 1/draftietfippmspatialcomposition03.txt 20070709 07:12:11.000000000 +0200
+++ 2/draftietfippmspatialcomposition04.txt 20070709 07:12:11.000000000 +0200
@@ 1,19 +1,19 @@
Network Working Group A. Morton
InternetDraft AT&T Labs
Intended status: Standards Track E. Stephan
Expires: September 16, 2007 France Telecom Division R&D
 March 15, 2007
+Expires: January 8, 2008 France Telecom Division R&D
+ July 7, 2007
Spatial Composition of Metrics
 draftietfippmspatialcomposition03
+ draftietfippmspatialcomposition04
Status of this Memo
By submitting this InternetDraft, each author represents that any
applicable patent or other IPR claims of which he or she is aware
have been or will be disclosed, and any of which he or she becomes
aware will be disclosed, in accordance with Section 6 of BCP 79.
InternetDrafts are working documents of the Internet Engineering
Task Force (IETF), its areas, and its working groups. Note that
@@ 24,21 +24,21 @@
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.
The list of InternetDraft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html.
 This InternetDraft will expire on September 16, 2007.
+ This InternetDraft will expire on January 8, 2008.
Copyright Notice
Copyright (C) The IETF Trust (2007).
Abstract
This memo utilizes IPPM metrics that are applicable to both complete
paths and subpaths, and defines relationships to compose a complete
path metric from the subpath metrics with some accuracy w.r.t. the
@@ 57,104 +57,115 @@
equal to" and ">=" as "greater than or equal to".
Table of Contents
1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Scope and Application . . . . . . . . . . . . . . . . . . . . 5
3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 6
3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 6
 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 7
+ 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 6
4. Common Specifications for Composed Metrics . . . . . . . . . . 7
4.1. Name: TypeP . . . . . . . . . . . . . . . . . . . . . . . 7
4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 7
4.1.2. Definition and Metric Units . . . . . . . . . . . . . 8
4.1.3. Discussion and other details . . . . . . . . . . . . . 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
4.1.7. Justification of the Composition Function . . . . . . 8
4.1.8. Sources of Deviation from the Ground Truth . . . . . . 9
4.1.9. Specific cases where the conjecture might fail . . . . 9
4.1.10. Application of Measurement Methodology . . . . . . . . 9
 5. Oneway Delay Composed Metrics and Statistics . . . . . . . . 9
+ 5. Oneway Delay Composed Metrics and Statistics . . . . . . . . 10
5.1. Name:
TypePFiniteOnewayDelayPoisson/PeriodicStream . . . 10
5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 10
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 10
5.1.3. Discussion and other details . . . . . . . . . . . . . 10
 5.1.4. Mean Statistic . . . . . . . . . . . . . . . . . . . . 10
 5.1.5. Composition Function: Sum of Means . . . . . . . . . . 11
 5.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 11
 5.1.7. Justification of the Composition Function . . . . . . 11
 5.1.8. Sources of Deviation from the Ground Truth . . . . . . 11
 5.1.9. Specific cases where the conjecture might fail . . . . 11
 5.1.10. Application of Measurement Methodology . . . . . . . . 12
 6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 12
 6.1. Name:
 TypePOnewayPacketLossPoisson/PeriodicStream . . . . 12
 6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 12
 6.1.2. Definition and Metric Units . . . . . . . . . . . . . 12
 6.1.3. Discussion and other details . . . . . . . . . . . . . 12
+ 5.2. Name: TypePFiniteCompositeOnewayDelayMean . . . . . 11
+ 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 11
+ 5.2.2. Definition and Metric Units of the Mean Statistic . . 11
+ 5.2.3. Discussion and other details . . . . . . . . . . . . . 11
+ 5.2.4. Composition Function: Sum of Means . . . . . . . . . . 11
+ 5.2.5. Statement of Conjecture . . . . . . . . . . . . . . . 12
+ 5.2.6. Justification of the Composition Function . . . . . . 12
+ 5.2.7. Sources of Deviation from the Ground Truth . . . . . . 12
+ 5.2.8. Specific cases where the conjecture might fail . . . . 12
+ 5.2.9. Application of Measurement Methodology . . . . . . . . 12
+ 5.3. Name: TypePFiniteCompositeOnewayDelayMinimum . . . 12
+ 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13
+ 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. TypePCompositeOnewayPacketLossEmpiricalProbability 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:
 TypePOnewayPacketLossEmpiricalProbability . . . 12
+ TypePOnewayPacketLossEmpiricalProbability . . . 15
6.1.5. Composition Function: Composition of Empirical
 Probabilities . . . . . . . . . . . . . . . . . . . . 13
 6.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 13
 6.1.7. Justification of the Composition Function . . . . . . 13
 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 13
 6.1.9. Specific cases where the conjecture might fail . . . . 13
 6.1.10. Application of Measurement Methodology . . . . . . . . 14
 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 14
 7.1. Name:
 TypePOnewayipdvrefminPoisson/PeriodicStream . . . . 14
 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 14
 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 15
 7.1.3. Discussion and other details . . . . . . . . . . . . . 15
 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 15
 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 16
 7.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 17
 7.1.7. Justification of the Composition Function . . . . . . 17
 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 17
 7.1.9. Specific cases where the conjecture might fail . . . . 18
 7.1.10. Application of Measurement Methodology . . . . . . . . 18
 8. Security Considerations . . . . . . . . . . . . . . . . . . . 18
 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 18
 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 18
 8.3. Interference with the metrics . . . . . . . . . . . . . . 18
 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19
 10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 19
 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 20
 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 20
 12.1. Normative References . . . . . . . . . . . . . . . . . . . 20
 12.2. Informative References . . . . . . . . . . . . . . . . . . 21
 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 21
 Intellectual Property and Copyright Statements . . . . . . . . . . 23
+ Probabilities . . . . . . . . . . . . . . . . . . . . 15
+ 6.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 15
+ 6.1.7. Justification of the Composition Function . . . . . . 15
+ 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 16
+ 6.1.9. Specific cases where the conjecture might fail . . . . 16
+ 6.1.10. Application of Measurement Methodology . . . . . . . . 16
+ 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 16
+ 7.1. Name: TypePOnewaypdvrefminPoisson/PeriodicStream . 16
+ 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 16
+ 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 17
+ 7.1.3. Discussion and other details . . . . . . . . . . . . . 17
+ 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 17
+ 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 18
+ 7.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 19
+ 7.1.7. Justification of the Composition Function . . . . . . 19
+ 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 19
+ 7.1.9. Specific cases where the conjecture might fail . . . . 20
+ 7.1.10. Application of Measurement Methodology . . . . . . . . 20
+ 8. Security Considerations . . . . . . . . . . . . . . . . . . . 20
+ 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 20
+ 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 20
+ 8.3. Interference with the metrics . . . . . . . . . . . . . . 21
+ 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 21
+ 10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 21
+ 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 22
+ 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 22
+ 12.1. Normative References . . . . . . . . . . . . . . . . . . . 22
+ 12.2. Informative References . . . . . . . . . . . . . . . . . . 23
+ Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 23
+ Intellectual Property and Copyright Statements . . . . . . . . . . 25
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
+  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
@@ 238,22 +249,21 @@
metric;
o different measurement techniques like active and passive
(recognizing that PSAMP WG will define capabilities to sample
packets to support measurement).
3.2. Application
The new composition framework [ID.ietfippmframeworkcompagg]
requires the specification of the applicable circumstances for each
 metric. In particular, the application of Spatial Composition
 metrics are addressed as to whether the metric:
+ 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
degree of flexibility (e.g., active or passive methods produce the
"same" metric). Also, the applicable sending streams will be
specified, such as Poisson, Periodic, or both.
Needs information or access that will only be available within an
@@ 265,24 +275,24 @@
Requires assumption of subpath independence w.r.t. the metric being
defined/composed, or other assumptions.
Has known sources of inaccuracy/error, and identifies the sources.
3.3. Incomplete Information
In practice, when measurements cannot be initiated on a subpath (and
perhaps the measurement system gives up during the test interval),
then there will not be a value for the subpath reported, and the
 result SHOULD be recorded as "undefined". This case should be
 distinguished from the case where the measurement system continued to
 send packets throughout the test interval, but all were declared
 lost.
+ entire test result SHOULD be recorded as "undefined". This case
+ should be distinguished from the case where the measurement system
+ continued to send packets throughout the test interval, but all were
+ declared lost.
When a composed metric requires measurements from sub paths A, B, and
C, and one or more of the subpath results are undefined, then the
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
@@ 334,75 +345,89 @@
This section is unique for every metric.
4.1.3. Discussion and other details
This section is unique for every metric.
4.1.4. Statistic:
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.
4.1.6. Statement of Conjecture
This section is unique for each metric.
4.1.7. Justification of the Composition Function
It is sometimes impractical to conduct active measurements between
 every SrcDst pair. For example, it may not be possible to collect
 the 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 lowspeed
 access link may be understood wellenough to permit use of a small
 sample size/rate, while a larger sample size/rate may be used on
 other subpaths.
+ every SrcDst pair. Since the full mesh of N measurement points
+ grows as N x N, the scope of measurement may be limited by testing
+ resources.
+
+ There may be varying limitations on active testing in different parts
+ of the network. For example, it may not be possible to collect the
+ 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 lowspeed access
+ link may be understood wellenough 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
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
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
 exchanges than packets with the source and destination addresses of
 the complete path. Therefore, the 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.
+ links when compared to packets with the source and destination
+ addresses of the complete path. Therefore, the composition of sub
+ path 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.
 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 subpath
+ metrics SHOULD be minimized as a source of error.
+
+ others???
4.1.9. Specific cases where the conjecture might fail
This section is unique for each metric.
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 (e.g., active or passive methods can
produce the "same" metric, but timing and correlation of passive
measurements is much more challenging).
Poisson and/or Periodic streams are RECOMMENDED.
 Applicable to both Interdomain and Intradomain composition.
+ Applies to both Interdomain and Intradomain composition.
SHOULD have synchronized measurement time intervals in all subpaths,
but largely overlapping intervals MAY suffice.
REQUIRES assumption of subpath independence w.r.t. the metric being
defined/composed.
5. Oneway Delay Composed Metrics and Statistics
5.1. Name: TypePFiniteOnewayDelayPoisson/PeriodicStream
@@ 419,103 +444,205 @@
Using the parameters above, we obtain the value of TypePOneway
Delay singleton as per [RFC2679].
For each packet [i] that has a finite Oneway Delay (in other words,
excluding packets which have undefined oneway delay):
TypePFiniteOnewayDelayPoisson/PeriodicStream[i] =
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
The "TypePFiniteOnewayDelay" metric permits calculation of the
sample mean statistic. This resolves the problem of including lost
packets in the sample (whose delay is undefined), and the issue with
the informal assignment of infinite delay to lost packets (practical
systems can only assign some very large value).
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. Mean Statistic
+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 \
  * > (FiniteDelay [i])
+ MeanDelay =  * > (FiniteDelay [i])
N /

i = 1
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 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.
+5.2.3. Discussion and other details
 Then the
+ The TypePFiniteOnewayDelayMean metric requires the conditional
+ delay distribution described in section 5.1.
+
+5.2.4. 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])
/

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
subpath during the interval [T, Tf] will be representative of the
true 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.
5.1.7. Justification of the Composition Function
+5.2.6. Justification of the Composition Function
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.
5.1.9. Specific cases where the conjecture might fail
+5.2.8. 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...
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: 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
+
+ We define
+
+ TypePFiniteOnewayDelayMinimum =
+ = 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 TypePFiniteOnewayDelayMinimum metric requires the
+ conditional delay distribution described in section 5.1.3.
+
+5.3.4. Composition Function: Sum of Means
+
+ 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])
+ /
+ 
+ i = 1
+
+5.3.5. Statement of Conjecture
+
+ The minimum of a sufficiently large stream of packets measured on
+ each subpath 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 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
The requirements of the common section apply here as well.
6. Loss Metrics and Statistics
6.1. Name: TypePOnewayPacketLossPoisson/PeriodicStream
+6.1. TypePCompositeOnewayPacketLossEmpiricalProbability
6.1.1. Metric Parameters:
Same as section 4.1.1.
6.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of TypePOneway
PacketLoss singleton and stream as per [RFC2680].
@@ 545,26 +672,26 @@
where all packets i= 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
 TypePOnewayCompositePacketLossEmpiricalProbability =
 CompEp = 1 ? {(1  Ep1) x (1 ? Ep2) x (1 ? Ep3) x ... x (1 ? Epn)}
+ TypePCompositeOnewayPacketLossEmpiricalProbability =
+ 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
 any CompEp that uses subpath N for that measurement interval is
+ any CompEp that uses subpath n for that measurement interval is
undefined.
6.1.6. Statement of Conjecture
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 true 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 loss probability.
@@ 576,197 +703,201 @@
6.1.8. Sources of Deviation from the Ground Truth
See the common section.
6.1.9. Specific cases where the conjecture might fail
A concern for loss measurements combined in this way is that root
causes may be correlated to some degree.
For example, if the links of different networks follow the same
 physical route, then a single event like a tunnel fire could cause an
 outage or congestion on remaining paths in multiple networks. Here
 it is important to ensure that measurements before the event and
 after the event are not combined to estimate the composite
 performance.
+ physical route, then a single catastrophic event like a fire in a
+ tunnel could cause an outage or congestion on remaining paths in
+ multiple networks. Here it is important to ensure that measurements
+ before the event and after the event are not combined to estimate the
+ composite performance.
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
network to carry its traffic without loss.
others...
6.1.10. Application of Measurement Methodology
See the common section.
7. Delay Variation Metrics and Statistics
7.1. Name: TypePOnewayipdvrefminPoisson/PeriodicStream
+7.1. Name: TypePOnewaypdvrefminPoisson/PeriodicStream
 This metric is a necessary element of Composed Delay Variation
 metrics, and its definition does not formally exist elsewhere in IPPM
 literature.
+ This packet delay variation (PDV) metric is a necessary element of
+ Composed Delay Variation metrics, and its definition does not
+ formally exist elsewhere in IPPM literature.
7.1.1. Metric Parameters:
In addition to the parameters of section 4.1.1:
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),
assigned to packets that arrive within a "reasonable" time.
o B, a packet length in bits

o F, a selection function unambiguously defining the packets from
the stream that are selected for the packetpair computation of
this metric. F(first packet), the first packet of the pair, MUST
have a valid TypePFiniteOnewayDelay less than Tmax (in other
 words, excluding packets which have undefined, or infinite oneway
 delay) and MUST have been transmitted during the interval T, Tf.
 The second packet in the pair MUST be the packet with the minimum
 valid value of TypePFiniteOnewayDelay for the stream, in
 addition to the criteria for F(first packet). If multiple packets
 have equal minimum TypePFiniteOnewayDelay values, then the
 value for the earliest arriving packet SHOULD be used.
+ words, excluding packets which have undefined oneway delay) and
+ MUST have been transmitted during the interval T, Tf. The second
+ packet in the pair, F(second packet) MUST be the packet with the
+ minimum valid value of TypePFiniteOnewayDelay for the stream,
+ in addition to the criteria for F(first packet). If multiple
+ packets have equal minimum TypePFiniteOnewayDelay values,
+ then the value for the earliest arriving packet SHOULD be used.
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 4.1.2, we obtain the value of
+ Using the definition above in section 5.1.2, we obtain the value of
TypePFiniteOnewayDelayPoisson/PeriodicStream[i], 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: TypePOnewayipdvrefminPoisson/PeriodicStream[i] =
+ above: TypePOnewaypdvrefminPoisson/PeriodicStream[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
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 IPDVRefMin as follows (where all packets i= 1
 through N have a value for IPDVRefMin):
+ We define the mean PDV as follows (where all packets i= 1 through N
+ have a value for PDV[i]):
 TypePOnewayipdvrefminMean = MeanIPDVRefMin =
+ TypePOnewaypdvrefminMean = MeanPDV =
N

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

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

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

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

i = 1
 
+ 
/ \
 ( 3/2 ) 
 \ (N  1) * VarIPDVRefMin /
+ \ (N  1) * VarPDV /
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:
This section gives two alternative composition functions. The
objective is to estimate a quantile of the complete path delay
variation distribution. The composed quantile will be estimated
using information from the subpath delay variation distributions.
7.1.5.1. Approximate Convolution
 The TypePOnewayDelayPoisson/PeriodicStream samples from each
 subpath are summarized as a histogram with 1 ms bins representing
 the oneway delay distribution.
+ The TypePFiniteOnewayDelayPoisson/PeriodicStream samples from
+ each subpath are summarized as a histogram with 1 ms bins
+ representing the oneway delay distribution.
From [TBP], the distribution of the sum of independent random
variables can be derived using the relation:
 TypePOnewayCompositeipdvrefminquantilea =
+ TypePCompositeOnewaypdvrefminquantilea =
/ /
P(X + Y + Z <= a) =   P(X <= ayz) * P(Y = y) * P(Z = z) dy dz
/ /
z y
where X, Y, and Z are random variables representing the delay
 variation distributions of the subpaths of the complete path, and a
 is the quantile of 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.
+ variation distributions of the subpaths of the complete path (in
+ this case, there are three subpaths), and a is the quantile of
+ 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. new section
+7.1.5.2. Normal Power Approximation
 TypePOnewayCompositeipdvrefmin for the complete
 Source to Destination path can be calculated by combining statistics
 of all the constituent subpaths in the following process:
+ 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] section 8 >
+ < see [Y.1541] clause 8 and Appendix X >
7.1.6. Statement of Conjecture
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.
7.1.7. Justification of the Composition Function
See the common section.
7.1.8. Sources of Deviation from the Ground Truth
 In addition to the common deviations, the a few additional sources
 exist here. For one, very tight distributions with range on the
 order of a few milliseconds are not accurately represented by a
 histogram with 1 ms bins. This size was chosen assuming an implicit
 requirement on accuracy: errors of a few milliseconds are acceptable
 when assessing a composed distribution quantile.
+ In addition to the common deviations, a few additional sources exist
+ here. For one, very tight distributions with range on the order of a
+ few milliseconds are not accurately represented by a histogram with 1
+ ms bins. This size was chosen assuming an implicit requirement on
+ accuracy: errors of a few milliseconds are acceptable when assessing
+ a composed distribution quantile.
Also, summary statistics cannot describe the subtleties of an
empirical distribution exactly, especially when the distribution is
very different from a classical form. Any procedure that uses these
statistics alone may incur error.
7.1.9. Specific cases where the conjecture might fail
If the delay distributions of the subpaths are somehow correlated,
then neither of these composition functions will be reliable
@@ 910,30 +1041,30 @@
[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network
performance measurement with periodic streams", RFC 3432,
November 2002.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005.
12.2. Informative References
 [ID.stephanippmmultimetrics]
+ [ID.ietfippmmultimetrics]
Stephan, E., "IP Performance Metrics (IPPM) for spatial
 and multicast", draftstephanippmmultimetrics02 (work
 in progress), October 2005.
+ and multicast", draftietfippmmultimetrics04 (work in
+ progress), July 2007.
[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.1540, "Network Performance
+ [Y.1541] ITUT Recommendation Y.1541, "Network Performance
Objectives for IPbased Services", February 2006.
Authors' Addresses
Al Morton
AT&T Labs
200 Laurel Avenue South
Middletown,, NJ 07748
USA