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-
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	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.
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	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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