 1/draftietfippmspatialcomposition02.txt 20070320 21:12:24.000000000 +0100
+++ 2/draftietfippmspatialcomposition03.txt 20070320 21:12:24.000000000 +0100
@@ 1,19 +1,19 @@
Network Working Group A. Morton
InternetDraft AT&T Labs
Intended status: Standards Track E. Stephan
Expires: April 25, 2007 France Telecom Division R&D
 October 22, 2006
+Expires: September 16, 2007 France Telecom Division R&D
+ March 15, 2007
Spatial Composition of Metrics
 draftietfippmspatialcomposition02
+ draftietfippmspatialcomposition03
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
@@ 24,25 +24,25 @@
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 April 25, 2007.
+ This InternetDraft will expire on September 16, 2007.
Copyright Notice
 Copyright (C) The Internet Society (2006).
+ 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
actual metrics. This is called Spatial Composition in RFC 2330. The
memo refers to the Framework for Metric Composition, and provides
background and motivation for combining metrics to derive others.
The descriptions of several composed metrics and statistics follow.
@@ 57,75 +57,86 @@
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
 4. Oneway Delay Composed Metrics and Statistics . . . . . . . . 7
 4.1. Name:
 TypePFiniteOnewayDelayPoisson/PeriodicStream . . . 7
 4.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 7
 4.1.2. Definition and Metric Units . . . . . . . . . . . . . 7
+ 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 7
+ 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. Mean Statistic . . . . . . . . . . . . . . . . . . . . 8
+ 4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 8
4.1.5. Composition Function: Sum of Means . . . . . . . . . . 8
 4.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 9
 4.1.7. Justification of the Composition Function . . . . . . 9
+ 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 . . . . . . . . 10
 5. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 10
+ 4.1.10. Application of Measurement Methodology . . . . . . . . 9
+ 5. Oneway Delay Composed Metrics and Statistics . . . . . . . . 9
5.1. Name:
 TypePOnewayPacketLossPoisson/PeriodicStream . . . . 10
 5.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 10
+ TypePFiniteOnewayDelayPoisson/PeriodicStream . . . 10
+ 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 10
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 10
 5.1.3. Discussion and other details . . . . . . . . . . . . . 11
 5.1.4. Statistic:
 TypePOnewayPacketLossEmpiricalProbability . . . 11
 5.1.5. Composition Function: Composition of Empirical
 Probabilities . . . . . . . . . . . . . . . . . . . . 11
+ 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 . . . . . . 12
 5.1.9. Specific cases where the conjecture might fail . . . . 12
+ 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. Delay Variation Metrics and Statistics . . . . . . . . . . . . 13
+ 6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 12
6.1. Name:

 TypePOnewayipdvrefminPoisson/PeriodicStream . . . . 13
 6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 13
 6.1.2. Definition and Metric Units . . . . . . . . . . . . . 14
 6.1.3. Discussion and other details . . . . . . . . . . . . . 14
 6.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 14
 6.1.5. Composition Functions: . . . . . . . . . . . . . . . . 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 . . . . . . 15
 6.1.9. Specific cases where the conjecture might fail . . . . 15
 6.1.10. Application of Measurement Methodology . . . . . . . . 15
 7. Other Metrics and Statistics: Oneway Combined Metric . . . . 16
 8. Security Considerations . . . . . . . . . . . . . . . . . . . 16
 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 16
 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 16
 8.3. Interference with the metrics . . . . . . . . . . . . . . 16
 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 16
 10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 17
 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 18
 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 18
 12.1. Normative References . . . . . . . . . . . . . . . . . . . 18
 12.2. Informative References . . . . . . . . . . . . . . . . . . 19
 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 19
 Intellectual Property and Copyright Statements . . . . . . . . . . 20
+ 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
+ 6.1.4. Statistic:
+ TypePOnewayPacketLossEmpiricalProbability . . . 12
+ 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
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
@@ 133,20 +144,22 @@
 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
Composition, one of the categories of metrics under the umbrella of
the composition framework.
Spatial composition encompasses the definition of performance metrics
@@ 247,30 +260,52 @@
operator's domain, or is applicable to Interdomain composition.
Requires synchronized measurement time intervals in all subpaths, or
largely overlapping, or no timing requirements.
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.
4. Oneway Delay Composed Metrics and Statistics
+3.3. Incomplete Information
4.1. Name: TypePFiniteOnewayDelayPoisson/PeriodicStream
+ 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.
 This metric is a necessary element of Delay Composition metrics, and
 its definition does not formally exist elsewhere in IPPM literature.
+ 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.
4.1.1. Metric Parameters:
+4. Common Specifications for Composed Metrics
 o Src, the IP address of a host + Dst, the IP address of a host
+ 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.
+
+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
o T, a time (start of test interval)
o Tf, a time (end of test interval)
o lambda, a rate in reciprocal seconds (for Poisson Streams)
o incT, the nominal duration of interpacket interval, first bit to
first bit (for Periodic Streams)
@@ 281,285 +315,306 @@
o TstampSrc, the wire time of the packet as measured at MP(Src)
o TstampDst, the wire time of the packet as measured at MP(Dst),
assigned to packets that arrive within a "reasonable" time.
o Tmax, a maximum waiting time for packets at the destination, set
sufficiently long to disambiguate packets with long delays from
packets that are discarded (lost), thus the distribution of delay
is not truncated.
+ 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
+ and Tf)
+
+ o S, the number of subpaths involved in the complete SrcDst path
+
4.1.2. Definition and Metric Units
+ 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
+
+ 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.
+
+ 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.
+
+ 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.
+
+ 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
+
+ This metric is a necessary element of Delay Composition metrics, and
+ its definition does not formally exist elsewhere in IPPM literature.
+
+5.1.1. Metric Parameters
+
+ See the common parameters section above.
+
+5.1.2. Definition and Metric Units
+
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
4.1.3. Discussion and other details
+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] .
4.1.4. Mean Statistic

 We add the following parameter:

 o N, the total number of packets received at Dst (sent between T0
 and Tf)

 and define
+5.1.4. Mean Statistic
+ We define
TypePFiniteOnewayDelayMean =
N

1 \
 * > (FiniteDelay [i])
N /

i = 1
where all packets i= 1 through N have finite singleton delays.
4.1.5. Composition Function: Sum of Means
+5.1.5. 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.
 o S, the number of subpaths involved in the complete SrcDst path.

Then the
TypePFiniteCompositeOnewayDelayMean =
 CompMeanDelay = (1/S)Sum(from i=1 to S, MeanDelay[i])
+ S
+ 
+ \
+ CompMeanDelay = > (MeanDelay [i])
+ /
+ 
+ i = 1
4.1.6. Statement of Conjecture
+5.1.6. 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.
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.

 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.
+5.1.7. Justification of the Composition Function
4.1.8. Sources of Deviation from the Ground Truth
+ See the common section.
 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.
+5.1.8. Sources of Deviation from the Ground Truth
 others...
+ See the common section.
4.1.9. Specific cases where the conjecture might fail
+5.1.9. 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...
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.

 SHOULD have synchronized measurement time intervals in all subpaths,
 but largely overlapping intervals MAY suffice.
+5.1.10. Application of Measurement Methodology
 REQUIRES assumption of subpath independence w.r.t. the metric being
 defined/composed.
+ The requirements of the common section apply here as well.
5. Loss Metrics and Statistics
+6. Loss Metrics and Statistics
5.1. Name: TypePOnewayPacketLossPoisson/PeriodicStream
+6.1. Name: TypePOnewayPacketLossPoisson/PeriodicStream
5.1.1. Metric Parameters:
+6.1.1. Metric Parameters:
Same as section 4.1.1.
5.1.2. Definition and Metric Units
+6.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of TypePOneway
PacketLoss singleton and stream as per [RFC2680].
We obtain a sequence of pairs with elements as follows:
o TstampSrc, as above
o L, either zero or one, where L=1 indicates loss and L=0 indicates
arrival at the destination within TstampSrc + Tmax.
5.1.3. Discussion and other details

5.1.4. Statistic: TypePOnewayPacketLossEmpiricalProbability

 Given the following stream parameter
+6.1.3. Discussion and other details
 o M, the total number of packets sent between T0 and Tf
+6.1.4. Statistic: TypePOnewayPacketLossEmpiricalProbability
 We can define the Empirical Probability of Loss Statistic (Ep),
 consistent with Average Loss in [RFC2680], as follows:
+ 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 =

 Ep = (1/M)Sum(from i=1 to M, L[i])
+ M
+ 
+ 1 \
+ Ep =  * > (L[i])
+ M /
+ 
+ i = 1
where all packets i= 1 through M have a value for L.
5.1.5. Composition Function: Composition of Empirical Probabilities
+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)}
+ TypePOnewayCompositePacketLossEmpiricalProbability =
+ CompEp = 1 ? {(1  Ep1) x (1 ? Ep2) x (1 ? Ep3) x ... x (1 ? Epn)}
5.1.6. Statement of Conjecture
+ 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
+ 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.
5.1.7. 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.

 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.
+6.1.7. Justification of the Composition Function
5.1.8. Sources of Deviation from the Ground Truth
+ See the common section.
 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.
+6.1.8. Sources of Deviation from the Ground Truth
 others...
+ See the common section.
5.1.9. Specific cases where the conjecture might fail
+6.1.9. Specific cases where the conjecture might fail
A concern for loss measurements combined in this way is that root
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.
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...
5.1.10. 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.

 SHOULD have synchronized measurement time intervals in all subpaths,
 but largely overlapping intervals MAY suffice.
+6.1.10. Application of Measurement Methodology
 REQUIRES assumption of subpath independence w.r.t. the metric being
 defined/composed.
+ See the common section.
6. Delay Variation Metrics and Statistics
+7. Delay Variation Metrics and Statistics
6.1. Name: TypePOnewayipdvrefminPoisson/PeriodicStream
+7.1. Name: TypePOnewayipdvrefminPoisson/PeriodicStream
This metric is a necessary element of Composed Delay Variation
metrics, and its definition does not formally exist elsewhere in IPPM
literature.
6.1.1. Metric Parameters:
+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)
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
@@ 574,44 +629,44 @@
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.
6.1.2. Definition and Metric Units
+7.1.2. Definition and Metric Units
Using the definition above in section 4.1.2, we obtain the value of
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] =
IPDVRefMin[i] = FiniteDelay[i]  MinDelay
where IPDVRefMin[i] is in units of time (seconds, milliseconds).
6.1.3. Discussion and other details
+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].
6.1.4. Statistics: Mean, Variance, Skewness, Quanitle
+7.1.4. Statistics: Mean, Variance, Skewness, Quanitle
We define the mean IPDVRefMin as follows (where all packets i= 1
through N have a value for IPDVRefMin):
TypePOnewayipdvrefminMean = MeanIPDVRefMin =
N

1 \
 * > (IPDVRefMin [i])
N /
@@ 640,39 +695,96 @@

i = 1

/ \
 ( 3/2 ) 
\ (N  1) * VarIPDVRefMin /
We define the Quantile of the IPDVRefMin sample as the value where
the specified fraction of points is less than the given value.
6.1.5. Composition Functions:
+7.1.5. Composition Functions:
 The TypePOnewayCompositeipdvrefmin for the complete
+ 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.
+
+ From [TBP], the distribution of the sum of independent random
+ variables can be derived using the relation:
+
+ TypePOnewayCompositeipdvrefminquantilea =
+ / /
+ 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.
+
+7.1.5.2. new section
+
+ TypePOnewayCompositeipdvrefmin 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] >
+ < see [Y.1541] section 8 >
6.1.6. Statement of Conjecture
+7.1.6. Statement of Conjecture
6.1.7. Justification of the Composition Function
+ 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.
6.1.8. Sources of Deviation from the Ground Truth
+7.1.7. Justification of the Composition Function
6.1.9. Specific cases where the conjecture might fail
+ See the common section.
6.1.10. Application of Measurement Methodology
+7.1.8. Sources of Deviation from the Ground Truth
7. Other Metrics and Statistics: Oneway Combined Metric
+ 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.
+
+ 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
+ estimators of the complete path distribution.
+
+ In practice, subpath delay distributions with extreme outliers have
+ increased the error of the composed metric estimate.
+
+7.1.10. Application of Measurement Methodology
+
+ See the common section.
8. Security Considerations
8.1. Denial of Service Attacks
This metric requires a stream of packets sent from one host (source)
to another host (destination) through intervening networks. This
method could be abused for denial of service attacks directed at
destination and/or the intervening network(s).
@@ 732,21 +844,21 @@
measurement to investigate the performance of different part of the
network.
Editor's Questions for clarification: What additional information
would be provided to the decomposition process, beyond the
measurement of the complete path?
Is the decomposition described above intended to estimate a metric
for some/all disjoint subpaths involved in the complete path?
 >>>>>>>>>>>>>>>>>>RESOLUTION: treat this topic in a seperate memo
+ >>>>>>>>>>>>>>>>>>RESOLUTION: treat this topic in a separate memo
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>Issue
Section 7 defines a new type of metric, a "combination" of metrics
for oneway delay and packet loss. The purpose of this metric is to
link these two primary metrics in a convenient way.
Readers are asked to comment on the efficiency of the combination
@@ 769,22 +881,22 @@
>>>>>>>>>>>>>>>>RESOLUTION: No and Yes.
11. Acknowledgements
12. References
12.1. Normative References
[ID.ietfippmframeworkcompagg]
Morton, A. and S. Berghe, "Framework for Metric
 Composition", draftietfippmframeworkcompagg01 (work
 in progress), June 2006.
+ Composition", draftietfippmframeworkcompagg03 (work
+ in progress), March 2007.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
"Framework for IP Performance Metrics", RFC 2330,
May 1998.
[RFC2679] Almes, G., Kalidindi, S., and M. Zekauskas, "A Oneway
Delay Metric for IPPM", RFC 2679, September 1999.
@@ 822,46 +934,45 @@
Al Morton
AT&T Labs
200 Laurel Avenue South
Middletown,, NJ 07748
USA
Phone: +1 732 420 1571
Fax: +1 732 368 1192
Email: acmorton@att.com
URI: http://home.comcast.net/~acmacm/

Emile Stephan
France Telecom Division R&D
2 avenue Pierre Marzin
Lannion, F22307
France
Phone:
Fax: +33 2 96 05 18 52
 Email: emile.stephan@francetelecom.com
+ Email: emile.stephan@orangeftgroup.com
URI:
Full Copyright Statement
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+ Copyright (C) The IETF Trust (2007).
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