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+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)
+
+Abstract
+
+   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.
+
+Status of This Memo
+
+   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 Notice
+
+   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
+
+
+
+Duffield, et al.             Standards Track                    [Page 1]
+
+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
+
+
+
+Duffield, et al.             Standards Track                    [Page 2]
+
+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
+
+
+
+
+
+
+
+
+
+Duffield, et al.             Standards Track                    [Page 3]
+
+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
+
+
+
+
+
+Duffield, et al.             Standards Track                    [Page 4]
+
+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).
+
+
+
+Duffield, et al.             Standards Track                    [Page 5]
+
+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.
+
+
+
+Duffield, et al.             Standards Track                    [Page 6]
+
+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.
+
+
+
+Duffield, et al.             Standards Track                    [Page 7]
+
+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
+
+
+
+
+
+Duffield, et al.             Standards Track                    [Page 8]
+
+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.
+
+
+
+
+
+Duffield, et al.             Standards Track                    [Page 9]
+
+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)
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 10]
+
+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.
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 11]
+
+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.
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 12]
+
+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)
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 13]
+
+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
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 14]
+
+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.
+
+
+
+
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 15]
+
+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.
+
+
+
+Duffield, et al.             Standards Track                   [Page 16]
+
+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
+
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 17]
+
+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.
+
+
+
+Duffield, et al.             Standards Track                   [Page 18]
+
+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.
+
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 19]
+
+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.
+
+
+
+
+
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 20]
+
+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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Duffield, et al.             Standards Track                   [Page 21]
+
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