draft-ietf-ippm-spatial-composition-03.txt | draft-ietf-ippm-spatial-composition-04.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 16, 2007 France Telecom Division R&D | Expires: January 8, 2008 France Telecom Division R&D | |||

March 15, 2007 | July 7, 2007 | |||

Spatial Composition of Metrics | Spatial Composition of Metrics | |||

draft-ietf-ippm-spatial-composition-03 | draft-ietf-ippm-spatial-composition-04 | |||

Status of this Memo | Status of this Memo | |||

By submitting this Internet-Draft, each author represents that any | By submitting this Internet-Draft, each author represents that any | |||

applicable patent or other IPR claims of which he or she is aware | 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 | 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. | aware will be disclosed, in accordance with Section 6 of BCP 79. | |||

Internet-Drafts are working documents of the Internet Engineering | Internet-Drafts are working documents of the Internet Engineering | |||

Task Force (IETF), its areas, and its working groups. Note that | Task Force (IETF), its areas, and its working groups. Note that | |||

skipping to change at page 1, line 35 | skipping to change at page 1, line 35 | |||

and may be updated, replaced, or obsoleted by other documents at any | and may be updated, replaced, or obsoleted by other documents at any | |||

time. It is inappropriate to use Internet-Drafts as reference | time. It is inappropriate to use Internet-Drafts as reference | |||

material or to cite them other than as "work in progress." | material or to cite them other than as "work in progress." | |||

The list of current Internet-Drafts can be accessed at | The list of current Internet-Drafts can be accessed at | |||

http://www.ietf.org/ietf/1id-abstracts.txt. | http://www.ietf.org/ietf/1id-abstracts.txt. | |||

The list of Internet-Draft Shadow Directories can be accessed at | The list of Internet-Draft Shadow Directories can be accessed at | |||

http://www.ietf.org/shadow.html. | http://www.ietf.org/shadow.html. | |||

This Internet-Draft will expire on September 16, 2007. | This Internet-Draft will expire on January 8, 2008. | |||

Copyright Notice | Copyright Notice | |||

Copyright (C) The IETF Trust (2007). | Copyright (C) The IETF Trust (2007). | |||

Abstract | Abstract | |||

This memo utilizes IPPM metrics that are applicable to both complete | This memo utilizes IPPM metrics that are applicable to both complete | |||

paths and sub-paths, and defines relationships to compose a complete | paths and sub-paths, and defines relationships to compose a complete | |||

path metric from the sub-path metrics with some accuracy w.r.t. the | path metric from the sub-path metrics with some accuracy w.r.t. the | |||

skipping to change at page 2, line 22 | skipping to change at page 2, line 22 | |||

equal to" and ">=" as "greater than or equal to". | equal to" and ">=" as "greater than or equal to". | |||

Table of Contents | Table of Contents | |||

1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 4 | 1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 4 | |||

2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4 | 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4 | |||

2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 5 | 2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 5 | |||

3. Scope and Application . . . . . . . . . . . . . . . . . . . . 5 | 3. Scope and Application . . . . . . . . . . . . . . . . . . . . 5 | |||

3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 6 | 3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 6 | |||

3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 6 | 3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 6 | |||

3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 7 | 3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 6 | |||

4. Common Specifications for Composed Metrics . . . . . . . . . . 7 | 4. Common Specifications for Composed Metrics . . . . . . . . . . 7 | |||

4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 7 | 4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 7 | |||

4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 7 | 4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 7 | |||

4.1.2. Definition and Metric Units . . . . . . . . . . . . . 8 | 4.1.2. Definition and Metric Units . . . . . . . . . . . . . 8 | |||

4.1.3. Discussion and other details . . . . . . . . . . . . . 8 | 4.1.3. Discussion and other details . . . . . . . . . . . . . 8 | |||

4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 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 | 4.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 8 | |||

4.1.7. Justification of the Composition Function . . . . . . 8 | 4.1.7. Justification of the Composition Function . . . . . . 8 | |||

4.1.8. Sources of Deviation from the Ground Truth . . . . . . 9 | 4.1.8. Sources of Deviation from the Ground Truth . . . . . . 9 | |||

4.1.9. Specific cases where the conjecture might fail . . . . 9 | 4.1.9. Specific cases where the conjecture might fail . . . . 9 | |||

4.1.10. Application of Measurement Methodology . . . . . . . . 9 | 4.1.10. Application of Measurement Methodology . . . . . . . . 9 | |||

5. One-way Delay Composed Metrics and Statistics . . . . . . . . 9 | 5. One-way Delay Composed Metrics and Statistics . . . . . . . . 10 | |||

5.1. Name: | 5.1. Name: | |||

Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 10 | Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 10 | |||

5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 10 | 5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 10 | |||

5.1.2. Definition and Metric Units . . . . . . . . . . . . . 10 | 5.1.2. Definition and Metric Units . . . . . . . . . . . . . 10 | |||

5.1.3. Discussion and other details . . . . . . . . . . . . . 10 | 5.1.3. Discussion and other details . . . . . . . . . . . . . 10 | |||

5.1.4. Mean Statistic . . . . . . . . . . . . . . . . . . . . 10 | 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 11 | |||

5.1.5. Composition Function: Sum of Means . . . . . . . . . . 11 | 5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 11 | |||

5.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 11 | 5.2.2. Definition and Metric Units of the Mean Statistic . . 11 | |||

5.1.7. Justification of the Composition Function . . . . . . 11 | 5.2.3. Discussion and other details . . . . . . . . . . . . . 11 | |||

5.1.8. Sources of Deviation from the Ground Truth . . . . . . 11 | 5.2.4. Composition Function: Sum of Means . . . . . . . . . . 11 | |||

5.1.9. Specific cases where the conjecture might fail . . . . 11 | 5.2.5. Statement of Conjecture . . . . . . . . . . . . . . . 12 | |||

5.1.10. Application of Measurement Methodology . . . . . . . . 12 | 5.2.6. Justification of the Composition Function . . . . . . 12 | |||

6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 12 | 5.2.7. Sources of Deviation from the Ground Truth . . . . . . 12 | |||

6.1. Name: | 5.2.8. Specific cases where the conjecture might fail . . . . 12 | |||

Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream . . . . 12 | 5.2.9. Application of Measurement Methodology . . . . . . . . 12 | |||

6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 12 | 5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 12 | |||

6.1.2. Definition and Metric Units . . . . . . . . . . . . . 12 | 5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13 | |||

6.1.3. Discussion and other details . . . . . . . . . . . . . 12 | 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. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 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: | 6.1.4. Statistic: | |||

Type-P-One-way-Packet-Loss-Empirical-Probability . . . 12 | Type-P-One-way-Packet-Loss-Empirical-Probability . . . 15 | |||

6.1.5. Composition Function: Composition of Empirical | 6.1.5. Composition Function: Composition of Empirical | |||

Probabilities . . . . . . . . . . . . . . . . . . . . 13 | Probabilities . . . . . . . . . . . . . . . . . . . . 15 | |||

6.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 13 | 6.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 15 | |||

6.1.7. Justification of the Composition Function . . . . . . 13 | 6.1.7. Justification of the Composition Function . . . . . . 15 | |||

6.1.8. Sources of Deviation from the Ground Truth . . . . . . 13 | 6.1.8. Sources of Deviation from the Ground Truth . . . . . . 16 | |||

6.1.9. Specific cases where the conjecture might fail . . . . 13 | 6.1.9. Specific cases where the conjecture might fail . . . . 16 | |||

6.1.10. Application of Measurement Methodology . . . . . . . . 14 | 6.1.10. Application of Measurement Methodology . . . . . . . . 16 | |||

7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 14 | 7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 16 | |||

7.1. Name: | 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 16 | |||

Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream . . . . 14 | 7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 16 | |||

7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 14 | 7.1.2. Definition and Metric Units . . . . . . . . . . . . . 17 | |||

7.1.2. Definition and Metric Units . . . . . . . . . . . . . 15 | 7.1.3. Discussion and other details . . . . . . . . . . . . . 17 | |||

7.1.3. Discussion and other details . . . . . . . . . . . . . 15 | 7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 17 | |||

7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 15 | 7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 18 | |||

7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 16 | 7.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 19 | |||

7.1.6. Statement of Conjecture . . . . . . . . . . . . . . . 17 | 7.1.7. Justification of the Composition Function . . . . . . 19 | |||

7.1.7. Justification of the Composition Function . . . . . . 17 | 7.1.8. Sources of Deviation from the Ground Truth . . . . . . 19 | |||

7.1.8. Sources of Deviation from the Ground Truth . . . . . . 17 | 7.1.9. Specific cases where the conjecture might fail . . . . 20 | |||

7.1.9. Specific cases where the conjecture might fail . . . . 18 | 7.1.10. Application of Measurement Methodology . . . . . . . . 20 | |||

7.1.10. Application of Measurement Methodology . . . . . . . . 18 | 8. Security Considerations . . . . . . . . . . . . . . . . . . . 20 | |||

8. Security Considerations . . . . . . . . . . . . . . . . . . . 18 | 8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 20 | |||

8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 18 | 8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 20 | |||

8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 18 | 8.3. Interference with the metrics . . . . . . . . . . . . . . 21 | |||

8.3. Interference with the metrics . . . . . . . . . . . . . . 18 | 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 21 | |||

9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 19 | 10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 21 | |||

10. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 19 | 11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 22 | |||

11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 20 | 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 22 | |||

12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 20 | 12.1. Normative References . . . . . . . . . . . . . . . . . . . 22 | |||

12.1. Normative References . . . . . . . . . . . . . . . . . . . 20 | 12.2. Informative References . . . . . . . . . . . . . . . . . . 23 | |||

12.2. Informative References . . . . . . . . . . . . . . . . . . 21 | Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 23 | |||

Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 21 | Intellectual Property and Copyright Statements . . . . . . . . . . 25 | |||

Intellectual Property and Copyright Statements . . . . . . . . . . 23 | ||||

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> | - Al Morton <acmorton@att.com> | |||

- Emile Stephan <emile.stephan@francetelecom.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 | |||

skipping to change at page 6, line 28 | skipping to change at page 6, line 28 | |||

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). | |||

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, the application of Spatial Composition | metric. In particular, each section addresses whether the metric: | |||

metrics are addressed as to 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 | |||

degree of flexibility (e.g., active or passive methods produce the | degree of flexibility (e.g., active or passive methods produce the | |||

"same" metric). Also, the applicable sending streams will be | "same" metric). Also, the applicable sending streams will be | |||

specified, such as Poisson, Periodic, or both. | specified, such as Poisson, Periodic, or both. | |||

Needs information or access that will only be available within an | Needs information or access that will only be available within an | |||

skipping to change at page 7, line 10 | skipping to change at page 7, line 5 | |||

Requires assumption of sub-path independence w.r.t. the metric being | Requires assumption of sub-path independence w.r.t. the metric being | |||

defined/composed, or other assumptions. | defined/composed, or other assumptions. | |||

Has known sources of inaccuracy/error, and identifies the sources. | Has known sources of inaccuracy/error, and identifies the sources. | |||

3.3. Incomplete Information | 3.3. Incomplete Information | |||

In practice, when measurements cannot be initiated on a sub-path (and | In practice, when measurements cannot be initiated on a sub-path (and | |||

perhaps the measurement system gives up during the test interval), | perhaps the measurement system gives up during the test interval), | |||

then there will not be a value for the sub-path reported, and the | then there will not be a value for the sub-path reported, and the | |||

result SHOULD be recorded as "undefined". This case should be | entire test result SHOULD be recorded as "undefined". This case | |||

distinguished from the case where the measurement system continued to | should be distinguished from the case where the measurement system | |||

send packets throughout the test interval, but all were declared | continued to send packets throughout the test interval, but all were | |||

lost. | declared lost. | |||

When a composed metric requires measurements from sub paths A, B, and | When a composed metric requires measurements from sub paths A, B, and | |||

C, and one or more of the sub-path results are undefined, then the | C, and one or more of the sub-path results are undefined, then the | |||

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 | |||

skipping to change at page 8, line 33 | skipping to change at page 8, line 29 | |||

This section is unique for every metric. | This section is unique for every metric. | |||

4.1.3. Discussion and other details | 4.1.3. Discussion and other details | |||

This section is unique for every metric. | This section is unique for every metric. | |||

4.1.4. Statistic: | 4.1.4. Statistic: | |||

This section is unique for every metric. | 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. | This section is unique for every metric. | |||

4.1.6. Statement of Conjecture | 4.1.6. Statement of Conjecture | |||

This section is unique for each metric. | This section is unique for each metric. | |||

4.1.7. Justification of the Composition Function | 4.1.7. Justification of the Composition Function | |||

It is sometimes impractical to conduct active measurements between | It is sometimes impractical to conduct active measurements between | |||

every Src-Dst pair. For example, it may not be possible to collect | every Src-Dst pair. Since the full mesh of N measurement points | |||

the desired sample size in each test interval when access link speed | grows as N x N, the scope of measurement may be limited by testing | |||

is limited, because of the potential for measurement traffic to | resources. | |||

degrade the user traffic performance. The conditions on a low-speed | ||||

access link may be understood well-enough to permit use of a small | There may be varying limitations on active testing in different parts | |||

sample size/rate, while a larger sample size/rate may be used on | of the network. For example, it may not be possible to collect the | |||

other sub-paths. | 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 low-speed access | ||||

link may be understood well-enough 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 | Also, since measurement operations have a real monetary cost, there | |||

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 | |||

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 parallel | |||

exchanges than packets with the source and destination addresses of | links when compared to packets with the source and destination | |||

the complete path. Therefore, the sub-path measurements may differ | addresses of the complete path. Therefore, the composition of sub- | |||

from the performance experienced by packets on the complete path. | path measurements may differ from the performance experienced by | |||

Multiple measurements employing sufficient sub-path address pairs | packets on the complete path. Multiple measurements employing | |||

might produce bounds on the extent of this error. | sufficient sub-path 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 sub-path | ||||

metrics SHOULD be minimized as a source of error. | ||||

others??? | ||||

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. | This section is unique for each metric. | |||

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 (e.g., active or passive methods can | Allows a degree of flexibility (e.g., active or passive methods can | |||

produce the "same" metric, but timing and correlation of passive | produce the "same" metric, but timing and correlation of passive | |||

measurements is much more challenging). | measurements is much more challenging). | |||

Poisson and/or Periodic streams are RECOMMENDED. | Poisson and/or Periodic streams are RECOMMENDED. | |||

Applicable to both Inter-domain and Intra-domain composition. | Applies to both Inter-domain and Intra-domain composition. | |||

SHOULD have synchronized measurement time intervals in all sub-paths, | SHOULD have synchronized measurement time intervals in all sub-paths, | |||

but largely overlapping intervals MAY suffice. | but largely overlapping intervals MAY suffice. | |||

REQUIRES assumption of sub-path independence w.r.t. the metric being | REQUIRES assumption of sub-path independence w.r.t. the metric being | |||

defined/composed. | defined/composed. | |||

5. One-way Delay Composed Metrics and Statistics | 5. One-way Delay Composed Metrics and Statistics | |||

5.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream | 5.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream | |||

skipping to change at page 10, line 26 | skipping to change at page 10, line 31 | |||

Using the parameters above, we obtain the value of Type-P-One-way- | Using the parameters above, we obtain the value of Type-P-One-way- | |||

Delay singleton as per [RFC2679]. | Delay singleton as per [RFC2679]. | |||

For each packet [i] that has a finite One-way Delay (in other words, | For each packet [i] that has a finite One-way Delay (in other words, | |||

excluding packets which have undefined one-way delay): | excluding packets which have undefined one-way delay): | |||

Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] = | Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] = | |||

FiniteDelay[i] = TstampDst - TstampSrc | 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 | 5.1.3. Discussion and other details | |||

The "Type-P-Finite-One-way-Delay" metric permits calculation of the | The "Type-P-Finite-One-way-Delay" metric permits calculation of the | |||

sample mean statistic. This resolves the problem of including lost | sample mean statistic. This resolves the problem of including lost | |||

packets in the sample (whose delay is undefined), and the issue with | packets in the sample (whose delay is undefined), and the issue with | |||

the informal assignment of infinite delay to lost packets (practical | the informal assignment of infinite delay to lost packets (practical | |||

systems can only assign some very large value). | systems can only assign some very large value). | |||

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. Mean Statistic | 5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean | |||

This section describes a statistic based on the Type-P-Finite-One- | ||||

way-Delay-Poisson/Periodic-Stream 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 | We define | |||

Type-P-Finite-One-way-Delay-Mean = | Type-P-Finite-One-way-Delay-Mean = | |||

N | N | |||

--- | --- | |||

1 \ | 1 \ | |||

- * > (FiniteDelay [i]) | MeanDelay = - * > (FiniteDelay [i]) | |||

N / | N / | |||

--- | --- | |||

i = 1 | i = 1 | |||

where all packets i= 1 through N have finite singleton delays. | 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 Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay for | 5.2.3. Discussion and other details | |||

the complete Source to Destination path can be calculated from sum of | ||||

the Mean Delays of all its S constituent sub-paths. | ||||

Then the | The Type-P-Finite-One-way-Delay-Mean metric requires the conditional | |||

delay distribution described in section 5.1. | ||||

5.2.4. Composition Function: Sum of Means | ||||

The Type-P-Finite--Composite-One-way-Delay-Mean, or CompMeanDelay, | ||||

for the complete Source to Destination path can be calculated from | ||||

sum of the Mean Delays of all its S constituent sub-paths. | ||||

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 [i]) | |||

/ | / | |||

--- | --- | |||

i = 1 | 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 | 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 | |||

true mean of the delay distribution (and the distributions themselves | true mean of the delay distribution (and the distributions themselves | |||

are sufficiently independent), such that the means may be added to | are sufficiently independent), such that the means may be added to | |||

produce an estimate of the complete path mean delay. | 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. | 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. | 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 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... | 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: Type-P-Finite-Composite-One-way-Delay-Minimum | ||||

This section describes is a statistic based on the Type-P-Finite-One- | ||||

way-Delay-Poisson/Periodic-Stream 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 | ||||

Type-P-Finite-One-way-Delay-Minimum = | ||||

= 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 Type-P-Finite-One-way-Delay-Minimum metric requires the | ||||

conditional delay distribution described in section 5.1.3. | ||||

5.3.4. Composition Function: Sum of Means | ||||

The Type-P-Finite--Composite-One-way-Delay-Minimum, or CompMinDelay, | ||||

for the complete Source to Destination path can be calculated from | ||||

sum of the Minimum Delays of all its S constituent sub-paths. | ||||

Then the | ||||

Type-P-Finite-Composite-One-way-Delay-Minimum = | ||||

S | ||||

--- | ||||

\ | ||||

CompMinDelay = > (MinDelay [i]) | ||||

/ | ||||

--- | ||||

i = 1 | ||||

5.3.5. Statement of Conjecture | ||||

The minimum of a sufficiently large stream of packets measured on | ||||

each sub-path 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 sub-paths 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. | The requirements of the common section apply here as well. | |||

6. Loss Metrics and Statistics | 6. Loss Metrics and Statistics | |||

6.1. Name: Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream | 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. | |||

6.1.2. Definition and Metric Units | 6.1.2. Definition and Metric Units | |||

Using the parameters above, we obtain the value of Type-P-One-way- | Using the parameters above, we obtain the value of Type-P-One-way- | |||

Packet-Loss singleton and stream as per [RFC2680]. | Packet-Loss singleton and stream as per [RFC2680]. | |||

skipping to change at page 13, line 23 | skipping to change at page 15, line 31 | |||

where all packets i= 1 through M have a value for L. | where all packets i= 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-One-way-Composite-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 - 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 | 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 n for that measurement interval is | |||

undefined. | undefined. | |||

6.1.6. Statement of Conjecture | 6.1.6. Statement of Conjecture | |||

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 true loss probability (and the | Tf] will be representative of the true loss probability (and the | |||

probabilities themselves are sufficiently independent), such that the | probabilities themselves are sufficiently independent), such that the | |||

sub-path probabilities may be combined to produce an estimate of the | sub-path probabilities may be combined to produce an estimate of the | |||

complete path loss probability. | complete path loss probability. | |||

skipping to change at page 14, line 6 | skipping to change at page 16, line 15 | |||

6.1.8. Sources of Deviation from the Ground Truth | 6.1.8. Sources of Deviation from the Ground Truth | |||

See the common section. | See the common section. | |||

6.1.9. 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 | A concern for loss measurements combined in this way is that root | |||

causes may be correlated to some degree. | causes may be correlated to some degree. | |||

For example, if the links of different networks follow the same | For example, if the links of different networks follow the same | |||

physical route, then a single event like a tunnel fire could cause an | physical route, then a single catastrophic event like a fire in a | |||

outage or congestion on remaining paths in multiple networks. Here | tunnel could cause an outage or congestion on remaining paths in | |||

it is important to ensure that measurements before the event and | multiple networks. Here it is important to ensure that measurements | |||

after the event are not combined to estimate the composite | before the event and after the event are not combined to estimate the | |||

performance. | composite performance. | |||

Or, when traffic volumes rise due to the rapid spread of an email- | Or, when traffic volumes rise due to the rapid spread of an email- | |||

born worm, loss due to queue overflow in one network may help another | born worm, loss due to queue overflow in one network may help another | |||

network to carry its traffic without loss. | network to carry its traffic without loss. | |||

others... | others... | |||

6.1.10. Application of Measurement Methodology | 6.1.10. Application of Measurement Methodology | |||

See the common section. | See the common section. | |||

7. Delay Variation Metrics and Statistics | 7. Delay Variation Metrics and Statistics | |||

7.1. Name: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream | 7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream | |||

This metric is a necessary element of Composed Delay Variation | This packet delay variation (PDV) metric is a necessary element of | |||

metrics, and its definition does not formally exist elsewhere in IPPM | Composed Delay Variation metrics, and its definition does not | |||

literature. | formally exist elsewhere in IPPM literature. | |||

7.1.1. Metric Parameters: | 7.1.1. Metric Parameters: | |||

In addition to the parameters of section 4.1.1: | In addition to the parameters of section 4.1.1: | |||

o TstampSrc[i], the wire time of packet[i] as measured at MP(Src) | o TstampSrc[i], the wire time of packet[i] as measured at MP(Src) | |||

(measurement point at the source) | ||||

o TstampDst[i], the wire time of packet[i] as measured at MP(Dst), | o TstampDst[i], the wire time of packet[i] as measured at MP(Dst), | |||

assigned to packets that arrive within a "reasonable" time. | assigned to packets that arrive within a "reasonable" time. | |||

o B, a packet length in bits | o B, a packet length in bits | |||

o F, a selection function unambiguously defining the packets from | o F, a selection function unambiguously defining the packets from | |||

the stream that are selected for the packet-pair computation of | the stream that are selected for the packet-pair computation of | |||

this metric. F(first packet), the first packet of the pair, MUST | this metric. F(first packet), the first packet of the pair, MUST | |||

have a valid Type-P-Finite-One-way-Delay less than Tmax (in other | have a valid Type-P-Finite-One-way-Delay less than Tmax (in other | |||

words, excluding packets which have undefined, or infinite one-way | words, excluding packets which have undefined one-way delay) and | |||

delay) and MUST have been transmitted during the interval T, Tf. | MUST have been transmitted during the interval T, Tf. The second | |||

The second packet in the pair MUST be the packet with the minimum | packet in the pair, F(second packet) MUST be the packet with the | |||

valid value of Type-P-Finite-One-way-Delay for the stream, in | minimum valid value of Type-P-Finite-One-way-Delay for the stream, | |||

addition to the criteria for F(first packet). If multiple packets | in addition to the criteria for F(first packet). If multiple | |||

have equal minimum Type-P-Finite-One-way-Delay values, then the | packets have equal minimum Type-P-Finite-One-way-Delay values, | |||

value for the earliest arriving packet SHOULD be used. | then the value for the earliest arriving packet SHOULD be used. | |||

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 4.1.2, 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[i], 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[i] that meets the F(first packet) criteria given | |||

above: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream[i] = | above: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream[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 | 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 IPDVRefMin as follows (where all packets i= 1 | We define the mean PDV as follows (where all packets i= 1 through N | |||

through N have a value for IPDVRefMin): | have a value for PDV[i]): | |||

Type-P-One-way-ipdv-refmin-Mean = MeanIPDVRefMin = | Type-P-One-way-pdv-refmin-Mean = MeanPDV = | |||

N | N | |||

--- | --- | |||

1 \ | 1 \ | |||

- * > (IPDVRefMin [i]) | - * > (PDV[i]) | |||

N / | N / | |||

--- | --- | |||

i = 1 | i = 1 | |||

We define the variance of IPDVRefMin as follows: | We define the variance of PDV as follows: | |||

Type-P-One-way-ipdv-refmin-Variance = VarIPDVRefMin = | Type-P-One-way-pdv-refmin-Variance = VarPDV = | |||

N | N | |||

--- | --- | |||

1 \ 2 | 1 \ 2 | |||

------- > (IPDVRefMin [i] - MeanIPDVRefMin) | ------- > (PDV[i] - MeanPDV) | |||

(N - 1) / | (N - 1) / | |||

--- | --- | |||

i = 1 | i = 1 | |||

We define the skewness of IPDVRefMin as follows: | We define the skewness of PDV as follows: | |||

Type-P-One-way-ipdv-refmin-Skewness = SkewIPDVRefMin = | Type-P-One-way-pdv-refmin-Skewness = SkewPDV = | |||

N | N | |||

--- 3 | --- 3 | |||

\ / \ | \ / \ | |||

> | IPDVRefMin[i]- MeanIPDVRefMin | | > | PDV[i]- MeanPDV | | |||

/ \ / | / \ / | |||

--- | --- | |||

i = 1 | i = 1 | |||

------------------------------------------- | ----------------------------------- | |||

/ \ | / \ | |||

| ( 3/2 ) | | | ( 3/2 ) | | |||

\ (N - 1) * VarIPDVRefMin / | \ (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 points 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: | |||

This section gives two alternative composition functions. The | This section gives two alternative composition functions. The | |||

objective is to estimate a quantile of the complete path delay | objective is to estimate a quantile of the complete path delay | |||

variation distribution. The composed quantile will be estimated | variation distribution. The composed quantile will be estimated | |||

using information from the sub-path delay variation distributions. | using information from the sub-path delay variation distributions. | |||

7.1.5.1. Approximate Convolution | 7.1.5.1. Approximate Convolution | |||

The Type-P-One-way-Delay-Poisson/Periodic-Stream samples from each | The Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream samples from | |||

sub-path are summarized as a histogram with 1 ms bins representing | each sub-path are summarized as a histogram with 1 ms bins | |||

the one-way delay distribution. | representing the one-way delay distribution. | |||

From [TBP], the distribution of the sum of independent random | From [TBP], the distribution of the sum of independent random | |||

variables can be derived using the relation: | variables can be derived using the relation: | |||

Type-P-One-way-Composite-ipdv-refmin-quantile-a = | Type-P-Composite-One-way-pdv-refmin-quantile-a = | |||

/ / | / / | |||

P(X + Y + Z <= a) = | | P(X <= a-y-z) * P(Y = y) * P(Z = z) dy dz | P(X + Y + Z <= a) = | | P(X <= a-y-z) * P(Y = y) * P(Z = z) dy dz | |||

/ / | / / | |||

z y | z y | |||

where X, Y, and Z are random variables representing the delay | where X, Y, and Z are random variables representing the delay | |||

variation distributions of the sub-paths of the complete path, and a | variation distributions of the sub-paths of the complete path (in | |||

is the quantile of interest. Note dy and dz indicate partial | this case, there are three sub-paths), and a is the quantile of | |||

integration here.This relation can be used to compose a quantile of | interest. Note dy and dz indicate partial integration here.This | |||

interest for the complete path from the sub-path delay distributions. | relation can be used to compose a quantile of interest for the | |||

The histograms with 1 ms bins are discrete approximations of the | complete path from the sub-path delay distributions. The histograms | |||

delay distributions. | with 1 ms bins are discrete approximations of the delay | |||

distributions. | ||||

7.1.5.2. new section | 7.1.5.2. Normal Power Approximation | |||

Type-P-One-way-Composite-ipdv-refmin-<something> for the complete | Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to | |||

Source to Destination path can be calculated by combining statistics | Destination path can be calculated by combining statistics of all the | |||

of all the constituent sub-paths in the following process: | constituent sub-paths in the following process: | |||

< see [Y.1541] section 8 > | < see [Y.1541] clause 8 and Appendix X > | |||

7.1.6. Statement of Conjecture | 7.1.6. Statement of Conjecture | |||

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. | |||

7.1.7. Justification of the Composition Function | 7.1.7. Justification of the Composition Function | |||

See the common section. | See the common section. | |||

7.1.8. Sources of Deviation from the Ground Truth | 7.1.8. Sources of Deviation from the Ground Truth | |||

In addition to the common deviations, the a few additional sources | In addition to the common deviations, a few additional sources exist | |||

exist here. For one, very tight distributions with range on the | here. For one, very tight distributions with range on the order of a | |||

order of a few milliseconds are not accurately represented by a | few milliseconds are not accurately represented by a histogram with 1 | |||

histogram with 1 ms bins. This size was chosen assuming an implicit | ms bins. This size was chosen assuming an implicit requirement on | |||

requirement on accuracy: errors of a few milliseconds are acceptable | accuracy: errors of a few milliseconds are acceptable when assessing | |||

when assessing a composed distribution quantile. | a composed distribution quantile. | |||

Also, summary statistics cannot describe the subtleties of an | Also, summary statistics cannot describe the subtleties of an | |||

empirical distribution exactly, especially when the distribution is | empirical distribution exactly, especially when the distribution is | |||

very different from a classical form. Any procedure that uses these | very different from a classical form. Any procedure that uses these | |||

statistics alone may incur error. | statistics alone may incur error. | |||

7.1.9. Specific cases where the conjecture might fail | 7.1.9. Specific cases where the conjecture might fail | |||

If the delay distributions of the sub-paths are somehow correlated, | If the delay distributions of the sub-paths are somehow correlated, | |||

then neither of these composition functions will be reliable | then neither of these composition functions will be reliable | |||

skipping to change at page 21, line 16 | skipping to change at page 23, line 26 | |||

[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network | [RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network | |||

performance measurement with periodic streams", RFC 3432, | performance measurement with periodic streams", RFC 3432, | |||

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. | |||

12.2. Informative References | 12.2. Informative References | |||

[I-D.stephan-ippm-multimetrics] | [I-D.ietf-ippm-multimetrics] | |||

Stephan, E., "IP Performance Metrics (IPPM) for spatial | Stephan, E., "IP Performance Metrics (IPPM) for spatial | |||

and multicast", draft-stephan-ippm-multimetrics-02 (work | and multicast", draft-ietf-ippm-multimetrics-04 (work in | |||

in progress), October 2005. | progress), July 2007. | |||

[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.1540, "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. | |||

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 | |||

End of changes. 66 change blocks. | ||||

150 lines changed or deleted | | 280 lines changed or added | ||

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