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 | |||

This Internet-Draft is submitted to IETF in full conformance with the | This Internet-Draft is submitted to IETF in full conformance with the | |||

provisions of BCP 78 and BCP 79. This document may contain material | provisions of BCP 78 and BCP 79. This document may contain material | |||

from IETF Documents or IETF Contributions published or made publicly | from IETF Documents or IETF Contributions published or made publicly | |||

available before November 10, 2008. The person(s) controlling the | available before November 10, 2008. The person(s) controlling the | |||

copyright in some of this material may not have granted the IETF | copyright in some of this material may not have granted the IETF | |||

Trust the right to allow modifications of such material outside the | Trust the right to allow modifications of such material outside the | |||

IETF Standards Process. Without obtaining an adequate license from | IETF Standards Process. Without obtaining an adequate license from | |||

skipping to change at page 1, line 43 | skipping to change at page 1, line 43 | |||

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 8, 2009. | This Internet-Draft will expire on December 23, 2009. | |||

Copyright Notice | Copyright Notice | |||

Copyright (c) 2009 IETF Trust and the persons identified as the | Copyright (c) 2009 IETF Trust and the persons identified as the | |||

document authors. All rights reserved. | document authors. All rights reserved. | |||

This document is subject to BCP 78 and the IETF Trust's Legal | This document is subject to BCP 78 and the IETF Trust's Legal | |||

Provisions Relating to IETF Documents in effect on the date of | Provisions Relating to IETF Documents in effect on the date of | |||

publication of this document (http://trustee.ietf.org/license-info). | publication of this document (http://trustee.ietf.org/license-info). | |||

Please review these documents carefully, as they describe your rights | Please review these documents carefully, as they describe your rights | |||

skipping to change at page 3, line 13 | skipping to change at page 3, line 13 | |||

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 . . . . . . . . . . . . . . . . . . . . . . . . . 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 | |||

skipping to change at page 10, line 16 | skipping to change at page 10, line 32 | |||

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. | |||

skipping to change at page 11, line 14 | skipping to change at page 11, line 37 | |||

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 | |||

skipping to change at page 12, line 39 | skipping to change at page 13, line 24 | |||

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 | |||

End of changes. 64 change blocks. | ||||

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