draft-ietf-ippm-loss-episode-metrics-04.txt | rfc6534.txt | |||
---|---|---|---|---|

Network Working Group N. Duffield | Internet Engineering Task Force (IETF) N. Duffield | |||

Internet-Draft AT&T Labs-Research | Request for Comments: 6534 AT&T Labs-Research | |||

Intended status: Standards Track A. Morton | Category: Standards Track A. Morton | |||

Expires: July 20, 2012 AT&T Labs | ISSN: 2070-1721 AT&T Labs | |||

J. Sommers | J. Sommers | |||

Colgate University | Colgate University | |||

January 17, 2012 | May 2012 | |||

Loss Episode Metrics for IPPM | Loss Episode Metrics for IP Performance Metrics (IPPM) | |||

draft-ietf-ippm-loss-episode-metrics-04 | ||||

Abstract | Abstract | |||

The IETF has developed a one way packet loss metric that measures the | The IETF has developed a one-way packet loss metric that measures the | |||

loss rate on a Poisson probe stream between two hosts. However, the | loss rate on a Poisson and Periodic probe streams between two hosts. | |||

impact of packet loss on applications is in general sensitive not | However, the impact of packet loss on applications is, in general, | |||

just to the average loss rate, but also to the way in which packet | sensitive not just to the average loss rate but also to the way in | |||

losses are distributed in loss episodes (i.e., maximal sets of | which packet losses are distributed in loss episodes (i.e., maximal | |||

consecutively lost probe packets). This document defines one-way | sets of consecutively lost probe packets). This document defines | |||

packet loss episode metrics, specifically the frequency and average | one-way packet loss episode metrics, specifically, the frequency and | |||

duration of loss episodes, and a probing methodology under which the | average duration of loss episodes and a probing methodology under | |||

loss episode metrics are to be measured. | which the loss episode metrics are to be measured. | |||

Requirements Language | ||||

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", | ||||

"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this | ||||

document are to be interpreted as described in RFC 2119 [RFC2119] | ||||

Status of this Memo | ||||

This Internet-Draft is submitted in full conformance with the | Status of This Memo | |||

provisions of BCP 78 and BCP 79. | ||||

Internet-Drafts are working documents of the Internet Engineering | This is an Internet Standards Track document. | |||

Task Force (IETF). Note that other groups may also distribute | ||||

working documents as Internet-Drafts. The list of current Internet- | ||||

Drafts is at http://datatracker.ietf.org/drafts/current/. | ||||

Internet-Drafts are draft documents valid for a maximum of six months | This document is a product of the Internet Engineering Task Force | |||

and may be updated, replaced, or obsoleted by other documents at any | (IETF). It represents the consensus of the IETF community. It has | |||

time. It is inappropriate to use Internet-Drafts as reference | received public review and has been approved for publication by the | |||

material or to cite them other than as "work in progress." | Internet Engineering Steering Group (IESG). Further information on | |||

Internet Standards is available in Section 2 of RFC 5741. | ||||

This Internet-Draft will expire on July 20, 2012. | Information about the current status of this document, any errata, | |||

and how to provide feedback on it may be obtained at | ||||

http://www.rfc-editor.org/info/rfc6534. | ||||

Copyright Notice | Copyright Notice | |||

Copyright (c) 2012 IETF Trust and the persons identified as the | Copyright (c) 2012 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 | Provisions Relating to IETF Documents | |||

(http://trustee.ietf.org/license-info) in effect on the date of | (http://trustee.ietf.org/license-info) in effect on the date of | |||

publication of this document. Please review these documents | publication of this document. Please review these documents | |||

carefully, as they describe your rights and restrictions with respect | carefully, as they describe your rights and restrictions with respect | |||

to this document. Code Components extracted from this document must | to this document. Code Components extracted from this document must | |||

include Simplified BSD License text as described in Section 4.e of | include Simplified BSD License text as described in Section 4.e of | |||

skipping to change at page 3, line 7 | skipping to change at page 2, line 22 | |||

modifications of such material outside the IETF Standards Process. | modifications of such material outside the IETF Standards Process. | |||

Without obtaining an adequate license from the person(s) controlling | Without obtaining an adequate license from the person(s) controlling | |||

the copyright in such materials, this document may not be modified | the copyright in such materials, this document may not be modified | |||

outside the IETF Standards Process, and derivative works of it may | outside the IETF Standards Process, and derivative works of it may | |||

not be created outside the IETF Standards Process, except to format | not be created outside the IETF Standards Process, except to format | |||

it for publication as an RFC or to translate it into languages other | it for publication as an RFC or to translate it into languages other | |||

than English. | than English. | |||

Table of Contents | Table of Contents | |||

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5 | 1. Introduction ....................................................4 | |||

1.1. Background and Motivation . . . . . . . . . . . . . . . . 5 | 1.1. Background and Motivation ..................................4 | |||

1.2. Loss Episode Metrics and Bi-Packet Probes . . . . . . . . 6 | 1.1.1. Requirements Language ...............................5 | |||

1.3. Outline and Contents . . . . . . . . . . . . . . . . . . . 7 | 1.2. Loss Episode Metrics and Bi-Packet Probes ..................5 | |||

2. Singleton Definition for Type-P-One-way Bi-Packet Loss . . . . 8 | 1.3. Outline and Contents .......................................6 | |||

2.1. Metric Name . . . . . . . . . . . . . . . . . . . . . . . 8 | 2. Singleton Definition for Type-P-One-way Bi-Packet Loss ..........7 | |||

2.2. Metric Parameters . . . . . . . . . . . . . . . . . . . . 8 | 2.1. Metric Name ................................................7 | |||

2.3. Metric Units . . . . . . . . . . . . . . . . . . . . . . . 8 | 2.2. Metric Parameters ..........................................7 | |||

2.4. Metric Definition . . . . . . . . . . . . . . . . . . . . 8 | 2.3. Metric Units ...............................................7 | |||

2.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . 9 | 2.4. Metric Definition ..........................................7 | |||

2.6. Methodologies . . . . . . . . . . . . . . . . . . . . . . 9 | 2.5. Discussion .................................................8 | |||

2.7. Errors and Uncertainties . . . . . . . . . . . . . . . . . 9 | 2.6. Methodologies ..............................................8 | |||

2.8. Reporting the Metric . . . . . . . . . . . . . . . . . . . 9 | 2.7. Errors and Uncertainties ...................................8 | |||

3. General Definition of samples for | 2.8. Reporting the Metric .......................................8 | |||

Type-P-One-way-Bi-Packet-Loss . . . . . . . . . . . . . . . . 9 | 3. General Definition of Samples for | |||

3.1. Metric Name . . . . . . . . . . . . . . . . . . . . . . . 10 | Type-P-One-way-Bi-Packet-Loss ...................................8 | |||

3.2. Metric Parameters . . . . . . . . . . . . . . . . . . . . 10 | 3.1. Metric Name ................................................9 | |||

3.3. Metric Units . . . . . . . . . . . . . . . . . . . . . . . 10 | 3.2. Metric Parameters ..........................................9 | |||

3.4. Metric Definition . . . . . . . . . . . . . . . . . . . . 10 | 3.3. Metric Units ...............................................9 | |||

3.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . 10 | 3.4. Metric Definition ..........................................9 | |||

3.6. Methodologies . . . . . . . . . . . . . . . . . . . . . . 10 | 3.5. Discussion .................................................9 | |||

3.7. Errors and Uncertainties . . . . . . . . . . . . . . . . . 11 | 3.6. Methodologies .............................................10 | |||

3.8. Reporting the Metric . . . . . . . . . . . . . . . . . . . 11 | 3.7. Errors and Uncertainties ..................................10 | |||

4. An active probing methodology for Bi-Packet Loss . . . . . . . 11 | 3.8. Reporting the Metric ......................................10 | |||

4.1. Metric Name . . . . . . . . . . . . . . . . . . . . . . . 11 | 4. An Active Probing Methodology for Bi-Packet Loss ...............10 | |||

4.2. Metric Parameters . . . . . . . . . . . . . . . . . . . . 11 | 4.1. Metric Name ...............................................10 | |||

4.3. Metric Units . . . . . . . . . . . . . . . . . . . . . . . 12 | 4.2. Metric Parameters .........................................10 | |||

4.4. Metric Definition . . . . . . . . . . . . . . . . . . . . 12 | 4.3. Metric Units ..............................................11 | |||

4.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . 12 | 4.4. Metric Definition .........................................11 | |||

4.6. Methodologies . . . . . . . . . . . . . . . . . . . . . . 12 | 4.5. Discussion ................................................11 | |||

4.7. Errors and Uncertainties . . . . . . . . . . . . . . . . . 13 | 4.6. Methodologies .............................................11 | |||

4.8. Reporting the Metric . . . . . . . . . . . . . . . . . . . 13 | 4.7. Errors and Uncertainties ..................................12 | |||

5. Loss Episode Proto-Metrics . . . . . . . . . . . . . . . . . . 13 | 4.8. Reporting the Metric ......................................12 | |||

5.1. Loss-Pair-Counts . . . . . . . . . . . . . . . . . . . . . 13 | 5. Loss Episode Proto-Metrics .....................................12 | |||

5.2. Bi-Packet-Loss-Ratio . . . . . . . . . . . . . . . . . . . 14 | 5.1. Loss-Pair-Counts ..........................................13 | |||

5.3. Bi-Packet-Loss-Episode-Duration-Number . . . . . . . . . . 14 | 5.2. Bi-Packet-Loss-Ratio ......................................13 | |||

5.4. Bi-Packet-Loss-Episode-Frequency-Number . . . . . . . . . 14 | 5.3. Bi-Packet-Loss-Episode-Duration-Number ....................13 | |||

6. Loss Episode Metrics derived from Bi-Packet Loss Probing . . . 14 | 5.4. Bi-Packet-Loss-Episode-Frequency-Number ...................13 | |||

6.1. Geometric Stream: Loss Ratio . . . . . . . . . . . . . . . 15 | 6. Loss Episode Metrics Derived from Bi-Packet Loss Probing .......14 | |||

6.1.1. Metric Name . . . . . . . . . . . . . . . . . . . . . 15 | 6.1. Geometric Stream: Loss Ratio ..............................14 | |||

6.1.2. Metric Parameters . . . . . . . . . . . . . . . . . . 15 | 6.1.1. Metric Name ........................................14 | |||

6.1.3. Metric Units . . . . . . . . . . . . . . . . . . . . . 16 | 6.1.2. Metric Parameters ..................................14 | |||

6.1.4. Metric Definition . . . . . . . . . . . . . . . . . . 16 | 6.1.3. Metric Units .......................................15 | |||

6.1.5. Discussion . . . . . . . . . . . . . . . . . . . . . . 16 | 6.1.4. Metric Definition ..................................15 | |||

6.1.6. Methodologies . . . . . . . . . . . . . . . . . . . . 16 | 6.1.5. Discussion .........................................15 | |||

6.1.7. Errors and Uncertainties . . . . . . . . . . . . . . . 16 | 6.1.6. Methodologies ......................................15 | |||

6.1.8. Reporting the Metric . . . . . . . . . . . . . . . . . 16 | 6.1.7. Errors and Uncertainties ...........................15 | |||

6.2. Geometric Stream: Loss Episode Duration . . . . . . . . . 16 | 6.1.8. Reporting the Metric ...............................15 | |||

6.2.1. Metric Name . . . . . . . . . . . . . . . . . . . . . 16 | 6.2. Geometric Stream: Loss Episode Duration ...................16 | |||

6.2.2. Metric Parameters . . . . . . . . . . . . . . . . . . 16 | 6.2.1. Metric Name ........................................16 | |||

6.2.3. Metric Units . . . . . . . . . . . . . . . . . . . . . 17 | 6.2.2. Metric Parameters ..................................16 | |||

6.2.4. Metric Definition . . . . . . . . . . . . . . . . . . 17 | 6.2.3. Metric Units .......................................16 | |||

6.2.5. Discussion . . . . . . . . . . . . . . . . . . . . . . 17 | 6.2.4. Metric Definition ..................................16 | |||

6.2.6. Methodologies . . . . . . . . . . . . . . . . . . . . 17 | 6.2.5. Discussion .........................................16 | |||

6.2.7. Errors and Uncertainties . . . . . . . . . . . . . . . 17 | 6.2.6. Methodologies ......................................16 | |||

6.2.8. Reporting the Metric . . . . . . . . . . . . . . . . . 18 | 6.2.7. Errors and Uncertainties ...........................17 | |||

6.3. Geometric Stream: Loss Episode Frequency . . . . . . . . . 18 | 6.2.8. Reporting the Metric ...............................17 | |||

6.3.1. Metric Name . . . . . . . . . . . . . . . . . . . . . 18 | 6.3. Geometric Stream: Loss Episode Frequency ..................17 | |||

6.3.2. Metric Parameters . . . . . . . . . . . . . . . . . . 18 | 6.3.1. Metric Name ........................................17 | |||

6.3.3. Metric Units . . . . . . . . . . . . . . . . . . . . . 18 | 6.3.2. Metric Parameters ..................................17 | |||

6.3.4. Metric Definition . . . . . . . . . . . . . . . . . . 18 | 6.3.3. Metric Units .......................................17 | |||

6.3.5. Discussion . . . . . . . . . . . . . . . . . . . . . . 19 | 6.3.4. Metric Definition ..................................18 | |||

6.3.6. Methodologies . . . . . . . . . . . . . . . . . . . . 19 | 6.3.5. Discussion .........................................18 | |||

6.3.7. Errors and Uncertainties . . . . . . . . . . . . . . . 19 | 6.3.6. Methodologies ......................................18 | |||

6.3.8. Reporting the Metric . . . . . . . . . . . . . . . . . 19 | 6.3.7. Errors and Uncertainties ...........................18 | |||

7. Applicability of Loss Episode Metrics . . . . . . . . . . . . 19 | 6.3.8. Reporting the Metric ...............................18 | |||

7.1. Relation to Gilbert Model . . . . . . . . . . . . . . . . 19 | 7. Applicability of Loss Episode Metrics ..........................18 | |||

8. IPR Considerations . . . . . . . . . . . . . . . . . . . . . . 20 | 7.1. Relation to Gilbert Model .................................18 | |||

9. Security Considerations . . . . . . . . . . . . . . . . . . . 20 | 8. Security Considerations ........................................19 | |||

10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 21 | 9. References .....................................................20 | |||

11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 21 | 9.1. Normative References ......................................20 | |||

12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 21 | 9.2. Informative References ....................................20 | |||

12.1. Normative References . . . . . . . . . . . . . . . . . . . 21 | ||||

12.2. Informative References . . . . . . . . . . . . . . . . . . 21 | ||||

Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 22 | ||||

1. Introduction | 1. Introduction | |||

1.1. Background and Motivation | 1.1. Background and Motivation | |||

Packet loss in the Internet is a complex phenomenon due to the bursty | Packet loss in the Internet is a complex phenomenon due to the bursty | |||

nature of traffic and congestion processes, influenced by both end- | nature of traffic and congestion processes, influenced by both end- | |||

users and applications, and the operation of transport protocols such | users and applications and the operation of transport protocols such | |||

as TCP. For these reasons, the simplest model of packet loss--the | as TCP. For these reasons, the simplest model of packet loss -- the | |||

single parameter Bernoulli (independent) loss model--does not | single parameter Bernoulli (independent) loss model -- does not | |||

represent the complexity of packet loss over periods of time. | represent the complexity of packet loss over periods of time. | |||

Correspondingly, a single loss metric--the average packet loss ratio | Correspondingly, a single loss metric -- the average packet loss | |||

over some period of time--arising, e.g., from a stream of Poisson | ratio over some period of time -- arising, e.g., from a stream of | |||

probes as in [RFC2680] is not sufficient to determine the effect of | Poisson probes as in [RFC2680] is not sufficient to determine the | |||

packet loss on traffic in general. | effect of packet loss on traffic in general. | |||

Moving beyond single parameter loss models, Markovian and Markov- | Moving beyond single parameter loss models, Markovian and Markov- | |||

modulated loss models involving transitions between a good and bad | modulated loss models involving transitions between a good and bad | |||

state, each with an associated loss rate, have been proposed by | state, each with an associated loss rate, have been proposed by | |||

Gilbert [Gilbert] and more generally by Elliot [Elliot]. In | Gilbert [Gilbert] and more generally by Elliot [Elliot]. In | |||

principle, Markovian models can be formulated over state spaces | principle, Markovian models can be formulated over state spaces | |||

involving patterns of loss of any desired number of packets. However | involving patterns of loss of any desired number of packets. | |||

further increase in the size of the state space makes such models | However, further increase in the size of the state space makes such | |||

cumbersome both for parameter estimation (accuracy decreases) and | models cumbersome both for parameter estimation (accuracy decreases) | |||

prediction in practice (due to computational complexity and | and prediction in practice (due to computational complexity and | |||

sensitivity to parameter inaccuracy). In general, the relevance and | sensitivity to parameter inaccuracy). In general, the relevance and | |||

importance of particular models can change in time, e.g. in response | importance of particular models can change in time, e.g., in response | |||

to the advent of new applications and services. For this reason we | to the advent of new applications and services. For this reason, we | |||

are drawn to empirical metrics that do not depend on a particular | are drawn to empirical metrics that do not depend on a particular | |||

model for their interpretation. | model for their interpretation. | |||

An empirical measure of packet loss complexity, the index of | An empirical measure of packet loss complexity, the index of | |||

dispersion of counts (IDC), comprise, for each t >0, the ratio v(t) / | dispersion of counts (IDC), comprise, for each t >0, the ratio v(t) / | |||

a(t) of the variance v(t) and average a(t) of the number of losses | a(t) of the variance v(t) and average a(t) of the number of losses | |||

over successive measurement windows of a duration t. However, a full | over successive measurement windows of a duration t. However, a full | |||

characterization of packet loss over time requires specification of | characterization of packet loss over time requires specification of | |||

the IDC for each window size t>0. | the IDC for each window size t>0. | |||

In the standards arena, loss pattern sample metrics are defined in | In the standards arena, loss pattern sample metrics are defined in | |||

[RFC3357]. Following the Gilbert-Elliot model, burst metrics | [RFC3357]. Following the Gilbert-Elliot model, burst metrics | |||

specific for VoIP that characterize complete episodes of lost, | specific for Voice over IP (VoIP) that characterize complete episodes | |||

transmitted and discarded packets are defined in [RFC3611] | of lost, transmitted, and discarded packets are defined in [RFC3611]. | |||

All these considerations motivate formulating empirical metrics of | The above considerations motivate the formulation of empirical | |||

one-way packet loss that provide the simplest generalization of the | metrics of one-way packet loss that provide the simplest | |||

successful [RFC2680] that can capture deviations from independent | generalization of [RFC2680] (which is widely adopted but only defines | |||

packet loss in a robust model-independent manner, and, to define | a single loss-to-total ratio metric). The metrics defined here | |||

efficient measurement methodologies for these metrics. | capture deviations from independent packet loss in a robust model- | |||

independent manner. The document also defines efficient measurement | ||||

methodologies for these metrics. | ||||

1.1.1. Requirements Language | ||||

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", | ||||

"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this | ||||

document are to be interpreted as described in RFC 2119 [RFC2119]. | ||||

1.2. Loss Episode Metrics and Bi-Packet Probes | 1.2. Loss Episode Metrics and Bi-Packet Probes | |||

The losses experienced by the packet stream can be viewed as | The losses experienced by the packet stream can be viewed as | |||

occurring in loss episodes, i.e., maximal set of consecutively lost | occurring in loss episodes, i.e., a maximal set of consecutively lost | |||

packets. This memo describes one-way loss episode metrics: their | packets. This memo describes one-way loss episode metrics: their | |||

frequency and average duration. Although the average loss ratio can | frequency and average duration. Although the average loss ratio can | |||

be expressed in terms of these quantities, they go further in | be expressed in terms of these quantities, they go further in | |||

characterizing the statistics of the patterns of packet loss within | characterizing the statistics of the patterns of packet loss within | |||

the stream of probes. This is useful information in understanding | the stream of probes. This is useful information in understanding | |||

the effect of packet losses on application performance, since | the effect of packet losses on application performance, since | |||

different applications can have different sensitivities to patterns | different applications can have different sensitivities to patterns | |||

of loss, being sensitive not only to the long term average loss rate, | of loss, being sensitive not only to the long-term average loss rate, | |||

but how losses are distributed in time. As an example: MPEG video | but how losses are distributed in time. As an example, MPEG video | |||

traffic may be sensitive to loss involving the I-frame in a group of | traffic may be sensitive to loss involving the I-frame in a group of | |||

pictures, but further losses within an episode of sufficiently short | pictures, but further losses within an episode of sufficiently short | |||

duration have no further impact; the damage is already done. | duration have no further impact; the damage is already done. | |||

The loss episode metrics presented here have the following useful | The loss episode metrics presented here have the following useful | |||

properties: | properties: | |||

1. the metrics are empirical and do not depend on an underlying | 1. the metrics are empirical and do not depend on an underlying | |||

model; e.g., the loss process is not assumed to be Markovian. On | model; e.g., the loss process is not assumed to be Markovian. On | |||

the other hand, it turns out that the metrics of this memo can be | the other hand, it turns out that the metrics of this memo can be | |||

skipping to change at page 6, line 39 | skipping to change at page 5, line 48 | |||

Section 7. | Section 7. | |||

2. the metric units can be directly compared with applications or | 2. the metric units can be directly compared with applications or | |||

user requirements or tolerance for network loss performance, in | user requirements or tolerance for network loss performance, in | |||

the frequency and duration of loss episodes, as well as the usual | the frequency and duration of loss episodes, as well as the usual | |||

packet loss ratio, which can be recovered from the loss episode | packet loss ratio, which can be recovered from the loss episode | |||

metrics upon dividing the average loss episode duration by the | metrics upon dividing the average loss episode duration by the | |||

loss episode frequency. | loss episode frequency. | |||

3. the metrics provide the smallest possible increment in complexity | 3. the metrics provide the smallest possible increment in complexity | |||

beyond, but in the spirit of, the IPPM average packet loss ratio | beyond, but in the spirit of, the IP Performance Metrics (IPPM) | |||

metrics [RFC2680] i.e., moving from a single metric (average | average packet loss ratio metrics [RFC2680], i.e., moving from a | |||

packet loss ratio) to a pair of metrics (loss episode frequency | single metric (average packet loss ratio) to a pair of metrics | |||

and average loss episode duration). | (loss episode frequency and average loss episode duration). | |||

The document also describes a probing methodology under which loss | The document also describes a probing methodology under which loss | |||

episode metrics are to be measured. The methodology comprises | episode metrics are to be measured. The methodology comprises | |||

sending probe packets in pairs, where packets within each probe pair | sending probe packets in pairs, where packets within each probe pair | |||

have a fixed separation, and the time between pairs takes the form of | have a fixed separation, and the time between pairs takes the form of | |||

a geometric distributed number multiplied by the same separation. | a geometric distributed number multiplied by the same separation. | |||

This can be regarded a generalization of Poisson probing where the | This can be regarded a generalization of Poisson probing where the | |||

probes are pairs rather than single packets as in [RFC2680], and also | probes are pairs rather than single packets as in [RFC2680], and also | |||

of geometric probing described in [RFC2330]. However, it should be | of geometric probing described in [RFC2330]. However, it should be | |||

distinguished from back to back packet pairs whose change in | distinguished from back-to-back packet pairs whose change in | |||

separation on traversing a link is used to probe bandwidth. In this | separation on traversing a link is used to probe bandwidth. In this | |||

document, the separation between the packets in a pair is the | document, the separation between the packets in a pair is the | |||

temporal resolution at which different loss episodes are to be | temporal resolution at which different loss episodes are to be | |||

distinguished. The methodology does not measure episodes of loss of | distinguished. The methodology does not measure episodes of loss of | |||

consecutive background packets on the measured path. One key feature | consecutive background packets on the measured path. One key feature | |||

of this methodology is its efficiency: it estimates the average | of this methodology is its efficiency: it estimates the average | |||

length of loss episodes without directly measuring the complete | length of loss episodes without directly measuring the complete | |||

episodes themselves. Instead, this information is encoded in the | episodes themselves. Instead, this information is encoded in the | |||

observed relative frequencies of the 4 possible outcomes arising from | observed relative frequencies of the four possible outcomes arising | |||

the loss or successful transmission of each of the two packets of the | from the loss or successful transmission of each of the two packets | |||

probe pairs. This is distinct from the approach of [RFC3611] that | of the probe pairs. This is distinct from the approach of [RFC3611], | |||

reports on directly measured episodes. | which reports on directly measured episodes. | |||

The metrics defined in this memo are "derived metrics", according to | The metrics defined in this memo are "derived metrics", according to | |||

Section 6.1 of [RFC2330] the IPPM framework. They are based on the | Section 6.1 of [RFC2330] (the IPPM framework). They are based on the | |||

singleton loss metric defined in Section 2 of [RFC2680] . | singleton loss metric defined in Section 2 of [RFC2680] . | |||

1.3. Outline and Contents | 1.3. Outline and Contents | |||

o Section 2 defines the fundamental singleton metric for the | o Section 2 defines the fundamental singleton metric for the | |||

possible outcomes of a probe pair: Type-P-One-way-Bi-Packet-Loss. | possible outcomes of a probe pair: Type-P-One-way-Bi-Packet-Loss. | |||

o Section 3 defines sample sets of this metric derived from a | o Section 3 defines sample sets of this metric derived from a | |||

general probe stream: Type-P-One-way-Bi-Packet-Loss-Stream. | general probe stream: Type-P-One-way-Bi-Packet-Loss-Stream. | |||

o Section 4 defines the prime example of the Bi-Packet-Loss-Stream | o Section 4 defines the prime example of the Bi-Packet-Loss-Stream | |||

metrics, specifically Type-P-One-way-Bi-Packet-Loss-Geometric- | metrics, specifically Type-P-One-way-Bi-Packet-Loss-Geometric- | |||

Stream arising from the geometric stream of packet-pair probes | Stream arising from the geometric stream of packet-pair probes | |||

that was described informally in Section 1. | that was described informally in Section 1. | |||

o Section 5 defines Loss episode proto-metrics that summarize the | o Section 5 defines loss episode proto-metrics that summarize the | |||

outcomes from a stream metrics as an intermediate step to forming | outcomes from a stream metrics as an intermediate step to forming | |||

the loss episode metrics; they need not be reported in general. | the loss episode metrics; they need not be reported in general. | |||

o Section 6 defines the final loss episode metrics that are the | o Section 6 defines the final loss episode metrics that are the | |||

focus of this memo, the new metrics | focus of this memo, the new metrics: | |||

* Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode- | * Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode- | |||

Duration, the average duration, in seconds, of a loss episode | Duration, the average duration, in seconds, of a loss episode. | |||

* Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode- | * Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode- | |||

Frequency, the average frequency, per second, at which loss | Frequency, the average frequency, per second, at which loss | |||

episodes start. | episodes start. | |||

* Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Ratio, which is | * Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Ratio, which is | |||

the average packet loss ratio metric arising from the geometric | the average packet loss ratio metric arising from the geometric | |||

stream probing methodology | stream probing methodology | |||

o Section 7 details applications and relations to existing loss | o Section 7 details applications and relations to existing loss | |||

skipping to change at page 8, line 25 | skipping to change at page 7, line 33 | |||

o Src, the IP address of a source host | o Src, the IP address of a source host | |||

o Dst, the IP address of a destination host | o Dst, the IP address of a destination host | |||

o T1, a sending time of the first packet | o T1, a sending time of the first packet | |||

o T2, a sending time of the second packet, with T2>T1 | o T2, a sending time of the second packet, with T2>T1 | |||

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

from the stream selected for the metric. | from the stream selected for the metric | |||

o P, the specification of the packet type, over and above the source | o P, the specification of the packet type, over and above the source | |||

and destination addresses | and destination addresses | |||

2.3. Metric Units | 2.3. Metric Units | |||

A Loss Pair is pair (l1, l2) where each of l1 and l2 is a binary | A Loss Pair is pair (l1, l2) where each of l1 and l2 is a binary | |||

value 0 or 1, where 0 signifies successful transmission of a packet | value 0 or 1, where 0 signifies successful transmission of a packet | |||

and 1 signifies loss. | and 1 signifies loss. | |||

The metric unit of Type-P-One-way-Bi-Packet-Loss is a Loss Pair. | The metric unit of Type-P-One-way-Bi-Packet-Loss is a Loss Pair. | |||

2.4. Metric Definition | 2.4. Metric Definition | |||

1. "The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | 1. "The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | |||

T2, F, P) is (1,1)" means that Src sent the first bit of a Type-P | T2, F, P) is (1,1)" means that Src sent the first bit of a Type-P | |||

packet to Dst at wire-time T1 and the first bit of a Type-P | packet to Dst at wire-time T1 and the first bit of a Type-P | |||

packet to Dst at wire-time T2>T1, and that neither packet was | packet to Dst at wire-time T2>T1 and that neither packet was | |||

received at Dst. | received at Dst. | |||

2. The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | 2. "The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | |||

T2, F, P) is (1,0)" means that Src sent the first bit of a Type-P | T2, F, P) is (1,0)" means that Src sent the first bit of a Type-P | |||

packet to Dst at wire-time T1 and the first bit of a Type-P | packet to Dst at wire-time T1 and the first bit of a Type-P | |||

packet to Dst at wire-time T2>T1, and that the first packet was | packet to Dst at wire-time T2>T1 and that the first packet was | |||

not received at Dst, and the second packet was received at Dst | not received at Dst, and the second packet was received at Dst | |||

3. The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | 3. "The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | |||

T2, F, P) is (0,1)" means that Src sent the first bit of a Type-P | T2, F, P) is (0,1)" means that Src sent the first bit of a Type-P | |||

packet to Dst at wire-time T1 and the first bit of a Type-P | packet to Dst at wire-time T1 and the first bit of a Type-P | |||

packet to Dst at wire-time T2>T1, and that the first packet was | packet to Dst at wire-time T2>T1 and that the first packet was | |||

received at Dst, and the second packet was not received at Dst | received at Dst, and the second packet was not received at Dst | |||

4. The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | 4. "The Type-P-One-way-Bi-Packet-Loss with parameters (Src, Dst, T1, | |||

T2, F, P) is (0,0)" means that Src sent the first bit of a Type-P | T2, F, P) is (0,0)" means that Src sent the first bit of a Type-P | |||

packet to Dst at wire-time T1 and the first bit of a Type-P | packet to Dst at wire-time T1 and the first bit of a Type-P | |||

packet to Dst at wire-time T2>T1, and that both packets were | packet to Dst at wire-time T2>T1 and that both packets were | |||

received at Dst. | received at Dst. | |||

2.5. Discussion | 2.5. Discussion | |||

The purpose of the selection function is to specify exactly which | The purpose of the selection function is to specify exactly which | |||

packets are to be used for measurement. The notion is taken from | packets are to be used for measurement. The notion is taken from | |||

Section 2.5 of [RFC3393], where examples are discussed. | Section 2.5 of [RFC3393], where examples are discussed. | |||

2.6. Methodologies | 2.6. Methodologies | |||

skipping to change at page 9, line 40 | skipping to change at page 8, line 46 | |||

2.7. Errors and Uncertainties | 2.7. Errors and Uncertainties | |||

Sources of error for the Type-P-One-way-Packet-Loss metric in Section | Sources of error for the Type-P-One-way-Packet-Loss metric in Section | |||

2.7 of [RFC2680] apply to each packet of the pair for the Type-P-One- | 2.7 of [RFC2680] apply to each packet of the pair for the Type-P-One- | |||

way-Bi-Packet-Loss metric. | way-Bi-Packet-Loss metric. | |||

2.8. Reporting the Metric | 2.8. Reporting the Metric | |||

Refer to Section 2.8 of [RFC2680]. | Refer to Section 2.8 of [RFC2680]. | |||

3. General Definition of samples for Type-P-One-way-Bi-Packet-Loss | 3. General Definition of Samples for Type-P-One-way-Bi-Packet-Loss | |||

Given the singleton metric for Type-P-One-way-Bi-Packet-Loss, we now | Given the singleton metric for Type-P-One-way-Bi-Packet-Loss, we now | |||

define examples of samples of singletons. The basic idea is as | define examples of samples of singletons. The basic idea is as | |||

follows. We first specify a set of times T1 < T2 <...<Tn, each of | follows. We first specify a set of times T1 < T2 <...<Tn, each of | |||

which acts as the first time of a packet pair for a single Type-P- | which acts as the first time of a packet pair for a single Type-P- | |||

One-way-Bi-Packet-Loss measurement. This results is a set of n | One-way-Bi-Packet-Loss measurement. This results is a set of n | |||

metric values of Type-P-One-way-Bi-Packet-Loss. | metric values of Type-P-One-way-Bi-Packet-Loss. | |||

3.1. Metric Name | 3.1. Metric Name | |||

skipping to change at page 10, line 20 | skipping to change at page 9, line 23 | |||

o Src, the IP address of a source host | o Src, the IP address of a source host | |||

o Dst, the IP address of a destination host | o Dst, the IP address of a destination host | |||

o (T11,T12), (T21,T22)....,(Tn1,Tn2) a set of n times of sending | o (T11,T12), (T21,T22)....,(Tn1,Tn2) a set of n times of sending | |||

times for packet pairs, with T11 < T12 <= T21 < T22 <=...<= Tn1 < | times for packet pairs, with T11 < T12 <= T21 < T22 <=...<= Tn1 < | |||

Tn2 | Tn2 | |||

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

from the stream selected for the metric. | from the stream selected for the metric | |||

o P, the specification of the packet type, over and above the source | o P, the specification of the packet type, over and above the source | |||

and destination address | and destination address | |||

3.3. Metric Units | 3.3. Metric Units | |||

A set L1,L2,...,Ln of loss pairs | A set L1,L2,...,Ln of Loss Pairs | |||

3.4. Metric Definition | 3.4. Metric Definition | |||

Each loss pair Li for i-1,....n is the Type-P-One-way-Bi-Packet-Loss | Each Loss Pair Li for i = 1,....n is the Type-P-One-way-Bi-Packet- | |||

with parameters (Src, Dst, Ti1, Ti2, Fi, P) where Fi is the | Loss with parameters (Src, Dst, Ti1, Ti2, Fi, P) where Fi is the | |||

restriction of the selection function F to the packet pair at time | restriction of the selection function F to the packet pair at time | |||

Ti1, Ti2. | Ti1, Ti2. | |||

3.5. Discussion | 3.5. Discussion | |||

The metric definition of Type-P-One-way-Bi-Packet-Loss-Stream is | The metric definition of Type-P-One-way-Bi-Packet-Loss-Stream is | |||

sufficiently general to describe the case where packets are sampled | sufficiently general to describe the case where packets are sampled | |||

from a pre-existing stream. This is useful in the case that there is | from a preexisting stream. This is useful in the case in which there | |||

a general purpose measurement stream setup between two hosts, and we | is a general purpose measurement stream set up between two hosts, and | |||

wish to select a substream from it for the purposes of loss episode | we wish to select a substream from it for the purposes of loss | |||

measurement. Packet pairs selected as bi-packet loss probes need not | episode measurement. Packet pairs selected as bi-packet loss probes | |||

be consecutive within such a stream. In the next section we | need not be consecutive within such a stream. In the next section, | |||

specialize this somewhat to more concretely describe a purpose built | we specialize this somewhat to more concretely describe a purpose | |||

packet stream for loss episode measurement. | built packet stream for loss episode measurement. | |||

3.6. Methodologies | 3.6. Methodologies | |||

The methodologies related to the Type-P-One-way-Packet-Loss metric in | The methodologies related to the Type-P-One-way-Packet-Loss metric in | |||

Section 2.6 of [RFC2680] are similar for the Type-P-One-way-Bi- | Section 2.6 of [RFC2680] are similar for the Type-P-One-way-Bi- | |||

Packet-Loss-Stream metric described above. In particular, the | Packet-Loss-Stream metric described above. In particular, the | |||

methodologies described in RFC 2680 apply to both packets of each | methodologies described in RFC 2680 apply to both packets of each | |||

pair. | pair. | |||

3.7. Errors and Uncertainties | 3.7. Errors and Uncertainties | |||

Sources of error for the Type-P-One-way-Packet-Loss metric in Section | Sources of error for the Type-P-One-way-Packet-Loss metric in Section | |||

2.7 of [RFC2680] apply to each packet of each pair for the Type-P- | 2.7 of [RFC2680] apply to each packet of each pair for the Type-P- | |||

One-way-Bi-Packet-Loss-Stream metric. | One-way-Bi-Packet-Loss-Stream metric. | |||

3.8. Reporting the Metric | 3.8. Reporting the Metric | |||

Refer to Section 2.8 of [RFC2680]. | Refer to Section 2.8 of [RFC2680]. | |||

4. An active probing methodology for Bi-Packet Loss | 4. An Active Probing Methodology for Bi-Packet Loss | |||

This section specializes the preceding section for an active probing | This section specializes the preceding section for an active probing | |||

methodology. The basic idea is a follows. We set up a sequence of | methodology. The basic idea is a follows. We set up a sequence of | |||

evenly spaced times T1 < T2 < ... < Tn. Each time Ti is potentially | evenly spaced times T1 < T2 < ... < Tn. Each time Ti is potentially | |||

the first packet time for a packet pair measurement. We make an | the first packet time for a packet pair measurement. We make an | |||

independent random decision at each time, whether to initiate such a | independent random decision at each time, whether to initiate such a | |||

measurement. Hence the interval count between successive times at | measurement. Hence, the interval count between successive times at | |||

which a pair is initiated follows a geometric distribution. We also | which a pair is initiated follows a geometric distribution. We also | |||

specify that the spacing between successive times Ti is the same as | specify that the spacing between successive times Ti is the same as | |||

the spacing between packets in a given pair. Thus if pairs happen to | the spacing between packets in a given pair. Thus, if pairs happen | |||

be launched at the successive times Ti T(i+1), the second packet of | to be launched at the successive times Ti and T(i+1), the second | |||

the first pair is actually used as the first packet of the second | packet of the first pair is actually used as the first packet of the | |||

pair. | second pair. | |||

4.1. Metric Name | 4.1. Metric Name | |||

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream | Type-P-One-way-Bi-Packet-Loss-Geometric-Stream | |||

4.2. Metric Parameters | 4.2. Metric Parameters | |||

o Src, the IP address of a source host | o Src, the IP address of a source host | |||

o Dst, the IP address of a destination host | o Dst, the IP address of a destination host | |||

o T0, the randomly selected starting time [RFC3432] for periodic | o T0, the randomly selected starting time [RFC3432] for periodic | |||

launch opportunities | launch opportunities | |||

o d, the time spacing between potential launch times, Ti and Ti+1 | o d, the time spacing between potential launch times, Ti and T(i+1) | |||

o n, a count of potential measurement instants | o n, a count of potential measurement instants | |||

o q, a launch probability | o q, a launch probability | |||

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

from the stream selected for the metric. | from the stream selected for the metric | |||

o P, the specification of the packet type, over and above the source | o P, the specification of the packet type, over and above the source | |||

and destination address | and destination address | |||

4.3. Metric Units | 4.3. Metric Units | |||

A set of Loss Pairs L1, L2, ..., Lm for some m <= n | A set of Loss Pairs L1, L2, ..., Lm for some m <= n | |||

4.4. Metric Definition | 4.4. Metric Definition | |||

for each i = 0, 1, ..., n-1 we form the potential measurement time Ti | For each i = 0, 1, ..., n-1 we form the potential measurement time Ti | |||

= T + i * d. With probability q, a packet pair measurement is | = T0 + i*d. With probability q, a packet pair measurement is | |||

launched at Ti, resulting in a Type-P-One-way-Bi-Packet-Loss with | launched at Ti, resulting in a Type-P-One-way-Bi-Packet-Loss with | |||

parameters (Src, Dst, Ti, Ti+1, Fi, P) where Fi is the restriction of | parameters (Src, Dst, Ti, T(i+1), Fi, P) where Fi is the restriction | |||

the selection function F to the packet pair at times Ti, Ti+1. L1, | of the selection function F to the packet pair at times Ti, T(i+1). | |||

L2,...Lm are the resulting Loss Pairs; m can be less than n since not | L1, L2,...Lm are the resulting Loss Pairs; m can be less than n since | |||

all time Ti have an associated measurement. | not all times Ti have an associated measurement. | |||

4.5. Discussion | 4.5. Discussion | |||

The above definition of Type-P-One-way-Bi-Packet-Loss-Geometric- | The above definition of Type-P-One-way-Bi-Packet-Loss-Geometric- | |||

Stream is equivalent to using Type-P-One-way-Bi-Packet-Loss-Stream | Stream is equivalent to using Type-P-One-way-Bi-Packet-Loss-Stream | |||

with an appropriate statistical definition of the selection function | with an appropriate statistical definition of the selection function | |||

F. | F. | |||

The number m of loss pairs in the metric can be less than the number | The number m of Loss Pairs in the metric can be less than the number | |||

of potential measurement instants because not all instants may | of potential measurement instants because not all instants may | |||

generate a probe when the launch probability q is strictly less than | generate a probe when the launch probability q is strictly less than | |||

1. | 1. | |||

4.6. Methodologies | 4.6. Methodologies | |||

The methodologies follow from: | The methodologies follow from: | |||

o the specific time T0, from which all successive Ti follow, and | o the specific time T0, from which all successive Ti follow, and | |||

skipping to change at page 13, line 21 | skipping to change at page 12, line 27 | |||

Loss metric, a key source of error when emitting packets for Bi- | Loss metric, a key source of error when emitting packets for Bi- | |||

Packet Loss relates to resource limits on the host used to send the | Packet Loss relates to resource limits on the host used to send the | |||

packets. In particular, the choice of T0, the choice of the time | packets. In particular, the choice of T0, the choice of the time | |||

spacing, and the choice of the launch probability results in a | spacing, and the choice of the launch probability results in a | |||

schedule for sending packets. Insufficient CPU resources on the | schedule for sending packets. Insufficient CPU resources on the | |||

sending host may result in an inability to send packets according to | sending host may result in an inability to send packets according to | |||

schedule. Note that the choice of time spacing directly affects the | schedule. Note that the choice of time spacing directly affects the | |||

ability of the host CPU to meet the required schedule (e.g., consider | ability of the host CPU to meet the required schedule (e.g., consider | |||

a 100 microsecond spacing versus a 100 millisecond spacing). | a 100 microsecond spacing versus a 100 millisecond spacing). | |||

For other considerations, refer to Section 3.7. [RFC2680]. | For other considerations, refer to Section 3.7 of [RFC2680]. | |||

4.8. Reporting the Metric | 4.8. Reporting the Metric | |||

Refer to Section 3.8. of [RFC2680]. | Refer to Section 3.8. of [RFC2680]. | |||

5. Loss Episode Proto-Metrics | 5. Loss Episode Proto-Metrics | |||

This section describes four generic proto-metric quantities | This section describes four generic proto-metric quantities | |||

associated with an arbitrary set of loss pairs. These are the Loss- | associated with an arbitrary set of Loss Pairs. These are the Loss- | |||

Pair-Counts, Bi-Packet-Loss-Ratio, Bi-Packet-Loss-Episode-Duration- | Pair-Counts, Bi-Packet-Loss-Ratio, Bi-Packet-Loss-Episode-Duration- | |||

Number, Bi-Packet-Loss-Episode-Frequency-Number. Specific loss | Number, Bi-Packet-Loss-Episode-Frequency-Number. Specific loss | |||

episode metrics can then be constructed when these proto metrics take | episode metrics can then be constructed when these proto-metrics | |||

as their input, sets of loss pairs samples generated by the Type-P- | take, as their input, sets of Loss Pairs samples generated by the | |||

One-way-Bi-Packet-Loss-Stream and Type-P-One-way-Bi-Packet-Loss- | Type-P-One-way-Bi-Packet-Loss-Stream and Type-P-One-way-Bi-Packet- | |||

Geometric Stream. The second of these is described in Section 4. It | Loss-Geometric-Stream. The second of these is described in | |||

is not expected that these proto-metrics would be reported | Section 4. It is not expected that these proto-metrics would be | |||

themselves. Rather they are intermediate quantities in the | reported themselves. Rather, they are intermediate quantities in the | |||

production of the final metrics of Section 6 below, and could be | production of the final metrics of Section 6 below, and could be | |||

rolled up into them in implementations. The metrics report loss | rolled up into metrics in implementations. The metrics report loss | |||

episode durations and frequencies in terms of packet counts, since | episode durations and frequencies in terms of packet counts, since | |||

they do not depend on the actual time between probe packets. The | they do not depend on the actual time between probe packets. The | |||

final metrics of Section 6 incorporate timescales and yield durations | final metrics of Section 6 incorporate timescales and yield durations | |||

in seconds, and frequencies as per second. | in seconds and frequencies as per second. | |||

5.1. Loss-Pair-Counts | 5.1. Loss-Pair-Counts | |||

Loss-Pair-Counts are the absolute frequencies of the 4 types of loss | Loss-Pair-Counts are the absolute frequencies of the four types of | |||

pair outcome in a sample. More precisely, the Loss-Pair-Counts | Loss Pair outcome in a sample. More precisely, the Loss-Pair-Counts | |||

associated with a set of loss pairs L1,,,,Ln are the numbers N(i,j) | associated with a set of Loss Pairs L1,,,,Ln are the numbers N(i,j) | |||

of such loss pairs that take each possible value (i,j) in the set ( | of such Loss Pairs that take each possible value (i,j) in the set ( | |||

(0,0), (0,1), (1,0), (1,1)). | (0,0), (0,1), (1,0), (1,1)). | |||

5.2. Bi-Packet-Loss-Ratio | 5.2. Bi-Packet-Loss-Ratio | |||

The Bi-Packet-loss-ratio associated with a set of n loss pairs | The Bi-Packet-Loss-Ratio associated with a set of n Loss Pairs | |||

L1,,,,Ln is defined in terms of their Loss-Pair-Counts by the | L1,,,,Ln is defined in terms of their Loss-Pair-Counts by the | |||

quantity (N(1,0) +N(1,1))/n. | quantity (N(1,0) + N(1,1))/n. | |||

Note this is formally equivalent to the loss metric Type-P-One-way- | Note this is formally equivalent to the loss metric Type-P-One-way- | |||

Packet-Loss-Average from[RFC2680] since it averages single packet | Packet-Loss-Average from [RFC2680], since it averages single packet | |||

losses. | losses. | |||

5.3. Bi-Packet-Loss-Episode-Duration-Number | 5.3. Bi-Packet-Loss-Episode-Duration-Number | |||

The Bi-Packet-Loss-Episode-Duration-Number associated with a set of n | The Bi-Packet-Loss-Episode-Duration-Number associated with a set of n | |||

loss pairs L1,,,,Ln is defined in terms of their Loss-Pair-Counts in | Loss Pairs L1,,,,Ln is defined in terms of their Loss-Pair-Counts in | |||

the following cases: | the following cases: | |||

o 2*(N(0,1) + N(1,0) + N(1,1)/ (N(0,1)+N(1,0)) - 1 if N(0,1) + | o (2*N(1,1) + N(0,1) + N(1,0)) / (N(0,1) + N(1,0)) if N(0,1) + | |||

N(1,0) >1 | N(1,0) > 0 | |||

o 0 if N(0,1) + N(1,0) + N(1,1) = 0 (no probe packets lost) | o 0 if N(0,1) + N(1,0) + N(1,1) = 0 (no probe packets lost) | |||

o Undefined if N(0,1) + N(1,0) + N(0,0) = 0 (all probe packets lost) | o Undefined if N(0,1) + N(1,0) + N(0,0) = 0 (all probe packets lost) | |||

Note N(0,1) + N(1,0) is zero if there are no transitions between loss | Note N(0,1) + N(1,0) is zero if there are no transitions between loss | |||

and no-loss outcomes. | and no-loss outcomes. | |||

5.4. Bi-Packet-Loss-Episode-Frequency-Number | 5.4. Bi-Packet-Loss-Episode-Frequency-Number | |||

The Bi-Packet-Loss-Episode-Frequency-Number associated with a set of | The Bi-Packet-Loss-Episode-Frequency-Number associated with a set of | |||

n loss pairs L1,,,,Ln is defined in terms of their Loss-Pair-Counts | n Loss Pairs L1,,,,Ln is defined in terms of their Loss-Pair-Counts | |||

as Bi-Packet-Loss-Ratio / Bi-Packet-Loss-Episode-Duration-Number, | as Bi-Packet-Loss-Ratio / Bi-Packet-Loss-Episode-Duration-Number, | |||

when this can be defined, specifically, it is: | when this can be defined, specifically, it is as follows: | |||

o (N(1,0)+N(1,1)) * (N(0,1)+N(1,0)) / (2*N(1,1)+N(0,1)+N(1,0) ) / n | o (N(1,0) + N(1,1)) * (N(0,1) + N(1,0)) / (2*N(1,1) + N(0,1) + | |||

if N(0,1)+N(0,1) > 0 | N(1,0) ) / n if N(0,1) + N(1,0) > 0 | |||

o 0 if N(0,1)+N(1,0) +N(1,1) = 0 (no probe packets lost) | o 0 if N(0,1) + N(1,0) + N(1,1) = 0 (no probe packets lost) | |||

o 1 if N(0,1) +N(1,0) +N(0,0) = 0 (all probe packets lost) | o 1 if N(0,1) + N(1,0) + N(0,0) = 0 (all probe packets lost) | |||

6. Loss Episode Metrics derived from Bi-Packet Loss Probing | 6. Loss Episode Metrics Derived from Bi-Packet Loss Probing | |||

Metrics for the time frequency and time duration of loss episodes are | Metrics for the time frequency and time duration of loss episodes are | |||

now defined as functions of set of n loss pairs L1,....,Ln. Although | now defined as functions of the set of n Loss Pairs L1,....,Ln. | |||

a loss episode is defined as a maximal set of successive lost | Although a loss episode is defined as a maximal set of successive | |||

packets, the loss episode metrics are not defined directly in terms | lost packets, the loss episode metrics are not defined directly in | |||

of the sequential patterns of packet loss exhibited by loss pairs. | terms of the sequential patterns of packet loss exhibited by Loss | |||

This is because samples, including Type-P-One-way-Bi-Packet-Loss- | Pairs. This is because samples, including Type-P-One-way-Bi-Packet- | |||

Geometric-Stream, generally do not report all lost packets in each | Loss-Geometric-Stream, generally do not report all lost packets in | |||

episode. Instead, the metrics are defined as functions of the Loss- | each episode. Instead, the metrics are defined as functions of the | |||

Pair-Counts of the sample, for reasons that are now described. | Loss-Pair-Counts of the sample, for reasons that are now described. | |||

Consider an idealized Type-P-One-way-Bi-Packet-Loss-Geometric-Stream | Consider an idealized Type-P-One-way-Bi-Packet-Loss-Geometric-Stream | |||

sample in which the launch probability q =1. It is shown in [SBDR08] | sample in which the launch probability q =1. It is shown in [SBDR08] | |||

that the average number of packets in a loss episode of this ideal | that the average number of packets in a loss episode of this ideal | |||

sample is exactly the Bi-Packet-Loss-Episode-Duration derived from | sample is exactly the Bi-Packet-Loss-Episode-Duration derived from | |||

its set of loss pairs. Note this computation makes no reference to | its set of Loss Pairs. Note this computation makes no reference to | |||

the position of lost packet in the sequence of probes. | the position of lost packet in the sequence of probes. | |||

A general Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample with | A general Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample with | |||

launch probability q < 1, independently samples, with probability q, | launch probability q < 1, independently samples, with probability q, | |||

each loss pair of an idealized sample. On average, the Loss-Pair- | each Loss Pair of an idealized sample. On average, the Loss-Pair- | |||

Counts (if normalized by the total number of pairs) will be the same | Counts (if normalized by the total number of pairs) will be the same | |||

as in the idealized sample. The loss episode metrics in the general | as in the idealized sample. The loss episode metrics in the general | |||

case are thus estimators of those for the idealized case; the | case are thus estimators of those for the idealized case; the | |||

statistical properties of this estimation, including a derivation of | statistical properties of this estimation, including a derivation of | |||

the estimation variance, is provided in [SBDR08]. | the estimation variance, is provided in [SBDR08]. | |||

6.1. Geometric Stream: Loss Ratio | 6.1. Geometric Stream: Loss Ratio | |||

6.1.1. Metric Name | 6.1.1. Metric Name | |||

skipping to change at page 15, line 43 | skipping to change at page 14, line 48 | |||

6.1.2. Metric Parameters | 6.1.2. Metric Parameters | |||

o Src, the IP address of a source host | o Src, the IP address of a source host | |||

o Dst, the IP address of a destination host | o Dst, the IP address of a destination host | |||

o T0, the randomly selected starting time [RFC3432] for periodic | o T0, the randomly selected starting time [RFC3432] for periodic | |||

launch opportunities | launch opportunities | |||

o d, the time spacing between potential launch times, Ti and Ti+1 | o d, the time spacing between potential launch times, Ti and T(i+1) | |||

o n, a count of potential measurement instants | o n, a count of potential measurement instants | |||

o q, a launch probability | o q, a launch probability | |||

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

from the stream selected for the metric. | from the stream selected for the metric | |||

o P, the specification of the packet type, over and above the source | o P, the specification of the packet type, over and above the source | |||

and destination address | and destination address | |||

6.1.3. Metric Units | 6.1.3. Metric Units | |||

A decimal number in the interval [0,1] | A decimal number in the interval [0,1] | |||

6.1.4. Metric Definition | 6.1.4. Metric Definition | |||

skipping to change at page 16, line 26 | skipping to change at page 15, line 30 | |||

parameters. | parameters. | |||

6.1.5. Discussion | 6.1.5. Discussion | |||

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Ratio estimates the | Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Ratio estimates the | |||

fraction of packets lost from the geometric stream of Bi-Packet | fraction of packets lost from the geometric stream of Bi-Packet | |||

probes. | probes. | |||

6.1.6. Methodologies | 6.1.6. Methodologies | |||

Refer to Section 4.6 | Refer to Section 4.6. | |||

6.1.7. Errors and Uncertainties | 6.1.7. Errors and Uncertainties | |||

Because Type-P-One-way-Bi-Packet-Loss-Geometric-Stream is sampled in | Because Type-P-One-way-Bi-Packet-Loss-Geometric-Stream is sampled in | |||

general (when the launch probability q <1) the metrics described in | general (when the launch probability q <1), the metrics described in | |||

this Section can be regarded as statistical estimators of the | this section can be regarded as statistical estimators of the | |||

corresponding idealized version corresponding to q = 1. Estimation | corresponding idealized version corresponding to q = 1. Estimation | |||

variance as it applies to Type-P-One-way-Bi-Packet-Loss-Geometric- | variance as it applies to Type-P-One-way-Bi-Packet-Loss-Geometric- | |||

Stream-Loss-Ratio is described in [SBDR08]. | Stream-Loss-Ratio is described in [SBDR08]. | |||

For other issues refer to Section 4.7 | For other issues, refer to Section 4.7 | |||

6.1.8. Reporting the Metric | 6.1.8. Reporting the Metric | |||

Refer to Section 4.8 | Refer to Section 4.8. | |||

6.2. Geometric Stream: Loss Episode Duration | 6.2. Geometric Stream: Loss Episode Duration | |||

6.2.1. Metric Name | 6.2.1. Metric Name | |||

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Duration | Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Duration | |||

6.2.2. Metric Parameters | 6.2.2. Metric Parameters | |||

o Src, the IP address of a source host | o Src, the IP address of a source host | |||

o Dst, the IP address of a destination host | o Dst, the IP address of a destination host | |||

o T0, the randomly selected starting time [RFC3432] for periodic | o T0, the randomly selected starting time [RFC3432] for periodic | |||

launch opportunities | launch opportunities | |||

o d, the time spacing between potential launch times, Ti and Ti+1 | o d, the time spacing between potential launch times, Ti and T(i+1) | |||

o n, a count of potential measurement instants | o n, a count of potential measurement instants | |||

o q, a launch probability | o q, a launch probability | |||

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

from the stream selected for the metric. | from the stream selected for the metric | |||

o P, the specification of the packet type, over and above the source | o P, the specification of the packet type, over and above the source | |||

and destination address | and destination address | |||

6.2.3. Metric Units | 6.2.3. Metric Units | |||

A non-negative number of seconds. | A non-negative number of seconds | |||

6.2.4. Metric Definition | 6.2.4. Metric Definition | |||

The result obtained by computing the Bi-Packet-Loss-Episode-Duration- | The result obtained by computing the Bi-Packet-Loss-Episode-Duration- | |||

Number over a Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample | Number over a Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample | |||

with the metric parameters, then multiplying the result by the launch | with the metric parameters, then multiplying the result by the launch | |||

spacing parameter d. | spacing parameter d. | |||

6.2.5. Discussion | 6.2.5. Discussion | |||

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Duration | Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Duration | |||

estimates the average duration of a loss episode, measured in | estimates the average duration of a loss episode, measured in | |||

seconds. The duration measured in packets is obtained by dividing | seconds. The duration measured in packets is obtained by dividing | |||

the metric value by the packet launch spacing parameter d. | the metric value by the packet launch spacing parameter d. | |||

6.2.6. Methodologies | 6.2.6. Methodologies | |||

Refer to Section 4.6 | Refer to Section 4.6. | |||

6.2.7. Errors and Uncertainties | 6.2.7. Errors and Uncertainties | |||

Because Type-P-One-way-Bi-Packet-Loss-Geometric-Stream is sampled in | Because Type-P-One-way-Bi-Packet-Loss-Geometric-Stream is sampled in | |||

general (when the launch probability q <1) the metrics described in | general (when the launch probability q <1), the metrics described in | |||

this Section can be regarded as statistical estimators of the | this section can be regarded as statistical estimators of the | |||

corresponding idealized version corresponding to q = 1. Estimation | corresponding idealized version corresponding to q = 1. Estimation | |||

variance as it applies to Type-P-One-way-Bi-Packet-Loss-Geometric- | variance as it applies to Type-P-One-way-Bi-Packet-Loss-Geometric- | |||

Stream-Episode-Duration is described in [SBDR08]. | Stream-Episode-Duration is described in [SBDR08]. | |||

For other issues refer to Section 4.7 | For other issues, refer to Section 4.7 | |||

6.2.8. Reporting the Metric | 6.2.8. Reporting the Metric | |||

Refer to Section 4.8 | Refer to Section 4.8. | |||

6.3. Geometric Stream: Loss Episode Frequency | 6.3. Geometric Stream: Loss Episode Frequency | |||

6.3.1. Metric Name | 6.3.1. Metric Name | |||

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Frequency | Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Frequency | |||

6.3.2. Metric Parameters | 6.3.2. Metric Parameters | |||

o Src, the IP address of a source host | o Src, the IP address of a source host | |||

o Dst, the IP address of a destination host | o Dst, the IP address of a destination host | |||

o T0, the randomly selected starting time [RFC3432] for periodic | o T0, the randomly selected starting time [RFC3432] for periodic | |||

launch opportunities | launch opportunities | |||

o d, the time spacing between potential launch times, Ti and Ti+1 | o d, the time spacing between potential launch times, Ti and T(i+1) | |||

o n, a count of potential measurement instants | o n, a count of potential measurement instants | |||

o q, a launch probability | o q, a launch probability | |||

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

from the stream selected for the metric. | from the stream selected for the metric | |||

o P, the specification of the packet type, over and above the source | o P, the specification of the packet type, over and above the source | |||

and destination address | and destination address | |||

6.3.3. Metric Units | 6.3.3. Metric Units | |||

A positive number. | A positive number | |||

6.3.4. Metric Definition | 6.3.4. Metric Definition | |||

The result obtained by computing the Bi-Packet-Loss-Episode-Frequency | The result obtained by computing the Bi-Packet-Loss-Episode- | |||

over a Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample with the | Frequency-Number over a Type-P-One-way-Bi-Packet-Loss-Geometric- | |||

metric parameters, then dividing the result by the launch spacing | Stream sample with the metric parameters, then dividing the result by | |||

parameter d. | the launch spacing parameter d. | |||

6.3.5. Discussion | 6.3.5. Discussion | |||

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Frequency | Type-P-One-way-Bi-Packet-Loss-Geometric-Stream-Episode-Frequency | |||

estimates the average frequency per unit time with which loss | estimates the average frequency per unit time with which loss | |||

episodes start (or finish). The frequency relative to the count of | episodes start (or finish). The frequency relative to the count of | |||

potential probe launches is obtained by multiplying the metric value | potential probe launches is obtained by multiplying the metric value | |||

by the packet launch spacing parameter d. | by the packet launch spacing parameter d. | |||

6.3.6. Methodologies | 6.3.6. Methodologies | |||

Refer to Section 4.6 | Refer to Section 4.6. | |||

6.3.7. Errors and Uncertainties | 6.3.7. Errors and Uncertainties | |||

Because Type-P-One-way-Bi-Packet-Loss-Geometric-Stream is sampled in | Because Type-P-One-way-Bi-Packet-Loss-Geometric-Stream is sampled in | |||

general (when the launch probability q <1) the metrics described in | general (when the launch probability q <1), the metrics described in | |||

this Section can be regarded as statistical estimators of the | this section can be regarded as statistical estimators of the | |||

corresponding idealized version corresponding to q = 1. Estimation | corresponding idealized version corresponding to q = 1. Estimation | |||

variance as it applies to Type-P-One-way-Bi-Packet-Loss-Geometric- | variance as it applies to Type-P-One-way-Bi-Packet-Loss-Geometric- | |||

Stream-Episode-Frequency is described in [SBDR08]. | Stream-Episode-Frequency is described in [SBDR08]. | |||

For other issues refer to Section 4.7 | For other issues, refer to Section 4.7 | |||

6.3.8. Reporting the Metric | 6.3.8. Reporting the Metric | |||

Refer to Section 4.8 | Refer to Section 4.8. | |||

7. Applicability of Loss Episode Metrics | 7. Applicability of Loss Episode Metrics | |||

7.1. Relation to Gilbert Model | 7.1. Relation to Gilbert Model | |||

The general Gilbert-Elliot model is a discrete time Markov chain over | The general Gilbert-Elliot model is a discrete time Markov chain over | |||

two states, Good (g) and Bad (b), each with its own independent | two states, Good (g) and Bad (b), each with its own independent | |||

packet loss rate. In the simplest case, the Good loss rate is 0 | packet loss ratio. In the simplest case, the Good loss ratio is 0, | |||

while the Bad loss rate is 1. Correspondingly, there are two | while the Bad loss ratio is 1. Correspondingly, there are two | |||

independent parameters, the Markov transition probabilities P(g|b) = | independent parameters, the Markov transition probabilities P(g|b) = | |||

1- P(b|b) and P(b|g) = 1- P(g|g), where P(i|j) is the probability to | 1- P(b|b) and P(b|g) = 1- P(g|g), where P(i|j) is the probability to | |||

transition from state j and step n to state i at step n+1. With | transition from state j and step n to state i at step n+1. With | |||

these parameters, the fraction of steps spent in the bad state is | these parameters, the fraction of steps spent in the bad state is | |||

P(b|g)/(P(b|g) + P(g|b)) while the average duration of a sojourn in | P(b|g)/(P(b|g) + P(g|b)), while the average duration of a sojourn in | |||

the bad state is 1/P(g|b) steps. | the bad state is 1/P(g|b) steps. | |||

Now identify the steps of the Markov chain with the possible sending | Now identify the steps of the Markov chain with the possible sending | |||

times of packets for a Type-P-One-way-Bi-Packet-Loss-Geometric-Stream | times of packets for a Type-P-One-way-Bi-Packet-Loss-Geometric-Stream | |||

with launch spacing d. Suppose the loss episode metrics Type-P-One- | with launch spacing d. Suppose the loss episode metrics Type-P-One- | |||

way-Bi-Packet-Loss-Geometric-Stream-Ratio and Type-P-One-way-Bi- | way-Bi-Packet-Loss-Geometric-Stream-Ratio and Type-P-One-way-Bi- | |||

Packet-Loss-Geometric-Stream-Episode-Duration take the values r and m | Packet-Loss-Geometric-Stream-Episode-Duration take the values r and | |||

respectively. Then from the discussion in Section 6.2.5 the | m, respectively. Then, from the discussion in Section 6.1.5, the | |||

following can be equated: | following can be equated: | |||

r = P(b|g)/(P(b|g) + P(g|b)) and m/d = 1/P(g|b). | r = P(b|g)/(P(b|g) + P(g|b)) and m/d = 1/P(g|b). | |||

These relationships can be inverted in order to recover the Gilbert | These relationships can be inverted in order to recover the Gilbert | |||

model parameters: | model parameters: | |||

P(g|b) = d/m and P(b|g)=d/m/(1/r - 1) | P(g|b) = d/m and P(b|g)=d/m/(1/r - 1) | |||

8. IPR Considerations | 8. Security Considerations | |||

An IPR disclosure concerning some of the material covered in this | ||||

document has been made to the IETF: see | ||||

https://datatracker.ietf.org/ipr/1354/ | ||||

9. Security Considerations | ||||

Conducting Internet measurements raises both security and privacy | Conducting Internet measurements raises both security and privacy | |||

concerns. This memo does not specify an implementation of the | concerns. This memo does not specify an implementation of the | |||

metrics, so it does not directly affect the security of the Internet | metrics, so it does not directly affect the security of the Internet | |||

nor of applications which run on the Internet. | or of applications that run on the Internet. However,implementations | |||

However,implementations of these metrics must be mindful of security | of these metrics must be mindful of security and privacy concerns. | |||

and privacy concerns. | ||||

There are two types of security concerns: potential harm caused by | There are two types of security concerns: potential harm caused by | |||

the measurements, and potential harm to the measurements. The | the measurements and potential harm to the measurements. The | |||

measurements could cause harm because they are active, and inject | measurements could cause harm because they are active and inject | |||

packets into the network. The measurement parameters MUST be | packets into the network. The measurement parameters MUST be | |||

carefully selected so that the measurements inject trivial amounts of | carefully selected so that the measurements inject trivial amounts of | |||

additional traffic into the networks they measure. If they inject | additional traffic into the networks they measure. If they inject | |||

"too much" traffic, they can skew the results of the measurement, and | "too much" traffic, they can skew the results of the measurement and, | |||

in extreme cases cause congestion and denial of service. The | in extreme cases, cause congestion and denial of service. The | |||

measurements themselves could be harmed by routers giving measurement | measurements themselves could be harmed by routers giving measurement | |||

traffic a different priority than "normal" traffic, or by an attacker | traffic a different priority than "normal" traffic, or by an attacker | |||

injecting artificial measurement traffic. If routers can recognize | injecting artificial measurement traffic. If routers can recognize | |||

measurement traffic and treat it separately, the measurements may not | measurement traffic and treat it separately, the measurements may not | |||

reflect actual user traffic. If an attacker injects artificial | reflect actual user traffic. If an attacker injects artificial | |||

traffic that is accepted as legitimate, the loss rate will be | traffic that is accepted as legitimate, the loss rate will be | |||

artificially lowered. Therefore, the measurement methodologies | artificially lowered. Therefore, the measurement methodologies | |||

SHOULD include appropriate techniques to reduce the probability that | SHOULD include appropriate techniques to reduce the probability that | |||

measurement traffic can be distinguished from "normal" traffic. | measurement traffic can be distinguished from "normal" traffic. | |||

Authentication techniques, such as digital signatures, may be used | Authentication techniques, such as digital signatures, may be used | |||

where appropriate to guard against injected traffic attacks. The | where appropriate to guard against injected traffic attacks. The | |||

privacy concerns of network measurement are limited by the active | privacy concerns of network measurement are limited by the active | |||

measurements described in this memo: they involve no release of user | measurements described in this memo: they involve no release of user | |||

data. | data. | |||

10. IANA Considerations | 9. References | |||

This document requests no actions from IANA. | ||||

11. Acknowledgements | ||||

12. References | ||||

12.1. Normative References | 9.1. Normative References | |||

[RFC2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way | [RFC2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way | |||

Packet Loss Metric for IPPM", RFC 2680, September 1999. | Packet Loss Metric for IPPM", RFC 2680, September 1999. | |||

[RFC3393] Demichelis, C. and P. Chimento, "IP Packet Delay Variation | [RFC3393] Demichelis, C. and P. Chimento, "IP Packet Delay Variation | |||

Metric for IP Performance Metrics (IPPM)", RFC 3393, | Metric for IP Performance Metrics (IPPM)", RFC 3393, | |||

November 2002. | November 2002. | |||

[RFC3611] Friedman, T., Caceres, R., and A. Clark, "RTP Control | [RFC3611] Friedman, T., Caceres, R., and A. Clark, "RTP Control | |||

Protocol Extended Reports (RTCP XR)", RFC 3611, | Protocol Extended Reports (RTCP XR)", RFC 3611, | |||

November 2003. | November 2003. | |||

[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate | [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate | |||

Requirement Levels", BCP 14, RFC 2119, March 1997. | Requirement Levels", BCP 14, RFC 2119, March 1997. | |||

[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. | |||

12.2. Informative References | 9.2. Informative References | |||

[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, | [RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, | |||

"Framework for IP Performance Metrics", RFC 2330, | "Framework for IP Performance Metrics", RFC 2330, | |||

May 1998. | May 1998. | |||

[RFC3357] Koodli, R. and R. Ravikanth, "One-way Loss Pattern Sample | [RFC3357] Koodli, R. and R. Ravikanth, "One-way Loss Pattern Sample | |||

Metrics", RFC 3357, August 2002. | Metrics", RFC 3357, August 2002. | |||

[SBDR08] IEEE/ACM Transactions on Networking, 16(2): 307-320, "A | [SBDR08] IEEE/ACM Transactions on Networking, 16(2): 307-320, "A | |||

Geometric Approach to Improving Active Packet Loss | Geometric Approach to Improving Active Packet Loss | |||

skipping to change at page 22, line 19 | skipping to change at page 21, line 15 | |||

Authors' Addresses | Authors' Addresses | |||

Nick Duffield | Nick Duffield | |||

AT&T Labs-Research | AT&T Labs-Research | |||

180 Park Avenue | 180 Park Avenue | |||

Florham Park, NJ 07932 | Florham Park, NJ 07932 | |||

USA | USA | |||

Phone: +1 973 360 8726 | Phone: +1 973 360 8726 | |||

Fax: +1 973 360 8871 | Fax: +1 973 360 8871 | |||

Email: duffield@research.att.com | EMail: duffield@research.att.com | |||

URI: http://www.research.att.com/people/Duffield_Nicholas_G | URI: http://www.research.att.com/people/Duffield_Nicholas_G | |||

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 | |||

Email: acmorton@att.com | EMail: acmorton@att.com | |||

URI: http://home.comcast.net/~acmacm/ | URI: http://home.comcast.net/~acmacm/ | |||

Joel Sommers | Joel Sommers | |||

Colgate University | Colgate University | |||

304 McGregory Hall | 304 McGregory Hall | |||

Hamilton, NY 13346 | Hamilton, NY 13346 | |||

USA | USA | |||

Phone: +1 315 228 7587 | Phone: +1 315 228 7587 | |||

Fax: | Fax: | |||

Email: jsommers@colgate.edu | EMail: jsommers@colgate.edu | |||

URI: http://cs.colgate.edu/faculty/jsommers | URI: http://cs.colgate.edu/faculty/jsommers | |||

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