . . . . . . 13
 5.2.5. Statement of Conjecture and Assumptions . . . . . . . 13
 5.2.6. Justification of the Composition Function . . . . . . 14
 5.2.7. Sources of Deviation from the Ground Truth . . . . . . 14
 5.2.8. Specific cases where the conjecture might fail . . . . 14
 5.2.9. Application of Measurement Methodology . . . . . . . . 14
 5.3. Name: TypePFiniteCompositeOnewayDelayMinimum . . . 14
 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 14
 5.3.2. Definition and Metric Units of the Mean Statistic . . 14
 5.3.3. Discussion and other details . . . . . . . . . . . . . 15
 5.3.4. Composition Function: Sum of Means . . . . . . . . . . 15
 5.3.5. Statement of Conjecture and Assumptions . . . . . . . 15
 5.3.6. Justification of the Composition Function . . . . . . 15
 5.3.7. Sources of Deviation from the Ground Truth . . . . . . 15
 5.3.8. Specific cases where the conjecture might fail . . . . 16
 5.3.9. Application of Measurement Methodology . . . . . . . . 16
 6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 16
 6.1. TypePCompositeOnewayPacketLossEmpiricalProbability 16
 6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 16
 6.1.2. Definition and Metric Units . . . . . . . . . . . . . 16
 6.1.3. Discussion and other details . . . . . . . . . . . . . 16
+ 5.1.3. Discussion and other details . . . . . . . . . . . . . 13
+ 5.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13
+ 5.2. Name: TypePFiniteCompositeOnewayDelayMean . . . . . 13
+ 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13
+ 5.2.2. Definition and Metric Units of the Mean Statistic . . 13
+ 5.2.3. Discussion and other details . . . . . . . . . . . . . 14
+ 5.2.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 14
+ 5.2.5. Composition Function: Sum of Means . . . . . . . . . . 14
+ 5.2.6. Statement of Conjecture and Assumptions . . . . . . . 14
+ 5.2.7. Justification of the Composition Function . . . . . . 15
+ 5.2.8. Sources of Deviation from the Ground Truth . . . . . . 15
+ 5.2.9. Specific cases where the conjecture might fail . . . . 15
+ 5.2.10. Application of Measurement Methodology . . . . . . . . 15
+ 5.3. Name: TypePFiniteCompositeOnewayDelayMinimum . . . 15
+ 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 15
+ 5.3.2. Definition and Metric Units of the Minimum
+ Statistic . . . . . . . . . . . . . . . . . . . . . . 15
+ 5.3.3. Discussion and other details . . . . . . . . . . . . . 16
+ 5.3.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 16
+ 5.3.5. Composition Function: Sum of Minima . . . . . . . . . 16
+ 5.3.6. Statement of Conjecture and Assumptions . . . . . . . 16
+ 5.3.7. Justification of the Composition Function . . . . . . 17
+ 5.3.8. Sources of Deviation from the Ground Truth . . . . . . 17
+ 5.3.9. Specific cases where the conjecture might fail . . . . 17
+ 5.3.10. Application of Measurement Methodology . . . . . . . . 17
+ 6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 17
+ 6.1. TypePCompositeOnewayPacketLossEmpiricalProbability 17
+ 6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 17
+ 6.1.2. Definition and Metric Units . . . . . . . . . . . . . 17
+ 6.1.3. Discussion and other details . . . . . . . . . . . . . 17
6.1.4. Statistic:
 TypePOnewayPacketLossEmpiricalProbability . . . 16
+ TypePOnewayPacketLossEmpiricalProbability . . . 18
6.1.5. Composition Function: Composition of Empirical
 Probabilities . . . . . . . . . . . . . . . . . . . . 17
 6.1.6. Statement of Conjecture and Assumptions . . . . . . . 17
 6.1.7. Justification of the Composition Function . . . . . . 17
 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 17
 6.1.9. Specific cases where the conjecture might fail . . . . 17
 6.1.10. Application of Measurement Methodology . . . . . . . . 18
 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 18
 7.1. Name: TypePOnewaypdvrefminPoisson/PeriodicStream . 18
 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 18
 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 19
 7.1.3. Discussion and other details . . . . . . . . . . . . . 19
 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 19
 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 20
 7.1.6. Statement of Conjecture and Assumptions . . . . . . . 21
 7.1.7. Justification of the Composition Function . . . . . . 21
 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 22
 7.1.9. Specific cases where the conjecture might fail . . . . 22
 7.1.10. Application of Measurement Methodology . . . . . . . . 22
 8. Security Considerations . . . . . . . . . . . . . . . . . . . 22
 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 22
 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 22
 8.3. Interference with the metrics . . . . . . . . . . . . . . 23
 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 23
 10. Acknowlegements . . . . . . . . . . . . . . . . . . . . . . . 23
 11. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 23
 12. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 25
 13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 25
 13.1. Normative References . . . . . . . . . . . . . . . . . . . 25
 13.2. Informative References . . . . . . . . . . . . . . . . . . 25
 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 26
+ Probabilities . . . . . . . . . . . . . . . . . . . . 18
+ 6.1.6. Statement of Conjecture and Assumptions . . . . . . . 18
+ 6.1.7. Justification of the Composition Function . . . . . . 18
+ 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 19
+ 6.1.9. Specific cases where the conjecture might fail . . . . 19
+ 6.1.10. Application of Measurement Methodology . . . . . . . . 19
+ 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 19
+ 7.1. Name: TypePOnewaypdvrefminPoisson/PeriodicStream . 19
+ 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 19
+ 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 20
+ 7.1.3. Discussion and other details . . . . . . . . . . . . . 20
+ 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 20
+ 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 21
+ 7.1.6. Statement of Conjecture and Assumptions . . . . . . . 22
+ 7.1.7. Justification of the Composition Function . . . . . . 22
+ 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 23
+ 7.1.9. Specific cases where the conjecture might fail . . . . 23
+ 7.1.10. Application of Measurement Methodology . . . . . . . . 23
+ 8. Security Considerations . . . . . . . . . . . . . . . . . . . 23
+ 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 23
+ 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 23
+ 8.3. Interference with the metrics . . . . . . . . . . . . . . 24
+ 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24
+ 10. Acknowlegements . . . . . . . . . . . . . . . . . . . . . . . 24
+ 11. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 24
+ 12. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 26
+ 13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 26
+ 13.1. Normative References . . . . . . . . . . . . . . . . . . . 26
+ 13.2. Informative References . . . . . . . . . . . . . . . . . . 26
+ Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
+ Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 27
1. Contributors
Thus far, the following people have contributed useful ideas,
suggestions, or the text of sections that have been incorporated into
this memo:
 Phil Chimento
 Reza Fardid
 Roman Krzanowski
 Maurizio Molina
  Al Morton

  Emile Stephan

 Lei Liang
 Dave Hoeflin
2. Introduction
The IPPM framework [RFC2330] describes two forms of metric
composition, spatial and temporal. The new composition framework
[ID.ietfippmframeworkcompagg] expands and further qualifies these
original forms into three categories. This memo describes Spatial
@@ 262,20 +263,26 @@
o multiple metrics for each subpath (possibly one that is the same
as the complete path metric);
o a single subpath metric that is different from the complete path
metric;
o different measurement techniques like active and passive
(recognizing that PSAMP WG will define capabilities to sample
packets to support measurement).
+ We note a possibility: Using a complete path metric and all but one
+ subpath metric to infer the performance of the missing subpath,
+ especially when the "last" subpath metric is missing. However, such
+ decomposition calculations, and the corresponding set of issues they
+ raise, are beyond the scope of this memo.
+
3.2. Application
The new composition framework [ID.ietfippmframeworkcompagg]
requires the specification of the applicable circumstances for each
metric. In particular, each section addresses whether the metric:
Requires the same test packets to traverse all subpaths, or may use
similar packets sent and collected separately in each subpath.
Requires homogeneity of measurement methodologies, or can allow a
@@ 309,20 +316,28 @@
composed metric SHOULD also be recorded as undefined.
4. Common Specifications for Composed Metrics
To reduce the redundant information presented in the detailed metrics
sections that follow, this section presents the specifications that
are common to two or more metrics. The section is organized using
the same subsections as the individual metrics, to simplify
comparisons.
+ Also, the following index variables represent the following:
+
+ o m = index for packets sent
+
+ o n = index for packets received
+
+ o s = index for involved subpaths
+
4.1. Name: TypeP
All metrics use the TypeP convention as described in [RFC2330]. The
rest of the name is unique to each metric.
4.1.1. Metric Parameters
o Src, the IP address of a host
o Dst, the IP address of a host
@@ 397,27 +411,33 @@
is value in reusing measurements where they are applicable, rather
than launching new measurements for every possible sourcedestination
pair.
4.1.8. Sources of Deviation from the Ground Truth
4.1.8.1. Subpath List Differs from Complete Path
The measurement packets, each having source and destination addresses
intended for collection at edges of the subpath, may take a
 different specific path through the network equipment and parallel
 links when compared to packets with the source and destination
 addresses of the complete path. Therefore, the performance estimated
 from the composition of subpath measurements may differ from the
 performance experienced by packets on the complete path. Multiple
 measurements employing sufficient subpath address pairs might
 produce bounds on the extent of this error.
+ different specific path through the network equipment and links when
+ compared to packets with the source and destination addresses of the
+ complete path. Examples sources of parallel paths include Equal Cost
+ MultiPath and parallel (or bundled) links. Therefore, the
+ performance estimated from the composition of subpath measurements
+ may differ from the performance experienced by packets on the
+ complete path. Multiple measurements employing sufficient subpath
+ address pairs might produce bounds on the extent of this error.
+
+ We also note the possibility of rerouting during a measurement
+ interval, as it may affect the correspondence between packets
+ traversing the complete path and the subpaths that were "involved"
+ prior to the reroute.
4.1.8.2. Subpath Contains Extra Network Elements
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 subpath
metrics SHOULD be minimized as a source of error.
@@ 444,23 +465,35 @@
Subpath destination addresses and complete path addresses do not
belong to the same network. Therefore routes selected to reach each
subpath destinations differ from the route that would be selected to
reach the destination address of the complete path. Consequently
spatial composition may produce finite estimation of a ground true
metric between a source Src and a destination Dst when the route
between Src and Dst is undefined.
4.1.9. Specific cases where the conjecture might fail
 This section is unique for each metric (see the metricspecific
+ This section is unique for most metrics (see the metricspecific
sections).
+ For delayrelated metrics, Oneway delay always depends on packet
+ size and link capacity, since it is measured in [RFC2679] from first
+ bit to last bit. If the size of an IP packet changes (due to
+ encapsulation for security reasons), this will influence delay
+ performance.
+
+ Fragmentation is a major issue for compostion accuracy, since all
+ metrics require all fragments to arrive before proceeding, and
+ fragmented complete path performance is likely to be different from
+ performance with nonfragmented packets and composed metrics based on
+ nonfragmented subpath measurements.
+
4.1.10. Application of Measurement Methodology
The methodology:
SHOULD use similar packets sent and collected separately in each sub
path.
Allows a degree of flexibility regarding test stream generation
(e.g., active or passive methods can produce an equivalent result,
but the lack of control over the source, timing and correlation of
@@ 514,184 +547,199 @@
The FiniteOnewayDelay approach handles the problem of lost packets
by reducing the event space. We consider conditional statistics, and
estimate the mean oneway delay conditioned on the event that all
packets in the sample arrive at the destination (within the specified
waiting time, Tmax). This offers a way to make some valid statements
about oneway delay, and at the same time avoiding events with
undefined outcomes. This approach is derived from the treatment of
lost packets in [RFC3393], and is similar to [Y.1540] .
+5.1.4. Statistic:
+
+ All statistics defined in [RFC2679] are applicable to the finite one
+ way delay,and additional metrics are possible, such as the mean (see
+ below).
+
5.2. Name: TypePFiniteCompositeOnewayDelayMean
This section describes a statistic based on the TypePFiniteOne
wayDelayPoisson/PeriodicStream 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
TypePFiniteOnewayDelayMean =
N

1 \
 MeanDelay =  * > (FiniteDelay [i])
+ MeanDelay =  * > (FiniteDelay [n])
N /

 i = 1
+ n = 1
 where all packets i= 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
 in sufficiently low resolution to convey meaningful quantitative
+ in sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
5.2.3. Discussion and other details
The TypePFiniteOnewayDelayMean metric requires the conditional
delay distribution described in section 5.1.
5.2.4. Composition Function: Sum of Means
+5.2.4. Statistic:
+
+ This metric, a mean, does not require additional statistics.
+
+5.2.5. Composition Function: Sum of Means
The TypePFiniteCompositeOnewayDelayMean, or CompMeanDelay,
for the complete Source to Destination path can be calculated from
sum of the Mean Delays of all its S constituent subpaths.
Then the
TypePFiniteCompositeOnewayDelayMean =
S

\
 CompMeanDelay = > (MeanDelay [i])
+ CompMeanDelay = > (MeanDelay [s])
/

 i = 1
+ s = 1
+ where subpaths s = 1 to S are invloved in the complete path.
5.2.5. Statement of Conjecture and Assumptions
+5.2.6. Statement of Conjecture and Assumptions
The mean of a sufficiently large stream of packets measured on each
subpath during the interval [T, Tf] will be representative of the
ground truth mean of the delay distribution (and the distributions
themselves are sufficiently independent), such that the means may be
added to produce an estimate of the complete path mean delay.
It is assumed that the oneway delay distributions of the subpaths
 and the complete path are continuous.
+ and the complete path are continuous. The mean of bimodal
+ distributions have the unfortunate property that such a value may
+ never occur.
5.2.6. Justification of the Composition Function
+5.2.7. Justification of the Composition Function
See the common section.
5.2.7. Sources of Deviation from the Ground Truth
+5.2.8. Sources of Deviation from the Ground Truth
See the common section.
5.2.8. Specific cases where the conjecture might fail
+5.2.9. Specific cases where the conjecture might fail
If any of the subpath distributions are bimodal, then the measured
means may not be stable, and in this case the mean will not be a
particularly useful statistic when describing the delay distribution
of the complete path.
The mean may not be sufficiently robust statistic to produce a
reliable estimate, or to be useful even if it can be measured.
 others...
+ If a link contributing nonnegligible delay is erroneously included
+ or excluded, the composition will be in error.
5.2.9. Application of Measurement Methodology
+5.2.10. Application of Measurement Methodology
The requirements of the common section apply here as well.
5.3. Name: TypePFiniteCompositeOnewayDelayMinimum
This section describes is a statistic based on the TypePFiniteOne
wayDelayPoisson/PeriodicStream 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
+5.3.2. Definition and Metric Units of the Minimum Statistic
We define

TypePFiniteOnewayDelayMinimum =
= MinDelay = (FiniteDelay [j])
such that for some index, j, where 1<= j <= N
 FiniteDelay[j] <= FiniteDelay[i] for all i
+ FiniteDelay[j] <= FiniteDelay[n] for all n
 where all packets i= 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
 in sufficiently low resolution to convey meaningful quantitative
+ in sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
5.3.3. Discussion and other details
The TypePFiniteOnewayDelayMinimum metric requires the
conditional delay distribution described in section 5.1.3.
5.3.4. Composition Function: Sum of Means
+5.3.4. Statistic:
+
+ This metric, a minimum, does not require additional statistics.
+
+5.3.5. Composition Function: Sum of Minima
The TypePFiniteCompositeOnewayDelayMinimum, or CompMinDelay,
for the complete Source to Destination path can be calculated from
sum of the Minimum Delays of all its S constituent subpaths.
Then the
TypePFiniteCompositeOnewayDelayMinimum =
S

\
 CompMinDelay = > (MinDelay [i])
+ CompMinDelay = > (MinDelay [s])
/

 i = 1
+ s = 1
5.3.5. Statement of Conjecture and Assumptions
+5.3.6. Statement of Conjecture and Assumptions
The minimum of a sufficiently large stream of packets measured on
each subpath during the interval [T, Tf] will be representative of
the ground truth 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.
It is assumed that the oneway delay distributions of the subpaths
and the complete path are continuous.
5.3.6. Justification of the Composition Function
+5.3.7. Justification of the Composition Function
See the common section.
5.3.7. Sources of Deviation from the Ground Truth
+5.3.8. Sources of Deviation from the Ground Truth
See the common section.
5.3.8. Specific cases where the conjecture might fail
+5.3.9. Specific cases where the conjecture might fail
If the routing on any of the subpaths 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
+5.3.10. Application of Measurement Methodology
The requirements of the common section apply here as well.
6. Loss Metrics and Statistics
6.1. TypePCompositeOnewayPacketLossEmpiricalProbability
6.1.1. Metric Parameters:
Same as section 4.1.1.
@@ 713,40 +761,40 @@
6.1.4. Statistic: TypePOnewayPacketLossEmpiricalProbability
Given the stream parameter M, the number of packets sent, we can
define the Empirical Probability of Loss Statistic (Ep), consistent
with Average Loss in [RFC2680], as follows:
TypePOnewayPacketLossEmpiricalProbability =
M

1 \
 Ep =  * > (L[i])
+ Ep =  * > (L[m])
M /

 i = 1
+ m = 1
 where all packets i= 1 through M have a value for L.
+ where all packets m = 1 through M have a value for L.
6.1.5. Composition Function: Composition of Empirical Probabilities
The TypePOnewayCompositePacketLossEmpiricalProbability, or
CompEp for the complete Source to Destination path can be calculated
by combining Ep of all its constituent subpaths (Ep1, Ep2, Ep3, ...
Epn) as
TypePCompositeOnewayPacketLossEmpiricalProbability =
 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  EpS)}
 If any Epn 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
 any CompEp that uses subpath n for that measurement interval is
+ any CompEp that uses subpath s for that measurement interval is
undefined.
6.1.6. Statement of Conjecture and Assumptions
The empirical probability of loss calculated on a sufficiently large
stream of packets measured on each subpath during the interval [T,
Tf] will be representative of the ground truth empirical loss
probability (and the probabilities themselves are sufficiently
independent), such that the subpath probabilities may be combined to
produce an estimate of the complete path empirical loss probability.
@@ 815,78 +862,78 @@
o MinDelay, the TypePFiniteOnewayDelay value for F(second
packet) given above.
o N, the number of packets received at the Destination meeting the
F(first packet) criteria.
7.1.2. Definition and Metric Units
Using the definition above in section 5.1.2, we obtain the value of
 TypePFiniteOnewayDelayPoisson/PeriodicStream[i], the singleton
+ TypePFiniteOnewayDelayPoisson/PeriodicStream[n], the singleton
for each packet[i] in the stream (a.k.a. FiniteDelay[i]).
 For each packet[i] that meets the F(first packet) criteria given
 above: TypePOnewaypdvrefminPoisson/PeriodicStream[i] =
+ For each packet[n] that meets the F(first packet) criteria given
+ above: TypePOnewaypdvrefminPoisson/PeriodicStream[n] =
 PDV[i] = FiniteDelay[i]  MinDelay
+ PDV[n] = FiniteDelay[n]  MinDelay
where PDV[i] is in units of time in seconds, expressed in
 sufficiently low resolution to convey meaningful quantitative
+ sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
7.1.3. Discussion and other details
This metric produces a sample of delay variation normalized to the
minimum delay of the sample. The resulting delay variation
distribution is independent of the sending sequence (although
specific FiniteDelay values within the distribution may be
correlated, depending on various stream parameters such as packet
spacing). This metric is equivalent to the IP Packet Delay Variation
parameter defined in [Y.1540].
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle
 We define the mean PDV as follows (where all packets i= 1 through N
 have a value for PDV[i]):
+ We define the mean PDV as follows (where all packets n = 1 through N
+ have a value for PDV[n]):
TypePOnewaypdvrefminMean = MeanPDV =
N

1 \
  * > (PDV[i])
+  * > (PDV[n])
N /

 i = 1
+ n = 1
We define the variance of PDV as follows:
TypePOnewaypdvrefminVariance = VarPDV =
N

1 \ 2
  > (PDV[i]  MeanPDV)
+  > (PDV[n]  MeanPDV)
(N  1) /

 i = 1
+ n = 1
We define the skewness of PDV as follows:
TypePOnewaypdvrefminSkewness = SkewPDV =
N
 3
\ / \
 >  PDV[i] MeanPDV 
+ >  PDV[n] MeanPDV 
/ \ /

 i = 1
+ n = 1

/ \
 ( 3/2 ) 
\ (N  1) * VarPDV /
We define the Quantile of the IPDVRefMin sample as the value where
the specified fraction of singletons is less than the given value.
7.1.5. Composition Functions:
@@ 915,23 +962,22 @@
interest. Note dy and dz indicate partial integration here.This
relation can be used to compose a quantile of interest for the
complete path from the subpath delay distributions. The histograms
with 1 ms bins are discrete approximations of the delay
distributions.
7.1.5.2. Normal Power Approximation
TypePOnewayCompositepdvrefminNPA for the complete Source to
Destination path can be calculated by combining statistics of all the
 constituent subpaths in the following process:

 < see [Y.1541] clause 8 and Appendix X >
+ constituent subpaths in the process described in [Y.1541] clause 8
+ and Appendix X.
7.1.6. Statement of Conjecture and Assumptions
The delay distribution of a sufficiently large stream of packets
measured on each subpath during the interval [T, Tf] will be
sufficiently stationary and the subpath distributions themselves are
sufficiently independent, so that summary information describing the
subpath distributions can be combined to estimate the delay
distribution of complete path.
@@ 1111,30 +1157,35 @@
November 2002.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005.
13.2. Informative References
[ID.ietfippmmultimetrics]
Stephan, E., Liang, L., and A. Morton, "IP Performance
Metrics (IPPM) for spatial and multicast",
 draftietfippmmultimetrics09 (work in progress),
 October 2008.
+ draftietfippmmultimetrics11 (work in progress),
+ April 2009.
[Y.1540] ITUT Recommendation Y.1540, "Internet protocol data
communication service  IP packet transfer and
availability performance parameters", December 2002.
[Y.1541] ITUT Recommendation Y.1541, "Network Performance
Objectives for IPbased Services", February 2006.
+Index
+
+ ?
+ ??? 14
+
Authors' Addresses
Al Morton
AT&T Labs
200 Laurel Avenue South
Middletown,, NJ 07748
USA
Phone: +1 732 420 1571
Fax: +1 732 368 1192