draft-ietf-ippm-spatial-composition-08.txt   draft-ietf-ippm-spatial-composition-09.txt 
Network Working Group A. Morton Network Working Group A. Morton
Internet-Draft AT&T Labs Internet-Draft AT&T Labs
Intended status: Standards Track E. Stephan Intended status: Standards Track E. Stephan
Expires: September 8, 2009 France Telecom Division R&D Expires: December 23, 2009 France Telecom Division R&D
March 7, 2009 June 21, 2009
Spatial Composition of Metrics Spatial Composition of Metrics
draft-ietf-ippm-spatial-composition-08 draft-ietf-ippm-spatial-composition-09
Status of this Memo Status of this Memo
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Table of Contents Table of Contents
1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 6
3. Scope and Application . . . . . . . . . . . . . . . . . . . . 6 3. Scope and Application . . . . . . . . . . . . . . . . . . . . 6
3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 7 3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 7
3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 7 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 8
4. Common Specifications for Composed Metrics . . . . . . . . . . 8 4. Common Specifications for Composed Metrics . . . . . . . . . . 8
4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 8 4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 8
4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 8 4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 8
4.1.2. Definition and Metric Units . . . . . . . . . . . . . 9 4.1.2. Definition and Metric Units . . . . . . . . . . . . . 9
4.1.3. Discussion and other details . . . . . . . . . . . . . 9 4.1.3. Discussion and other details . . . . . . . . . . . . . 9
4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9 4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9
4.1.5. Composition Function . . . . . . . . . . . . . . . . . 9 4.1.5. Composition Function . . . . . . . . . . . . . . . . . 9
4.1.6. Statement of Conjecture and Assumptions . . . . . . . 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 4.1.8. Sources of Deviation from the Ground Truth . . . . . . 10
4.1.9. Specific cases where the conjecture might fail . . . . 11 4.1.9. Specific cases where the conjecture might fail . . . . 11
4.1.10. Application of Measurement Methodology . . . . . . . . 11 4.1.10. Application of Measurement Methodology . . . . . . . . 12
5. One-way Delay Composed Metrics and Statistics . . . . . . . . 11 5. One-way Delay Composed Metrics and Statistics . . . . . . . . 12
5.1. Name: 5.1. Name:
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 11 Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 12
5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 11 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 12 5.1.2. Definition and Metric Units . . . . . . . . . . . . . 12
5.1.3. Discussion and other details . . . . . . . . . . . . . 12 5.1.3. Discussion and other details . . . . . . . . . . . . . 13
5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 12 5.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13
5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 13
5.2.2. Definition and Metric Units of the Mean Statistic . . 12 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13
5.2.3. Discussion and other details . . . . . . . . . . . . . 13 5.2.2. Definition and Metric Units of the Mean Statistic . . 13
5.2.4. Composition Function: Sum of Means . . . . . . . . . . 13 5.2.3. Discussion and other details . . . . . . . . . . . . . 14
5.2.5. Statement of Conjecture and Assumptions . . . . . . . 13 5.2.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 14
5.2.6. Justification of the Composition Function . . . . . . 14 5.2.5. Composition Function: Sum of Means . . . . . . . . . . 14
5.2.7. Sources of Deviation from the Ground Truth . . . . . . 14 5.2.6. Statement of Conjecture and Assumptions . . . . . . . 14
5.2.8. Specific cases where the conjecture might fail . . . . 14 5.2.7. Justification of the Composition Function . . . . . . 15
5.2.9. Application of Measurement Methodology . . . . . . . . 14 5.2.8. Sources of Deviation from the Ground Truth . . . . . . 15
5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 14 5.2.9. Specific cases where the conjecture might fail . . . . 15
5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 14 5.2.10. Application of Measurement Methodology . . . . . . . . 15
5.3.2. Definition and Metric Units of the Mean Statistic . . 14 5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 15
5.3.3. Discussion and other details . . . . . . . . . . . . . 15 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 15
5.3.4. Composition Function: Sum of Means . . . . . . . . . . 15 5.3.2. Definition and Metric Units of the Minimum
5.3.5. Statement of Conjecture and Assumptions . . . . . . . 15 Statistic . . . . . . . . . . . . . . . . . . . . . . 15
5.3.6. Justification of the Composition Function . . . . . . 15 5.3.3. Discussion and other details . . . . . . . . . . . . . 16
5.3.7. Sources of Deviation from the Ground Truth . . . . . . 15 5.3.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 16
5.3.8. Specific cases where the conjecture might fail . . . . 16 5.3.5. Composition Function: Sum of Minima . . . . . . . . . 16
5.3.9. Application of Measurement Methodology . . . . . . . . 16 5.3.6. Statement of Conjecture and Assumptions . . . . . . . 16
6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 16 5.3.7. Justification of the Composition Function . . . . . . 17
6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 16 5.3.8. Sources of Deviation from the Ground Truth . . . . . . 17
6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 16 5.3.9. Specific cases where the conjecture might fail . . . . 17
6.1.2. Definition and Metric Units . . . . . . . . . . . . . 16 5.3.10. Application of Measurement Methodology . . . . . . . . 17
6.1.3. Discussion and other details . . . . . . . . . . . . . 16 6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 17
6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 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: 6.1.4. Statistic:
Type-P-One-way-Packet-Loss-Empirical-Probability . . . 16 Type-P-One-way-Packet-Loss-Empirical-Probability . . . 18
6.1.5. Composition Function: Composition of Empirical 6.1.5. Composition Function: Composition of Empirical
Probabilities . . . . . . . . . . . . . . . . . . . . 17 Probabilities . . . . . . . . . . . . . . . . . . . . 18
6.1.6. Statement of Conjecture and Assumptions . . . . . . . 17 6.1.6. Statement of Conjecture and Assumptions . . . . . . . 18
6.1.7. Justification of the Composition Function . . . . . . 17 6.1.7. Justification of the Composition Function . . . . . . 18
6.1.8. Sources of Deviation from the Ground Truth . . . . . . 17 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 19
6.1.9. Specific cases where the conjecture might fail . . . . 17 6.1.9. Specific cases where the conjecture might fail . . . . 19
6.1.10. Application of Measurement Methodology . . . . . . . . 18 6.1.10. Application of Measurement Methodology . . . . . . . . 19
7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 18 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 19
7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 18 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 19
7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 18 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 19
7.1.2. Definition and Metric Units . . . . . . . . . . . . . 19 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 20
7.1.3. Discussion and other details . . . . . . . . . . . . . 19 7.1.3. Discussion and other details . . . . . . . . . . . . . 20
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 19 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 20
7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 20 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 21
7.1.6. Statement of Conjecture and Assumptions . . . . . . . 21 7.1.6. Statement of Conjecture and Assumptions . . . . . . . 22
7.1.7. Justification of the Composition Function . . . . . . 21 7.1.7. Justification of the Composition Function . . . . . . 22
7.1.8. Sources of Deviation from the Ground Truth . . . . . . 22 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 23
7.1.9. Specific cases where the conjecture might fail . . . . 22 7.1.9. Specific cases where the conjecture might fail . . . . 23
7.1.10. Application of Measurement Methodology . . . . . . . . 22 7.1.10. Application of Measurement Methodology . . . . . . . . 23
8. Security Considerations . . . . . . . . . . . . . . . . . . . 22 8. Security Considerations . . . . . . . . . . . . . . . . . . . 23
8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 22 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 23
8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 22 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 23
8.3. Interference with the metrics . . . . . . . . . . . . . . 23 8.3. Interference with the metrics . . . . . . . . . . . . . . 24
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 23 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24
10. Acknowlegements . . . . . . . . . . . . . . . . . . . . . . . 23 10. Acknowlegements . . . . . . . . . . . . . . . . . . . . . . . 24
11. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 23 11. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 24
12. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 25 12. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 26
13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 25 13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 26
13.1. Normative References . . . . . . . . . . . . . . . . . . . 25 13.1. Normative References . . . . . . . . . . . . . . . . . . . 26
13.2. Informative References . . . . . . . . . . . . . . . . . . 25 13.2. Informative References . . . . . . . . . . . . . . . . . . 26
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 26 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 27
1. Contributors 1. Contributors
Thus far, the following people have contributed useful ideas, Thus far, the following people have contributed useful ideas,
suggestions, or the text of sections that have been incorporated into suggestions, or the text of sections that have been incorporated into
this memo: this memo:
- Phil Chimento <vze275m9@verizon.net> - Phil Chimento <vze275m9@verizon.net>
- Reza Fardid <RFardid@Covad.COM> - Reza Fardid <RFardid@Covad.COM>
- Roman Krzanowski <roman.krzanowski@verizon.com> - Roman Krzanowski <roman.krzanowski@verizon.com>
- Maurizio Molina <maurizio.molina@dante.org.uk> - Maurizio Molina <maurizio.molina@dante.org.uk>
- Al Morton <acmorton@att.com>
- Emile Stephan <emile.stephan@orange-ftgroup.com>
- Lei Liang <L.Liang@surrey.ac.uk> - Lei Liang <L.Liang@surrey.ac.uk>
- Dave Hoeflin <dhoeflin@att.com> - Dave Hoeflin <dhoeflin@att.com>
2. Introduction 2. Introduction
The IPPM framework [RFC2330] describes two forms of metric The IPPM framework [RFC2330] describes two forms of metric
composition, spatial and temporal. The new composition framework composition, spatial and temporal. The new composition framework
[I-D.ietf-ippm-framework-compagg] expands and further qualifies these [I-D.ietf-ippm-framework-compagg] expands and further qualifies these
original forms into three categories. This memo describes Spatial original forms into three categories. This memo describes Spatial
skipping to change at page 7, line 24 skipping to change at page 7, line 24
o multiple metrics for each sub-path (possibly one that is the same o multiple metrics for each sub-path (possibly one that is the same
as the complete path metric); as the complete path metric);
o a single sub-path metric that is different from the complete path o a single sub-path metric that is different from the complete path
metric; metric;
o different measurement techniques like active and passive o different measurement techniques like active and passive
(recognizing that PSAMP WG will define capabilities to sample (recognizing that PSAMP WG will define capabilities to sample
packets to support measurement). packets to support measurement).
We note a possibility: Using a complete path metric and all but one
sub-path metric to infer the performance of the missing sub-path,
especially when the "last" sub-path metric is missing. However, such
de-composition calculations, and the corresponding set of issues they
raise, are beyond the scope of this memo.
3.2. Application 3.2. Application
The new composition framework [I-D.ietf-ippm-framework-compagg] The new composition framework [I-D.ietf-ippm-framework-compagg]
requires the specification of the applicable circumstances for each requires the specification of the applicable circumstances for each
metric. In particular, each section addresses whether the metric: metric. In particular, each section addresses whether the metric:
Requires the same test packets to traverse all sub-paths, or may use Requires the same test packets to traverse all sub-paths, or may use
similar packets sent and collected separately in each sub-path. similar packets sent and collected separately in each sub-path.
Requires homogeneity of measurement methodologies, or can allow a Requires homogeneity of measurement methodologies, or can allow a
skipping to change at page 8, line 22 skipping to change at page 8, line 29
composed metric SHOULD also be recorded as undefined. composed metric SHOULD also be recorded as undefined.
4. Common Specifications for Composed Metrics 4. Common Specifications for Composed Metrics
To reduce the redundant information presented in the detailed metrics To reduce the redundant information presented in the detailed metrics
sections that follow, this section presents the specifications that sections that follow, this section presents the specifications that
are common to two or more metrics. The section is organized using are common to two or more metrics. The section is organized using
the same subsections as the individual metrics, to simplify the same subsections as the individual metrics, to simplify
comparisons. 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 sub-paths
4.1. Name: Type-P 4.1. Name: Type-P
All metrics use the Type-P convention as described in [RFC2330]. The All metrics use the Type-P convention as described in [RFC2330]. The
rest of the name is unique to each metric. rest of the name is unique to each metric.
4.1.1. Metric Parameters 4.1.1. Metric Parameters
o Src, the IP address of a host o Src, the IP address of a host
o Dst, the IP address of a host o Dst, the IP address of a host
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is value in re-using measurements where they are applicable, rather is value in re-using measurements where they are applicable, rather
than launching new measurements for every possible source-destination than launching new measurements for every possible source-destination
pair. pair.
4.1.8. Sources of Deviation from the Ground Truth 4.1.8. Sources of Deviation from the Ground Truth
4.1.8.1. Sub-path List Differs from Complete Path 4.1.8.1. Sub-path List Differs from Complete Path
The measurement packets, each having source and destination addresses The measurement packets, each having source and destination addresses
intended for collection at edges of the sub-path, may take a intended for collection at edges of the sub-path, may take a
different specific path through the network equipment and parallel different specific path through the network equipment and links when
links when compared to packets with the source and destination compared to packets with the source and destination addresses of the
addresses of the complete path. Therefore, the performance estimated complete path. Examples sources of parallel paths include Equal Cost
from the composition of sub-path measurements may differ from the Multi-Path and parallel (or bundled) links. Therefore, the
performance experienced by packets on the complete path. Multiple performance estimated from the composition of sub-path measurements
measurements employing sufficient sub-path address pairs might may differ from the performance experienced by packets on the
produce bounds on the extent of this error. complete path. Multiple measurements employing sufficient sub-path
address pairs might produce bounds on the extent of this error.
We also note the possibility of re-routing during a measurement
interval, as it may affect the correspondence between packets
traversing the complete path and the sub-paths that were "involved"
prior to the re-route.
4.1.8.2. Sub-path Contains Extra Network Elements 4.1.8.2. Sub-path Contains Extra Network Elements
Related to the case of an alternate path described above is the case Related to the case of an alternate path described above is the case
where elements in the measured path are unique to measurement system where elements in the measured path are unique to measurement system
connectivity. For example, a measurement system may use a dedicated connectivity. For example, a measurement system may use a dedicated
link to a LAN switch, and packets on the complete path do not link to a LAN switch, and packets on the complete path do not
traverse that link. The performance of such a dedicated link would traverse that link. The performance of such a dedicated link would
be measured continuously, and its contribution to the sub-path be measured continuously, and its contribution to the sub-path
metrics SHOULD be minimized as a source of error. metrics SHOULD be minimized as a source of error.
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Sub-path destination addresses and complete path addresses do not Sub-path destination addresses and complete path addresses do not
belong to the same network. Therefore routes selected to reach each belong to the same network. Therefore routes selected to reach each
sub-path destinations differ from the route that would be selected to sub-path destinations differ from the route that would be selected to
reach the destination address of the complete path. Consequently reach the destination address of the complete path. Consequently
spatial composition may produce finite estimation of a ground true spatial composition may produce finite estimation of a ground true
metric between a source Src and a destination Dst when the route metric between a source Src and a destination Dst when the route
between Src and Dst is undefined. between Src and Dst is undefined.
4.1.9. Specific cases where the conjecture might fail 4.1.9. Specific cases where the conjecture might fail
This section is unique for each metric (see the metric-specific This section is unique for most metrics (see the metric-specific
sections). sections).
For delay-related metrics, One-way delay always depends on packet
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 non-fragmented packets and composed metrics based on
non-fragmented sub-path measurements.
4.1.10. Application of Measurement Methodology 4.1.10. Application of Measurement Methodology
The methodology: The methodology:
SHOULD use similar packets sent and collected separately in each sub- SHOULD use similar packets sent and collected separately in each sub-
path. path.
Allows a degree of flexibility regarding test stream generation Allows a degree of flexibility regarding test stream generation
(e.g., active or passive methods can produce an equivalent result, (e.g., active or passive methods can produce an equivalent result,
but the lack of control over the source, timing and correlation of but the lack of control over the source, timing and correlation of
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The Finite-One-way-Delay approach handles the problem of lost packets The Finite-One-way-Delay approach handles the problem of lost packets
by reducing the event space. We consider conditional statistics, and by reducing the event space. We consider conditional statistics, and
estimate the mean one-way delay conditioned on the event that all estimate the mean one-way delay conditioned on the event that all
packets in the sample arrive at the destination (within the specified packets in the sample arrive at the destination (within the specified
waiting time, Tmax). This offers a way to make some valid statements waiting time, Tmax). This offers a way to make some valid statements
about one-way delay, and at the same time avoiding events with about one-way delay, and at the same time avoiding events with
undefined outcomes. This approach is derived from the treatment of undefined outcomes. This approach is derived from the treatment of
lost packets in [RFC3393], and is similar to [Y.1540] . lost packets in [RFC3393], and is similar to [Y.1540] .
5.1.4. 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: Type-P-Finite-Composite-One-way-Delay-Mean 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean
This section describes a statistic based on the Type-P-Finite-One- This section describes a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric. way-Delay-Poisson/Periodic-Stream metric.
5.2.1. Metric Parameters 5.2.1. Metric Parameters
See the common parameters section above. See the common parameters section above.
5.2.2. Definition and Metric Units of the Mean Statistic 5.2.2. Definition and Metric Units of the Mean Statistic
We define We define
Type-P-Finite-One-way-Delay-Mean = Type-P-Finite-One-way-Delay-Mean =
N N
--- ---
1 \ 1 \
MeanDelay = - * > (FiniteDelay [i]) MeanDelay = - * > (FiniteDelay [n])
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 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 information. For example, resolution of microseconds is usually
sufficient. sufficient.
5.2.3. Discussion and other details 5.2.3. Discussion and other details
The Type-P-Finite-One-way-Delay-Mean metric requires the conditional The Type-P-Finite-One-way-Delay-Mean metric requires the conditional
delay distribution described in section 5.1. delay distribution described in section 5.1.
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 Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay, The Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay,
for the complete Source to Destination path can be calculated from for the complete Source to Destination path can be calculated from
sum of the Mean Delays of all its S constituent sub-paths. sum of the Mean Delays of all its S constituent sub-paths.
Then the Then the
Type-P-Finite-Composite-One-way-Delay-Mean = Type-P-Finite-Composite-One-way-Delay-Mean =
S S
--- ---
\ \
CompMeanDelay = > (MeanDelay [i]) CompMeanDelay = > (MeanDelay [s])
/ /
--- ---
i = 1 s = 1
where sub-paths 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 The mean of a sufficiently large stream of packets measured on each
sub-path during the interval [T, Tf] will be representative of the sub-path during the interval [T, Tf] will be representative of the
ground truth mean of the delay distribution (and the distributions ground truth mean of the delay distribution (and the distributions
themselves are sufficiently independent), such that the means may be themselves are sufficiently independent), such that the means may be
added to produce an estimate of the complete path mean delay. added to produce an estimate of the complete path mean delay.
It is assumed that the one-way delay distributions of the sub-paths It is assumed that the one-way delay distributions of the sub-paths
and the complete path are continuous. and the complete path are continuous. The mean of bi-modal
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. 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. 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 sub-path distributions are bimodal, then the measured If any of the sub-path distributions are bimodal, then the measured
means may not be stable, and in this case the mean will not be a means may not be stable, and in this case the mean will not be a
particularly useful statistic when describing the delay distribution particularly useful statistic when describing the delay distribution
of the complete path. of the complete path.
The mean may not be sufficiently robust statistic to produce a The mean may not be sufficiently robust statistic to produce a
reliable estimate, or to be useful even if it can be measured. reliable estimate, or to be useful even if it can be measured.
others... If a link contributing non-negligible 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. The requirements of the common section apply here as well.
5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum 5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum
This section describes is a statistic based on the Type-P-Finite-One- This section describes is a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric, and the composed metric way-Delay-Poisson/Periodic-Stream metric, and the composed metric
based on that statistic. based on that statistic.
5.3.1. Metric Parameters 5.3.1. Metric Parameters
See the common parameters section above. 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 We define
Type-P-Finite-One-way-Delay-Minimum = Type-P-Finite-One-way-Delay-Minimum =
= MinDelay = (FiniteDelay [j]) = MinDelay = (FiniteDelay [j])
such that for some index, j, where 1<= j <= N 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 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 information. For example, resolution of microseconds is usually
sufficient. sufficient.
5.3.3. Discussion and other details 5.3.3. Discussion and other details
The Type-P-Finite-One-way-Delay-Minimum metric requires the The Type-P-Finite-One-way-Delay-Minimum metric requires the
conditional delay distribution described in section 5.1.3. conditional delay distribution described in section 5.1.3.
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 Type-P-Finite--Composite-One-way-Delay-Minimum, or CompMinDelay, The Type-P-Finite--Composite-One-way-Delay-Minimum, or CompMinDelay,
for the complete Source to Destination path can be calculated from for the complete Source to Destination path can be calculated from
sum of the Minimum Delays of all its S constituent sub-paths. sum of the Minimum Delays of all its S constituent sub-paths.
Then the Then the
Type-P-Finite-Composite-One-way-Delay-Minimum = Type-P-Finite-Composite-One-way-Delay-Minimum =
S S
--- ---
\ \
CompMinDelay = > (MinDelay [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 The minimum of a sufficiently large stream of packets measured on
each sub-path during the interval [T, Tf] will be representative of each sub-path during the interval [T, Tf] will be representative of
the ground truth minimum of the delay distribution (and the the ground truth minimum of the delay distribution (and the
distributions themselves are sufficiently independent), such that the distributions themselves are sufficiently independent), such that the
minima may be added to produce an estimate of the complete path minima may be added to produce an estimate of the complete path
minimum delay. minimum delay.
It is assumed that the one-way delay distributions of the sub-paths It is assumed that the one-way delay distributions of the sub-paths
and the complete path are continuous. 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. 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. 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 sub-paths is not stable, then the If the routing on any of the sub-paths is not stable, then the
measured minimum may not be stable. In this case the composite measured minimum may not be stable. In this case the composite
minimum would tend to produce an estimate for the complete path that minimum would tend to produce an estimate for the complete path that
may be too low for the current path. may be too low for the current path.
others??? 5.3.10. Application of Measurement Methodology
5.3.9. Application of Measurement Methodology
The requirements of the common section apply here as well. The requirements of the common section apply here as well.
6. Loss Metrics and Statistics 6. Loss Metrics and Statistics
6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability
6.1.1. Metric Parameters: 6.1.1. Metric Parameters:
Same as section 4.1.1. Same as section 4.1.1.
skipping to change at page 17, line 9 skipping to change at page 18, line 15
6.1.4. Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability 6.1.4. Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability
Given the stream parameter M, the number of packets sent, we can Given the stream parameter M, the number of packets sent, we can
define the Empirical Probability of Loss Statistic (Ep), consistent define the Empirical Probability of Loss Statistic (Ep), consistent
with Average Loss in [RFC2680], as follows: with Average Loss in [RFC2680], as follows:
Type-P-One-way-Packet-Loss-Empirical-Probability = Type-P-One-way-Packet-Loss-Empirical-Probability =
M M
--- ---
1 \ 1 \
Ep = - * > (L[i]) Ep = - * > (L[m])
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 6.1.5. Composition Function: Composition of Empirical Probabilities
The Type-P-One-way-Composite-Packet-Loss-Empirical-Probability, or The Type-P-One-way-Composite-Packet-Loss-Empirical-Probability, or
CompEp for the complete Source to Destination path can be calculated CompEp for the complete Source to Destination path can be calculated
by combining Ep of all its constituent sub-paths (Ep1, Ep2, Ep3, ... by combining Ep of all its constituent sub-paths (Ep1, Ep2, Ep3, ...
Epn) as Epn) as
Type-P-Composite-One-way-Packet-Loss-Empirical-Probability = Type-P-Composite-One-way-Packet-Loss-Empirical-Probability =
CompEp = 1 - {(1 - Ep1) x (1 - Ep2) x (1 - Ep3) x ... x (1 - 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 possibly because a measurement system failed to report a value, then
any CompEp that uses sub-path n for that measurement interval is any CompEp that uses sub-path s for that measurement interval is
undefined. undefined.
6.1.6. Statement of Conjecture and Assumptions 6.1.6. Statement of Conjecture and Assumptions
The empirical probability of loss calculated on a sufficiently large The empirical probability of loss calculated on a sufficiently large
stream of packets measured on each sub-path during the interval [T, stream of packets measured on each sub-path during the interval [T,
Tf] will be representative of the ground truth empirical loss Tf] will be representative of the ground truth empirical loss
probability (and the probabilities themselves are sufficiently probability (and the probabilities themselves are sufficiently
independent), such that the sub-path probabilities may be combined to independent), such that the sub-path probabilities may be combined to
produce an estimate of the complete path empirical loss probability. produce an estimate of the complete path empirical loss probability.
skipping to change at page 19, line 15 skipping to change at page 20, line 25
o MinDelay, the Type-P-Finite-One-way-Delay value for F(second o MinDelay, the Type-P-Finite-One-way-Delay value for F(second
packet) given above. packet) given above.
o N, the number of packets received at the Destination meeting the o N, the number of packets received at the Destination meeting the
F(first packet) criteria. F(first packet) criteria.
7.1.2. Definition and Metric Units 7.1.2. Definition and Metric Units
Using the definition above in section 5.1.2, we obtain the value of Using the definition above in section 5.1.2, we obtain the value of
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i], the singleton Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[n], the singleton
for each packet[i] in the stream (a.k.a. FiniteDelay[i]). for each packet[i] in the stream (a.k.a. FiniteDelay[i]).
For each packet[i] that meets the F(first packet) criteria given For each packet[n] that meets the F(first packet) criteria given
above: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream[i] = above: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream[n] =
PDV[i] = FiniteDelay[i] - MinDelay PDV[n] = FiniteDelay[n] - MinDelay
where PDV[i] is in units of time in seconds, expressed in where PDV[i] is in units of time in seconds, expressed in
sufficiently low resolution to convey meaningful quantitative sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually information. For example, resolution of microseconds is usually
sufficient. sufficient.
7.1.3. Discussion and other details 7.1.3. Discussion and other details
This metric produces a sample of delay variation normalized to the This metric produces a sample of delay variation normalized to the
minimum delay of the sample. The resulting delay variation minimum delay of the sample. The resulting delay variation
distribution is independent of the sending sequence (although distribution is independent of the sending sequence (although
specific FiniteDelay values within the distribution may be specific FiniteDelay values within the distribution may be
correlated, depending on various stream parameters such as packet correlated, depending on various stream parameters such as packet
spacing). This metric is equivalent to the IP Packet Delay Variation spacing). This metric is equivalent to the IP Packet Delay Variation
parameter defined in [Y.1540]. parameter defined in [Y.1540].
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle
We define the mean PDV as follows (where all packets i= 1 through N We define the mean PDV as follows (where all packets n = 1 through N
have a value for PDV[i]): have a value for PDV[n]):
Type-P-One-way-pdv-refmin-Mean = MeanPDV = Type-P-One-way-pdv-refmin-Mean = MeanPDV =
N N
--- ---
1 \ 1 \
- * > (PDV[i]) - * > (PDV[n])
N / N /
--- ---
i = 1 n = 1
We define the variance of PDV as follows: We define the variance of PDV as follows:
Type-P-One-way-pdv-refmin-Variance = VarPDV = Type-P-One-way-pdv-refmin-Variance = VarPDV =
N N
--- ---
1 \ 2 1 \ 2
------- > (PDV[i] - MeanPDV) ------- > (PDV[n] - MeanPDV)
(N - 1) / (N - 1) /
--- ---
i = 1 n = 1
We define the skewness of PDV as follows: We define the skewness of PDV as follows:
Type-P-One-way-pdv-refmin-Skewness = SkewPDV = Type-P-One-way-pdv-refmin-Skewness = SkewPDV =
N N
--- 3 --- 3
\ / \ \ / \
> | PDV[i]- MeanPDV | > | PDV[n]- MeanPDV |
/ \ / / \ /
--- ---
i = 1 n = 1
----------------------------------- -----------------------------------
/ \ / \
| ( 3/2 ) | | ( 3/2 ) |
\ (N - 1) * VarPDV / \ (N - 1) * VarPDV /
We define the Quantile of the IPDVRefMin sample as the value where We define the Quantile of the IPDVRefMin sample as the value where
the specified fraction of singletons is less than the given value. the specified fraction of singletons is less than the given value.
7.1.5. Composition Functions: 7.1.5. Composition Functions:
skipping to change at page 21, line 32 skipping to change at page 22, line 32
interest. Note dy and dz indicate partial integration here.This interest. Note dy and dz indicate partial integration here.This
relation can be used to compose a quantile of interest for the relation can be used to compose a quantile of interest for the
complete path from the sub-path delay distributions. The histograms complete path from the sub-path delay distributions. The histograms
with 1 ms bins are discrete approximations of the delay with 1 ms bins are discrete approximations of the delay
distributions. distributions.
7.1.5.2. Normal Power Approximation 7.1.5.2. Normal Power Approximation
Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to
Destination path can be calculated by combining statistics of all the Destination path can be calculated by combining statistics of all the
constituent sub-paths in the following process: constituent sub-paths in the process described in [Y.1541] clause 8
and Appendix X.
< see [Y.1541] clause 8 and Appendix X >
7.1.6. Statement of Conjecture and Assumptions 7.1.6. Statement of Conjecture and Assumptions
The delay distribution of a sufficiently large stream of packets The delay distribution of a sufficiently large stream of packets
measured on each sub-path during the interval [T, Tf] will be measured on each sub-path during the interval [T, Tf] will be
sufficiently stationary and the sub-path distributions themselves are sufficiently stationary and the sub-path distributions themselves are
sufficiently independent, so that summary information describing the sufficiently independent, so that summary information describing the
sub-path distributions can be combined to estimate the delay sub-path distributions can be combined to estimate the delay
distribution of complete path. distribution of complete path.
skipping to change at page 25, line 41 skipping to change at page 26, line 41
November 2002. November 2002.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics [RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005. Registry", BCP 108, RFC 4148, August 2005.
13.2. Informative References 13.2. Informative References
[I-D.ietf-ippm-multimetrics] [I-D.ietf-ippm-multimetrics]
Stephan, E., Liang, L., and A. Morton, "IP Performance Stephan, E., Liang, L., and A. Morton, "IP Performance
Metrics (IPPM) for spatial and multicast", Metrics (IPPM) for spatial and multicast",
draft-ietf-ippm-multimetrics-09 (work in progress), draft-ietf-ippm-multimetrics-11 (work in progress),
October 2008. April 2009.
[Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data [Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data
communication service - IP packet transfer and communication service - IP packet transfer and
availability performance parameters", December 2002. availability performance parameters", December 2002.
[Y.1541] ITU-T Recommendation Y.1541, "Network Performance [Y.1541] ITU-T Recommendation Y.1541, "Network Performance
Objectives for IP-based Services", February 2006. Objectives for IP-based Services", February 2006.
Index
?
??? 14
Authors' Addresses Authors' Addresses
Al Morton Al Morton
AT&T Labs AT&T Labs
200 Laurel Avenue South 200 Laurel Avenue South
Middletown,, NJ 07748 Middletown,, NJ 07748
USA USA
Phone: +1 732 420 1571 Phone: +1 732 420 1571
Fax: +1 732 368 1192 Fax: +1 732 368 1192
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