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rfc:rfc6534

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.

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 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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