RFC 6534

Internet Engineering Task Force (IETF) N. Duffield

Request for Comments: 6534 AT&T Labs-Research

Category: Standards Track A. Morton

ISSN: 2070-1721 AT&T Labs

J. Sommers

Colgate University

May 2012

Loss Episode Metrics for IP Performance Metrics (IPPM)

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

loss rate on a Poisson and Periodic probe streams between two hosts.

However, the impact of packet loss on applications is, in general,

sensitive not just to the average loss rate but also to the way in

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

sets of consecutively lost probe packets). This document defines

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

average duration of loss episodes and a probing methodology under

which the loss episode metrics are to be measured.

This is an Internet Standards Track document.

This document is a product of the Internet Engineering Task Force

(IETF). It represents the consensus of the IETF community. It has

received public review and has been approved for publication by the

Internet Engineering Steering Group (IESG). Further information on

Internet Standards is available in Section 2 of RFC 5741.

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 (c) 2012 IETF Trust and the persons identified as the

document authors. All rights reserved.

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

Provisions Relating to IETF Documents

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

publication of this document. Please review these documents

carefully, as they describe your rights and restrictions with respect

to this document. Code Components extracted from this document must

RFC 6534 Loss Episode Metrics for IPPM May 2012

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

the Trust Legal Provisions and are provided without warranty as

described in the Simplified BSD License.

This document may contain material from IETF Documents or IETF

Contributions published or made publicly available before November

10, 2008. The person(s) controlling the copyright in some of this

material may not have granted the IETF Trust the right to allow

modifications of such material outside the IETF Standards Process.

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

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

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

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

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

than English.

# Table of Contents

1. Introduction ....................................................4

1.1. Background and Motivation ..................................4

1.1.1. Requirements Language ...............................5

1.2. Loss Episode Metrics and Bi-Packet Probes ..................5

1.3. Outline and Contents .......................................6

2. Singleton Definition for Type-P-One-way Bi-Packet Loss ..........7

2.1. Metric Name ................................................7

2.2. Metric Parameters ..........................................7

2.3. Metric Units ...............................................7

2.4. Metric Definition ..........................................7

2.5. Discussion .................................................8

2.6. Methodologies ..............................................8

2.7. Errors and Uncertainties ...................................8

2.8. Reporting the Metric .......................................8

3. General Definition of Samples for

Type-P-One-way-Bi-Packet-Loss ...................................8

3.1. Metric Name ................................................9

3.2. Metric Parameters ..........................................9

3.3. Metric Units ...............................................9

3.4. Metric Definition ..........................................9

3.5. Discussion .................................................9

3.6. Methodologies .............................................10

3.7. Errors and Uncertainties ..................................10

3.8. Reporting the Metric ......................................10

4. An Active Probing Methodology for Bi-Packet Loss ...............10

4.1. Metric Name ...............................................10

4.2. Metric Parameters .........................................10

4.3. Metric Units ..............................................11

4.4. Metric Definition .........................................11

4.5. Discussion ................................................11

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

the Trust Legal Provisions and are provided without warranty as

described in the Simplified BSD License.

This document may contain material from IETF Documents or IETF

Contributions published or made publicly available before November

10, 2008. The person(s) controlling the copyright in some of this

material may not have granted the IETF Trust the right to allow

modifications of such material outside the IETF Standards Process.

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

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

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

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

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

than English.

1. Introduction ....................................................4

1.1. Background and Motivation ..................................4

1.1.1. Requirements Language ...............................5

1.2. Loss Episode Metrics and Bi-Packet Probes ..................5

1.3. Outline and Contents .......................................6

2. Singleton Definition for Type-P-One-way Bi-Packet Loss ..........7

2.1. Metric Name ................................................7

2.2. Metric Parameters ..........................................7

2.3. Metric Units ...............................................7

2.4. Metric Definition ..........................................7

2.5. Discussion .................................................8

2.6. Methodologies ..............................................8

2.7. Errors and Uncertainties ...................................8

2.8. Reporting the Metric .......................................8

3. General Definition of Samples for

Type-P-One-way-Bi-Packet-Loss ...................................8

3.1. Metric Name ................................................9

3.2. Metric Parameters ..........................................9

3.3. Metric Units ...............................................9

3.4. Metric Definition ..........................................9

3.5. Discussion .................................................9

3.6. Methodologies .............................................10

3.7. Errors and Uncertainties ..................................10

3.8. Reporting the Metric ......................................10

4. An Active Probing Methodology for Bi-Packet Loss ...............10

4.1. Metric Name ...............................................10

4.2. Metric Parameters .........................................10

4.3. Metric Units ..............................................11

4.4. Metric Definition .........................................11

4.5. Discussion ................................................11

RFC 6534 Loss Episode Metrics for IPPM May 2012

4.6. Methodologies .............................................11

4.7. Errors and Uncertainties ..................................12

4.8. Reporting the Metric ......................................12

5. Loss Episode Proto-Metrics .....................................12

5.1. Loss-Pair-Counts ..........................................13

5.2. Bi-Packet-Loss-Ratio ......................................13

5.3. Bi-Packet-Loss-Episode-Duration-Number ....................13

5.4. Bi-Packet-Loss-Episode-Frequency-Number ...................13

6. Loss Episode Metrics Derived from Bi-Packet Loss Probing .......14

6.1. Geometric Stream: Loss Ratio ..............................14

6.1.1. Metric Name ........................................14

6.1.2. Metric Parameters ..................................14

6.1.3. Metric Units .......................................15

6.1.4. Metric Definition ..................................15

6.1.5. Discussion .........................................15

6.1.6. Methodologies ......................................15

6.1.7. Errors and Uncertainties ...........................15

6.1.8. Reporting the Metric ...............................15

6.2. Geometric Stream: Loss Episode Duration ...................16

6.2.1. Metric Name ........................................16

6.2.2. Metric Parameters ..................................16

6.2.3. Metric Units .......................................16

6.2.4. Metric Definition ..................................16

6.2.5. Discussion .........................................16

6.2.6. Methodologies ......................................16

6.2.7. Errors and Uncertainties ...........................17

6.2.8. Reporting the Metric ...............................17

6.3. Geometric Stream: Loss Episode Frequency ..................17

6.3.1. Metric Name ........................................17

6.3.2. Metric Parameters ..................................17

6.3.3. Metric Units .......................................17

6.3.4. Metric Definition ..................................18

6.3.5. Discussion .........................................18

6.3.6. Methodologies ......................................18

6.3.7. Errors and Uncertainties ...........................18

6.3.8. Reporting the Metric ...............................18

7. Applicability of Loss Episode Metrics ..........................18

7.1. Relation to Gilbert Model .................................18

8. Security Considerations ........................................19

9. References .....................................................20

9.1. Normative References ......................................20

9.2. Informative References ....................................20

4.6. Methodologies .............................................11

4.7. Errors and Uncertainties ..................................12

4.8. Reporting the Metric ......................................12

5. Loss Episode Proto-Metrics .....................................12

5.1. Loss-Pair-Counts ..........................................13

5.2. Bi-Packet-Loss-Ratio ......................................13

5.3. Bi-Packet-Loss-Episode-Duration-Number ....................13

5.4. Bi-Packet-Loss-Episode-Frequency-Number ...................13

6. Loss Episode Metrics Derived from Bi-Packet Loss Probing .......14

6.1. Geometric Stream: Loss Ratio ..............................14

6.1.1. Metric Name ........................................14

6.1.2. Metric Parameters ..................................14

6.1.3. Metric Units .......................................15

6.1.4. Metric Definition ..................................15

6.1.5. Discussion .........................................15

6.1.6. Methodologies ......................................15

6.1.7. Errors and Uncertainties ...........................15

6.1.8. Reporting the Metric ...............................15

6.2. Geometric Stream: Loss Episode Duration ...................16

6.2.1. Metric Name ........................................16

6.2.2. Metric Parameters ..................................16

6.2.3. Metric Units .......................................16

6.2.4. Metric Definition ..................................16

6.2.5. Discussion .........................................16

6.2.6. Methodologies ......................................16

6.2.7. Errors and Uncertainties ...........................17

6.2.8. Reporting the Metric ...............................17

6.3. Geometric Stream: Loss Episode Frequency ..................17

6.3.1. Metric Name ........................................17

6.3.2. Metric Parameters ..................................17

6.3.3. Metric Units .......................................17

6.3.4. Metric Definition ..................................18

6.3.5. Discussion .........................................18

6.3.6. Methodologies ......................................18

6.3.7. Errors and Uncertainties ...........................18

6.3.8. Reporting the Metric ...............................18

7. Applicability of Loss Episode Metrics ..........................18

7.1. Relation to Gilbert Model .................................18

8. Security Considerations ........................................19

9. References .....................................................20

9.1. Normative References ......................................20

9.2. Informative References ....................................20

RFC 6534 Loss Episode Metrics for IPPM May 2012

# 1. Introduction

## 1.1. Background and Motivation

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

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

users and applications and the operation of transport protocols such

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

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

represent the complexity of packet loss over periods of time.

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

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

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

effect of packet loss on traffic in general.

Moving beyond single parameter loss models, Markovian and Markov-

modulated loss models involving transitions between a good and bad

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

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

principle, Markovian models can be formulated over state spaces

involving patterns of loss of any desired number of packets.

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

models cumbersome both for parameter estimation (accuracy decreases)

and prediction in practice (due to computational complexity and

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

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

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

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

model for their interpretation.

An empirical measure of packet loss complexity, the index of

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

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

characterization of packet loss over time requires specification of

the IDC for each window size t>0.

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

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

specific for Voice over IP (VoIP) that characterize complete episodes

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

The above considerations motivate the formulation of empirical

metrics of one-way packet loss that provide the simplest

generalization of [RFC2680] (which is widely adopted but only defines

a single loss-to-total ratio metric). The metrics defined here

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

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

users and applications and the operation of transport protocols such

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

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

represent the complexity of packet loss over periods of time.

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

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

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

effect of packet loss on traffic in general.

Moving beyond single parameter loss models, Markovian and Markov-

modulated loss models involving transitions between a good and bad

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

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

principle, Markovian models can be formulated over state spaces

involving patterns of loss of any desired number of packets.

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

models cumbersome both for parameter estimation (accuracy decreases)

and prediction in practice (due to computational complexity and

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

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

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

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

model for their interpretation.

An empirical measure of packet loss complexity, the index of

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

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

characterization of packet loss over time requires specification of

the IDC for each window size t>0.

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

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

specific for Voice over IP (VoIP) that characterize complete episodes

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

The above considerations motivate the formulation of empirical

metrics of one-way packet loss that provide the simplest

generalization of [RFC2680] (which is widely adopted but only defines

a single loss-to-total ratio metric). The metrics defined here

RFC 6534 Loss Episode Metrics for IPPM May 2012

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

The losses experienced by the packet stream can be viewed as

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

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

frequency and average duration. Although the average loss ratio can

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

characterizing the statistics of the patterns of packet loss within

the stream of probes. This is useful information in understanding

the effect of packet losses on application performance, since

different applications can have different sensitivities to patterns

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

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

pictures, but further losses within an episode of sufficiently short

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

The loss episode metrics presented here have the following useful

properties:

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

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

related to the special case of the Gilbert Model parameters; see

Section 7.

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

user requirements or tolerance for network loss performance, in

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

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

metrics upon dividing the average loss episode duration by the

loss episode frequency.

3. the metrics provide the smallest possible increment in complexity

beyond, but in the spirit of, the IP Performance Metrics (IPPM)

average packet loss ratio metrics [RFC2680], i.e., moving from a

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

(loss episode frequency and average loss episode duration).

capture deviations from independent packet loss in a robust model-

independent manner. The document also defines efficient measurement

methodologies for these metrics.

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].

The losses experienced by the packet stream can be viewed as

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

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

frequency and average duration. Although the average loss ratio can

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

characterizing the statistics of the patterns of packet loss within

the stream of probes. This is useful information in understanding

the effect of packet losses on application performance, since

different applications can have different sensitivities to patterns

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

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

pictures, but further losses within an episode of sufficiently short

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

The loss episode metrics presented here have the following useful

properties:

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

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

related to the special case of the Gilbert Model parameters; see

Section 7.

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

user requirements or tolerance for network loss performance, in

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

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

metrics upon dividing the average loss episode duration by the

loss episode frequency.

3. the metrics provide the smallest possible increment in complexity

beyond, but in the spirit of, the IP Performance Metrics (IPPM)

average packet loss ratio metrics [RFC2680], i.e., moving from a

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

(loss episode frequency and average loss episode duration).

RFC 6534 Loss Episode Metrics for IPPM May 2012

The document also describes a probing methodology under which loss

episode metrics are to be measured. The methodology comprises

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

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

a geometric distributed number multiplied by the same separation.

This can be regarded a generalization of Poisson probing where the

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

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

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

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

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

temporal resolution at which different loss episodes are to be

distinguished. The methodology does not measure episodes of loss of

consecutive background packets on the measured path. One key feature

of this methodology is its efficiency: it estimates the average

length of loss episodes without directly measuring the complete

episodes themselves. Instead, this information is encoded in the

observed relative frequencies of the four possible outcomes arising

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

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

which reports on directly measured episodes.

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

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

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

## 1.3. Outline and Contents

o Section 2 defines the fundamental singleton metric for the

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

general probe stream: Type-P-One-way-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-

Stream arising from the geometric stream of packet-pair probes

that was described informally in Section 1.

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

outcomes from a stream metrics as an intermediate step to forming

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

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

focus of this memo, the new metrics:

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

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

The document also describes a probing methodology under which loss

episode metrics are to be measured. The methodology comprises

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

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

a geometric distributed number multiplied by the same separation.

This can be regarded a generalization of Poisson probing where the

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

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

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

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

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

temporal resolution at which different loss episodes are to be

distinguished. The methodology does not measure episodes of loss of

consecutive background packets on the measured path. One key feature

of this methodology is its efficiency: it estimates the average

length of loss episodes without directly measuring the complete

episodes themselves. Instead, this information is encoded in the

observed relative frequencies of the four possible outcomes arising

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

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

which reports on directly measured episodes.

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

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

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

o Section 2 defines the fundamental singleton metric for the

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

general probe stream: Type-P-One-way-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-

Stream arising from the geometric stream of packet-pair probes

that was described informally in Section 1.

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

outcomes from a stream metrics as an intermediate step to forming

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

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

focus of this memo, the new metrics:

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

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

RFC 6534 Loss Episode Metrics for IPPM May 2012

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

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

episodes start.

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

the average packet loss ratio metric arising from the geometric

stream probing methodology

o Section 7 details applications and relations to existing loss

models.

# 2. Singleton Definition for Type-P-One-way Bi-Packet Loss

## 2.1. Metric Name

Type-P-One-way-Bi-Packet-Loss

## 2.2. Metric Parameters

o Src, the IP address of a source host

o Dst, the IP address of a destination host

o T1, a sending time of the first packet

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

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination addresses

## 2.3. Metric Units

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

and 1 signifies loss.

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

## 2.4. Metric Definition

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

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

received at Dst.

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

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

episodes start.

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

the average packet loss ratio metric arising from the geometric

stream probing methodology

o Section 7 details applications and relations to existing loss

models.

Type-P-One-way-Bi-Packet-Loss

o Src, the IP address of a source host

o Dst, the IP address of a destination host

o T1, a sending time of the first packet

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

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination addresses

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

and 1 signifies loss.

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

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

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

received at Dst.

RFC 6534 Loss Episode Metrics for IPPM May 2012

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

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

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,

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 T2>T1 and that the first packet was

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,

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 T2>T1 and that both packets were

received at Dst.

## 2.5. Discussion

The purpose of the selection function is to specify exactly which

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

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

## 2.6. Methodologies

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-

Packet-Loss metric described above. In particular, the methodologies

described in RFC 2680 apply to both packets of the pair.

## 2.7. Errors and Uncertainties

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-

way-Bi-Packet-Loss metric.

## 2.8. Reporting the Metric

Refer to Section 2.8 of [RFC2680].

# 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

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

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

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

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

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,

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 T2>T1 and that the first packet was

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,

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 T2>T1 and that both packets were

received at Dst.

The purpose of the selection function is to specify exactly which

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

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

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-

Packet-Loss metric described above. In particular, the methodologies

described in RFC 2680 apply to both packets of the pair.

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-

way-Bi-Packet-Loss metric.

Refer to Section 2.8 of [RFC2680].

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

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

RFC 6534 Loss Episode Metrics for IPPM May 2012

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

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

## 3.1. Metric Name

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

## 3.2. Metric Parameters

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

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

Tn2

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

## 3.3. Metric Units

A set L1,L2,...,Ln of Loss Pairs

## 3.4. Metric Definition

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

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

Ti1, Ti2.

## 3.5. Discussion

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

sufficiently general to describe the case where packets are sampled

from a preexisting stream. This is useful in the case in which there

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

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

episode measurement. Packet pairs selected as bi-packet loss probes

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

we specialize this somewhat to more concretely describe a purpose

built packet stream for loss episode measurement.

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

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

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

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

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

Tn2

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

A set L1,L2,...,Ln of Loss Pairs

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

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

Ti1, Ti2.

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

sufficiently general to describe the case where packets are sampled

from a preexisting stream. This is useful in the case in which there

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

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

episode measurement. Packet pairs selected as bi-packet loss probes

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

we specialize this somewhat to more concretely describe a purpose

built packet stream for loss episode measurement.

RFC 6534 Loss Episode Metrics for IPPM May 2012

## 3.6. Methodologies

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-

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

methodologies described in RFC 2680 apply to both packets of each

pair.

## 3.7. Errors and Uncertainties

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-

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

## 3.8. Reporting the Metric

Refer to Section 2.8 of [RFC2680].

# 4. An Active Probing Methodology for Bi-Packet Loss

This section specializes the preceding section for an active probing

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

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

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

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

measurement. Hence, the interval count between successive times at

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

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

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

second pair.

## 4.1. Metric Name

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

## 4.2. Metric Parameters

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

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-

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

methodologies described in RFC 2680 apply to both packets of each

pair.

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-

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

Refer to Section 2.8 of [RFC2680].

This section specializes the preceding section for an active probing

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

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

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

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

measurement. Hence, the interval count between successive times at

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

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

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

second pair.

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

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

RFC 6534 Loss Episode Metrics for IPPM May 2012

o n, a count of potential measurement instants

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

## 4.3. Metric Units

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

## 4.4. Metric Definition

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

= 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

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

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

L1, L2,...Lm are the resulting Loss Pairs; m can be less than n since

not all times Ti have an associated measurement.

## 4.5. Discussion

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

with an appropriate statistical definition of the selection function

F.

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

of potential measurement instants because not all instants may

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

1.

## 4.6. Methodologies

The methodologies follow from:

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

o the specific time spacing, and

o the methodologies discussion given above for the singleton Type-P-

One-way-Bi-Packet-Loss metric.

o n, a count of potential measurement instants

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

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

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

= 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

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

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

L1, L2,...Lm are the resulting Loss Pairs; m can be less than n since

not all times Ti have an associated measurement.

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

with an appropriate statistical definition of the selection function

F.

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

of potential measurement instants because not all instants may

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

1.

The methodologies follow from:

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

o the specific time spacing, and

o the methodologies discussion given above for the singleton Type-P-

One-way-Bi-Packet-Loss metric.

RFC 6534 Loss Episode Metrics for IPPM May 2012

The issue of choosing an appropriate time spacing (e.g., one that is

matched to expected characteristics of loss episodes) is outside the

scope of this document.

Note that as with any active measurement methodology, consideration

must be made to handle out-of-order arrival of packets; see also

Section 3.6. of [RFC2680].

## 4.7. Errors and Uncertainties

In addition to sources of errors and uncertainties related to

methodologies for measuring the singleton Type-P-One-way-Bi-Packet-

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

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

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

schedule for sending packets. Insufficient CPU resources on the

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

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

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

a 100 microsecond spacing versus a 100 millisecond spacing).

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

## 4.8. Reporting the Metric

Refer to Section 3.8. of [RFC2680].

# 5. Loss Episode Proto-Metrics

This section describes four generic proto-metric quantities

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

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

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

episode metrics can then be constructed when these proto-metrics

take, as their input, sets of Loss Pairs samples generated by the

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

Loss-Geometric-Stream. The second of these is described in

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

reported themselves. Rather, they are intermediate quantities in the

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

rolled up into metrics in implementations. The metrics report loss

episode durations and frequencies in terms of packet counts, since

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

final metrics of Section 6 incorporate timescales and yield durations

in seconds and frequencies as per second.

The issue of choosing an appropriate time spacing (e.g., one that is

matched to expected characteristics of loss episodes) is outside the

scope of this document.

Note that as with any active measurement methodology, consideration

must be made to handle out-of-order arrival of packets; see also

Section 3.6. of [RFC2680].

In addition to sources of errors and uncertainties related to

methodologies for measuring the singleton Type-P-One-way-Bi-Packet-

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

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

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

schedule for sending packets. Insufficient CPU resources on the

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

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

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

a 100 microsecond spacing versus a 100 millisecond spacing).

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

Refer to Section 3.8. of [RFC2680].

This section describes four generic proto-metric quantities

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

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

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

episode metrics can then be constructed when these proto-metrics

take, as their input, sets of Loss Pairs samples generated by the

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

Loss-Geometric-Stream. The second of these is described in

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

reported themselves. Rather, they are intermediate quantities in the

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

rolled up into metrics in implementations. The metrics report loss

episode durations and frequencies in terms of packet counts, since

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

final metrics of Section 6 incorporate timescales and yield durations

in seconds and frequencies as per second.

RFC 6534 Loss Episode Metrics for IPPM May 2012

## 5.1. Loss-Pair-Counts

Loss-Pair-Counts are the absolute frequencies of the four types of

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)

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

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

## 5.2. Bi-Packet-Loss-Ratio

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

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

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

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

losses.

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

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

the following cases:

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

and no-loss outcomes.

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

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

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

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

Loss-Pair-Counts are the absolute frequencies of the four types of

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)

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

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

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

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

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

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

losses.

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

the following cases:

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

and no-loss outcomes.

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

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

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

RFC 6534 Loss Episode Metrics for IPPM May 2012

# 6. Loss Episode Metrics Derived from Bi-Packet Loss Probing

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

now defined as functions of the set of n Loss Pairs L1,....,Ln.

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

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

terms of the sequential patterns of packet loss exhibited by Loss

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

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

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

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

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]

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

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

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

the position of lost packet in the sequence of probes.

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

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

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

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

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

statistical properties of this estimation, including a derivation of

the estimation variance, is provided in [SBDR08].

## 6.1. Geometric Stream: Loss Ratio

### 6.1.1. Metric Name

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

### 6.1.2. Metric Parameters

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

o n, a count of potential measurement instants

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

now defined as functions of the set of n Loss Pairs L1,....,Ln.

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

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

terms of the sequential patterns of packet loss exhibited by Loss

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

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

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

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

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]

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

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

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

the position of lost packet in the sequence of probes.

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

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

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

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

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

statistical properties of this estimation, including a derivation of

the estimation variance, is provided in [SBDR08].

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

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

o n, a count of potential measurement instants

RFC 6534 Loss Episode Metrics for IPPM May 2012

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

### 6.1.3. Metric Units

A decimal number in the interval [0,1]

### 6.1.4. Metric Definition

The result obtained by computing the Bi-Packet-Loss-Ratio over a

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample with the metric

parameters.

### 6.1.5. Discussion

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

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

probes.

### 6.1.6. Methodologies

Refer to Section 4.6.

### 6.1.7. Errors and Uncertainties

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

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

this section can be regarded as statistical estimators of the

corresponding idealized version corresponding to q = 1. Estimation

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

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

For other issues, refer to Section 4.7

### 6.1.8. Reporting the Metric

Refer to Section 4.8.

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

A decimal number in the interval [0,1]

The result obtained by computing the Bi-Packet-Loss-Ratio over a

Type-P-One-way-Bi-Packet-Loss-Geometric-Stream sample with the metric

parameters.

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

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

probes.

Refer to Section 4.6.

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

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

this section can be regarded as statistical estimators of the

corresponding idealized version corresponding to q = 1. Estimation

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

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

For other issues, refer to Section 4.7

Refer to Section 4.8.

RFC 6534 Loss Episode Metrics for IPPM May 2012

## 6.2. Geometric Stream: Loss Episode Duration

### 6.2.1. Metric Name

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

### 6.2.2. Metric Parameters

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

o n, a count of potential measurement instants

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

### 6.2.3. Metric Units

A non-negative number of seconds

### 6.2.4. Metric Definition

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

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

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

spacing parameter d.

### 6.2.5. Discussion

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

estimates the average duration of a loss episode, measured in

seconds. The duration measured in packets is obtained by dividing

the metric value by the packet launch spacing parameter d.

### 6.2.6. Methodologies

Refer to Section 4.6.

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

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

o n, a count of potential measurement instants

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

A non-negative number of seconds

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

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

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

spacing parameter d.

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

estimates the average duration of a loss episode, measured in

seconds. The duration measured in packets is obtained by dividing

the metric value by the packet launch spacing parameter d.

Refer to Section 4.6.

RFC 6534 Loss Episode Metrics for IPPM May 2012

### 6.2.7. Errors and Uncertainties

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

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

this section can be regarded as statistical estimators of the

corresponding idealized version corresponding to q = 1. Estimation

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

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

For other issues, refer to Section 4.7

### 6.2.8. Reporting the Metric

Refer to Section 4.8.

## 6.3. Geometric Stream: Loss Episode Frequency

### 6.3.1. Metric Name

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

### 6.3.2. Metric Parameters

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

o n, a count of potential measurement instants

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

### 6.3.3. Metric Units

A positive number

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

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

this section can be regarded as statistical estimators of the

corresponding idealized version corresponding to q = 1. Estimation

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

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

For other issues, refer to Section 4.7

Refer to Section 4.8.

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

o Src, the IP address of a source host

o Dst, the IP address of a destination host

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

launch opportunities

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

o n, a count of potential measurement instants

o q, a launch probability

o F, a selection function defining unambiguously the two packets

from the stream selected for the metric

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

and destination address

A positive number

RFC 6534 Loss Episode Metrics for IPPM May 2012

### 6.3.4. Metric Definition

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

Frequency-Number over a Type-P-One-way-Bi-Packet-Loss-Geometric-

Stream sample with the metric parameters, then dividing the result by

the launch spacing parameter d.

### 6.3.5. Discussion

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

estimates the average frequency per unit time with which loss

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

potential probe launches is obtained by multiplying the metric value

by the packet launch spacing parameter d.

### 6.3.6. Methodologies

Refer to Section 4.6.

### 6.3.7. Errors and Uncertainties

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

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

this section can be regarded as statistical estimators of the

corresponding idealized version corresponding to q = 1. Estimation

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

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

For other issues, refer to Section 4.7

### 6.3.8. Reporting the Metric

Refer to Section 4.8.

# 7. Applicability of Loss Episode Metrics

## 7.1. Relation to Gilbert Model

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

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

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

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

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

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

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 result obtained by computing the Bi-Packet-Loss-Episode-

Frequency-Number over a Type-P-One-way-Bi-Packet-Loss-Geometric-

Stream sample with the metric parameters, then dividing the result by

the launch spacing parameter d.

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

estimates the average frequency per unit time with which loss

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

potential probe launches is obtained by multiplying the metric value

by the packet launch spacing parameter d.

Refer to Section 4.6.

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

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

this section can be regarded as statistical estimators of the

corresponding idealized version corresponding to q = 1. Estimation

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

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

For other issues, refer to Section 4.7

Refer to Section 4.8.

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

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

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

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

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

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

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.

RFC 6534 Loss Episode Metrics for IPPM May 2012

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

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-

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

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

following can be equated:

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

model parameters:

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

# 8. Security Considerations

Conducting Internet measurements raises both security and privacy

concerns. This memo does not specify an implementation of the

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

or of applications that run on the Internet. However,implementations

of these metrics must be mindful of security and privacy concerns.

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

the measurements and potential harm to the measurements. The

measurements could cause harm because they are active and inject

packets into the network. The measurement parameters MUST be

carefully selected so that the measurements inject trivial amounts of

additional traffic into the networks they measure. If they inject

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

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

measurements themselves could be harmed by routers giving measurement

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

injecting artificial measurement traffic. If routers can recognize

measurement traffic and treat it separately, the measurements may not

reflect actual user traffic. If an attacker injects artificial

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

artificially lowered. Therefore, the measurement methodologies

SHOULD include appropriate techniques to reduce the probability that

measurement traffic can be distinguished from "normal" traffic.

Authentication techniques, such as digital signatures, may be used

where appropriate to guard against injected traffic attacks. The

privacy concerns of network measurement are limited by the active

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

data.

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

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-

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

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

following can be equated:

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

model parameters:

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

Conducting Internet measurements raises both security and privacy

concerns. This memo does not specify an implementation of the

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

or of applications that run on the Internet. However,implementations

of these metrics must be mindful of security and privacy concerns.

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

the measurements and potential harm to the measurements. The

measurements could cause harm because they are active and inject

packets into the network. The measurement parameters MUST be

carefully selected so that the measurements inject trivial amounts of

additional traffic into the networks they measure. If they inject

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

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

measurements themselves could be harmed by routers giving measurement

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

injecting artificial measurement traffic. If routers can recognize

measurement traffic and treat it separately, the measurements may not

reflect actual user traffic. If an attacker injects artificial

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

artificially lowered. Therefore, the measurement methodologies

SHOULD include appropriate techniques to reduce the probability that

measurement traffic can be distinguished from "normal" traffic.

Authentication techniques, such as digital signatures, may be used

where appropriate to guard against injected traffic attacks. The

privacy concerns of network measurement are limited by the active

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

data.

RFC 6534 Loss Episode Metrics for IPPM May 2012

# 9. References

## 9.1. Normative References

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

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

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

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

November 2002.

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

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

November 2003.

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

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

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

performance measurement with periodic streams", RFC 3432,

November 2002.

## 9.2. Informative References

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

"Framework for IP Performance Metrics", RFC 2330,

May 1998.

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

Metrics", RFC 3357, August 2002.

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

Geometric Approach to Improving Active Packet Loss

Measurement", 2008.

[Gilbert] Gilbert, E.N., "Capacity of a Burst-Noise Channel. Bell

System Technical Journal 39 pp 1253-1265", 1960.

[Elliot] Elliott, E.O., "Estimates of Error Rates for Codes on

Burst-Noise Channels. Bell System Technical Journal 42 pp

1977-1997", 1963.

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

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

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

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

November 2002.

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

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

November 2003.

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

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

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

performance measurement with periodic streams", RFC 3432,

November 2002.

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

"Framework for IP Performance Metrics", RFC 2330,

May 1998.

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

Metrics", RFC 3357, August 2002.

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

Geometric Approach to Improving Active Packet Loss

Measurement", 2008.

[Gilbert] Gilbert, E.N., "Capacity of a Burst-Noise Channel. Bell

System Technical Journal 39 pp 1253-1265", 1960.

[Elliot] Elliott, E.O., "Estimates of Error Rates for Codes on

Burst-Noise Channels. Bell System Technical Journal 42 pp

1977-1997", 1963.

RFC 6534 Loss Episode Metrics for IPPM May 2012

# Authors' Addresses

Nick Duffield

AT&T Labs-Research

180 Park Avenue

Florham Park, NJ 07932

USA

Phone: +1 973 360 8726

Fax: +1 973 360 8871

EMail: duffield@research.att.com

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

Al Morton

AT&T Labs

200 Laurel Avenue South

Middletown,, NJ 07748

USA

Phone: +1 732 420 1571

Fax: +1 732 368 1192

EMail: acmorton@att.com

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

Joel Sommers

Colgate University

304 McGregory Hall

Hamilton, NY 13346

USA

Phone: +1 315 228 7587

Fax:

EMail: jsommers@colgate.edu

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

Nick Duffield

AT&T Labs-Research

180 Park Avenue

Florham Park, NJ 07932

USA

Phone: +1 973 360 8726

Fax: +1 973 360 8871

EMail: duffield@research.att.com

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

Al Morton

AT&T Labs

200 Laurel Avenue South

Middletown,, NJ 07748

USA

Phone: +1 732 420 1571

Fax: +1 732 368 1192

EMail: acmorton@att.com

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

Joel Sommers

Colgate University

304 McGregory Hall

Hamilton, NY 13346

USA

Phone: +1 315 228 7587

Fax:

EMail: jsommers@colgate.edu

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