Network Working Group                                     A. Morton, Ed.
Internet-Draft                                                 AT&T Labs
Intended status: Informational                    S. Van den Berghe, Ed.
Expires: May 2, December 23, 2009                       Ghent University - IBBT
                                                        October 29, 2008
                                                           June 21, 2009

                    Framework for Metric Composition

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   This memo describes a detailed framework for composing and
   aggregating metrics (both in time and in space) originally defined by
   the IP Performance Metrics (IPPM) RFC 2330 and developed by the IETF.
   This new framework memo describes the generic composition and
   aggregation mechanisms.  The memo provides a basis for additional
   documents that implement the framework to define detailed
   compositions and aggregations of metrics which are useful in

Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in RFC 2119 [RFC2119].

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
     1.1.  Motivation . . . . . . . . . . . . . . . . . . . . . . . .  4
       1.1.1.  Reducing Measurement Overhead  . . . . . . . . . . . .  4
       1.1.2.  Measurement Re-use . . . . . . . . . . . . . . . . . .  5
       1.1.3.  Data Reduction and Consolidation . . . . . . . . . . .  5
       1.1.4.  Implications on Measurement Design and Reporting . . .  6
   2.  Purpose and Scope  . . . . . . . . . . . . . . . . . . . . . .  6
   3.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  6
     3.1.  Measurement Point  . . . . . . . . . . . . . . . . . . . .  6
     3.2.  Complete Path  . . . . . . . . . . . . . . . . . . . . . .  7
     3.3.  Complete Path Metric . . . . . . . . . . . . . . . . . . .  7
     3.4.  Complete Time Interval . . . . . . . . . . . . . . . . . .  7
     3.5.  Composed Metric  . . . . . . . . . . . . . . . . . . . . .  7
     3.6.  Composition Function . . . . . . . . . . . . . . . . . . .  7
     3.7.  Index  . . . . . . . . . . . . . . . . . . . . . . . . . .  7
     3.8.  Ground Truth . . . . . . . . . . . . . . . . . . . . . . .  8
     3.9.  7
     3.8.  Interval . . . . . . . . . . . . . . . . . . . . . . . . .  8
     3.10.  7
     3.9.  Sub-interval . . . . . . . . . . . . . . . . . . . . . . .  8
     3.10. Sub-path . . . . . . . . . . . . . . . . . . . . . . . . .  8
     3.11. Sub-path Metrics . . . . . . . . . . . . . . . . . . . . .  8
   4.  Description of Metric Types  . . . . . . . . . . . . . . . . .  8
     4.1.  Temporal Aggregation Description . . . . . . . . . . . . .  8
     4.2.  Spatial Aggregation Description  . . . . . . . . . . . . .  9
     4.3.  Spatial Composition Description  . . . . . . . . . . . . . 10
     4.4.  Help Metrics . . . . . . . . . . . . . . . . . . . . . . . 10
     4.5.  Higher Order Composition . . . . . . . . . . . . . . . . . 10
   5.  Requirements for Composed Metrics  . . . . . . . . . . . . . . 11
     5.1.  Note on IPR  . . . . . . . . . . . . . . . . . . . . . . . 12
   6.  Guidelines for Defining Composed Metrics . . . . . . . . . . . 12
     6.1.  Ground Truth: Comparison with other IPPM Metrics . . . . . 12
       6.1.1.  Ground Truth for Temporal Aggregation  . . . . . . . . 14
       6.1.2.  Ground Truth for Spatial Aggregation . . . . . . . . . 14 15
     6.2.  Deviation from the Ground Truth  . . . . . . . . . . . . . 14 15
     6.3.  Incomplete Information . . . . . . . . . . . . . . . . . . 15
     6.4.  Time Varying Metrics . . . . . . . . . . . . . . . . . . . 15
   7.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 15 16
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 15 16
   9.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 15 16
   10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 16
     10.1. Normative References . . . . . . . . . . . . . . . . . . . 16
     10.2. Informative References . . . . . . . . . . . . . . . . . . 16 17
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 16
   Intellectual Property and Copyright Statements . . . . . . . . . . 18 17

1.  Introduction

   The IPPM framework [RFC2330] describes two forms of metric
   composition, spatial and temporal.  The text also suggests that the
   concepts of the analytical framework (or A-frame) would help to
   develop useful relationships to derive the composed metrics from real
   metrics.  The effectiveness of composed metrics is dependent on their
   usefulness in analysis and applicability to practical measurement

   This memo expands on the notion of composition, and provides a
   detailed framework for several classes of metrics that were described
   in the original IPPM framework.  The classes include temporal
   aggregation, spatial aggregation, and spatial composition.

1.1.  Motivation

   Network operators have deployed measurement systems to serve many
   purposes, including performance monitoring, maintenance support,
   network engineering, and reporting performance to customers.  The
   collection of elementary measurements alone is not enough to
   understand a network's behaviour.  In general, measurements need to
   be post-processed to present the most relevant information for each
   purpose.  The first step is often a process of "composition" of
   single measurements or measurement sets into other forms.
   Composition and aggregation present several more post-processing
   opportunities to the network operator, and we describe the key
   motivations below.

1.1.1.  Reducing Measurement Overhead

   A network's measurement possibilities scale upward with the square of
   the number of nodes.  But each measurement implies overhead, in terms
   of the storage for the results, the traffic on the network (assuming
   active methods), and the operation and administration of the
   measurement system itself.  In a large network, it is impossible to
   perform measurements from each node to all others.

   An individual network operator should be able to organize their
   measurement paths along the lines of physical topology, or routing
   areas/Autonomous Systems, and thus minimize dependencies and overlap
   between different measurement paths.  This way, the sheer number of
   measurements can be reduced, as long as the operator has a set of
   methods to estimate performance between any particular pair of nodes
   when needed.

   Composition and aggregation play a key role when the path of interest
   spans multiple networks, and where each operator conducts their own
   measurements.  Here, the complete path performance may be estimated
   from measurements on the component parts.

   Operators that take advantage of the composition and aggregation
   methods recognize that the estimates may exhibit some additional
   error beyond that inherent in the measurements themselves, and so
   they are making a trade-off to achieve reasonable measurement system

1.1.2.  Measurement Re-use

   There are many different measurement users, each bringing specific
   requirements for the reporting timescale.  Network managers and
   maintenance forces prefer to see results presented very rapidly, to
   detect problems quickly or see if their action has corrected a
   problem.  On the other hand, network capacity planners and even
   network users sometimes prefer a long-term view of performance, for
   example to check trends.  How can one set of measurements serve both

   The answer lies in temporal aggregation, where the short-term
   measurements needed by the operations community are combined to
   estimate a longer-term result for others.  Also, problems with the
   measurement system itself may be isolated to one or more of the
   short-term measurements, rather than possibly invalidating an entire
   long-term measurement if the problem was undetected.

1.1.3.  Data Reduction and Consolidation

   Another motivation is data reduction.  Assume there is a network in
   which delay measurements are performed among a subset of its nodes.
   A network manager might ask whether there is a problem with the
   network delay in general.  It would be desirable to obtain a single
   value that gives an indication of the overall network delay.  Spatial
   aggregation methods would address this need, and can produce the
   desired "single figure of merit" asked for, one that may also be
   useful in trend analysis.

   The overall value would be calculated from the elementary delay
   measurements, but it not obvious how: for example, it may not to be
   reasonable to average all delay measurements, as some paths (e.g.
   having a higher bandwidth or more important customers) might be
   considered more critical than others.

   Metric composition can help to provide, from raw measurement data,
   some tangible, well-understood and agreed upon information about the
   service guarantees provided by a network.  Such information can be
   used in the Service Level Agreement/Service Level Specification (SLA/
   SLS) contracts between a service provider and its customers.

1.1.4.  Implications on Measurement Design and Reporting

   If a network measurement system operator anticipates needing to
   produce overall metrics by composition, then it is prudent to keep
   that requirement in mind when considering the measurement design and
   sampling plan.  Also, certain summary statistics are more conducive
   to composition than others, and this figures prominently in the
   design of measurements and when reporting the results.

2.  Purpose and Scope

   The purpose of this memo is provide a common framework for the
   various classes of metrics that are composed from primary metrics.
   The scope is limited to the definitions of metrics that are composed
   from primary metrics using a deterministic function.  Key information
   about each composed metric, such as the assumptions under which the
   relationship holds and possible sources of error/circumstances where
   the composition may fail, are included.

   At this time, the scope of effort is limited to composed metrics for
   packet loss, delay, and delay variation.  Composition of packet
   reordering metrics is considered a research topic at the time this
   memo was prepared, and beyond its scope.

   This memo will retain the terminology of the IPPM Framework
   [RFC2330]as much as possible, but will extend the terminology when
   necessary.  It is assumed that the reader is familiar with the
   concepts introduced in [RFC2330], as they will not be repeated here.

3.  Terminology

   This section defines the terminology applicable to the processes of
   Metric Composition and Aggregation.

3.1.  Measurement Point

   The logical or physical location where packet observations are made.
   The term Measurement Point is synonymous with the term "observation
   position" used in [RFC2330] when describing the notion of wire time.
   A measurement point may be at the boundary between a host and an
   adjacent link (physical), or it may be within a host (logical) that
   performs measurements where the difference between host time and wire
   time is understood.

3.2.  Complete Path

   The complete path is the actual path that a packet would follow as it
   travels from the packet's Source to its Destination.  A Complete path
   may span the administrative boundaries of one or more networks.

3.3.  Complete Path Metric

   The complete path metric is the Source to Destination metric that a
   composed metric attempts to estimate.  A complete path metric
   represents the ground-truth for a composed metric.

3.4.  Complete Time Interval

   The complete time interval is comprised of two or more contiguous
   sub-intervals, and is the interval whose performance will be
   estimated through temporal aggregation.

3.5.  Composed Metric

   A composed metric is an estimate of an actual metric describing the
   performance of a path over some time interval.  A composed metric is
   derived from other metrics by applying a deterministic process or
   function (e.g., a composition function).  The process may use metrics
   that are identical to the metric being composed, or metrics that are
   dissimilar, or some combination of both types.

3.6.  Composition Function

   A composition function is a deterministic process applied to
   individual metrics to derive another metric (such as a Composed

3.7.  Index

   An Index is a metric for which the output value range has been
   selected for convenience or clarity, and the behavior of which is
   selected to support ease of understanding.  The deterministic
   function for an index is often developed after the index range and
   index behavior have been determined.  Examples include the Effective
   Equipment Impairment Factor as described in section 3.5 of ITU-T
   Recommendation [G.107].

   >>> Comment: Perhaps the definition of an Index should move to the
   PMOL Framework?

3.8.  Ground Truth

   As applied here,  Ground Truth

   As applied here, the notion of ground truth is defined as the actual
   performance of a network path over some time interval.  The ground
   truth is a metric on the (unavailable) packet transfer information
   for the desired path and time interval that a composed metric seeks
   to estimate.


3.8.  Interval

   A span of time.


3.9.  Sub-interval

   A Sub-interval is a time interval that is included in another


3.10.  Sub-path

   A Sub-path is a portion of the complete path where at least the Sub-
   path Source and Destination hosts are constituents of the complete
   path.  We say that this such a sub-path is "involved" in the complete


   Since sub-paths terminate on hosts, it is important to describe how
   sub-paths are considered to be joined.  In practice, the Source and
   Desitination hosts may perform the funtion of measurement points.

   If the Destination and Source hosts of two adjoining paths are co-
   located and the link between them would contribute negligible
   performance, then these hosts can be considered equivalent (even if
   there is no physical link between them, this is a practical

   If the Destination and Source hosts of two adjoining paths have a
   link between them that contributes to the complete path performance,
   then the link and hosts constitutes another sub-path that is involved
   in the complete path, and should be characterized and included in the
   composed metric.

3.11.  Sub-path Metrics

   A sub-path path metric is an element of the process to derive a
   Composite metric, quantifying some aspect of the performance a
   particular sub-path from its Source to Destination.

4.  Description of Metric Types

   This section defines the various classes of Composition.  There are
   two classes more accurately described as aggregation over time and
   space, and the third involves concatenation in space.

4.1.  Temporal Aggregation Description

   Aggregation in time is defined as the composition of metrics with the
   same type and scope obtained in different time instants or time
   windows.  For example, starting from a time series of the
   measurements of maximum and minimum One-Way Delay on a certain
   network path obtained over 5-minute intervals, we obtain a time
   series measurement with a coarser resolution (60 minutes) by taking
   the max of 12 consecutive 5-minute maxima and the min of 12
   consecutive 5-minute minima.

   The main reason for doing time aggregation is to reduce the amount of
   data that has to be stored, and make the visualization/spotting of
   regular cycles and/or growing or decreasing trends easier.  Another
   useful application is to detect anomalies or abnormal changes in the
   network characteristics.

   In RFC 2330, the term "temporal composition" is introduced and
   differs from temporal aggregation in that it refers to methodologies
   to predict future metrics on the basis of past observations (of the
   same metrics), exploiting the time correlation that certain metrics
   can exhibit.  We do not consider this type of composition here.

   >>>>>>>>Comment: Why no forecasting?  This was apparently a limit on
   the Geant2 project, but may not apply here.

4.2.  Spatial Aggregation Description

   Aggregation in space is defined as the combination of metrics of the
   same type and different scope, in order to estimate the overall
   performance of a larger network.  This combination may involve
   weighing the contributions of the input metrics.

   Suppose we want to compose the average One-Way-Delay (OWD)
   experienced by flows traversing all the Origin-Destination (OD) pairs
   of a network (where the inputs are already metric "statistics").
   Since we wish to include the effect of the traffic matrix on the
   result, it makes sense to weight each metric according to the traffic
   carried on the corresponding OD pair:


   where fi=load_OD_i/total_load.

   A simple average OWD across all network OD pairs would not use the
   traffic weighting.

   Another example metric that is "aggregated in space", is the maximum
   edge-to-edge delay across a single network.  Assume that a Service
   Provider wants to advertise the maximum delay that transit traffic
   will experience while passing through his/her network.  There can be
   multiple edge-to-edge paths across a network, and the Service
   Provider chooses either to publish a list of delays (each
   corresponding to a specific edge-to-edge path), or publish a single
   maximum value.  The latter approach simplifies the publication of
   measurement information, and may be sufficient for some purposes.
   Similar operations can be provided to other metrics, e.g. "maximum
   edge-to-edge packet loss", etc.

   We suggest that space aggregation is generally useful to obtain a
   summary view of the behaviour of large network portions, or in
   general of coarser aggregates.  The metric collection time instant,
   i.e. the metric collection time window of measured metrics is not
   considered in space aggregation.  We assume that either it is
   consistent for all the composed metrics, e.g. compose a set of
   average delays all referred to the same time window, or the time
   window of each composed metric does not affect aggregated metric.

4.3.  Spatial Composition Description

   Concatenation in space is defined as the composition of metrics of
   same type and (ideally) different spatial scope, so that the
   resulting metric is representative of what the metric would be if
   obtained with a direct measurement over the sequence of the several
   spatial scopes.  An example is the sum of OWDs of different edge-to-
   edge network's delays, where the intermediate edge points are close
   to each other or happen to be the same.  In this way, we can for
   example estimate OWD_AC starting from the knowledge of OWD_AB and
   OWD_BC.  Note that there may be small gaps in measurement coverage,
   likewise there may be small overlaps (e.g., the link where test
   equipment connects to the network).

   One key difference from examples of aggregation in space is that all
   sub-paths contribute equally to the composed metric, independent of
   the traffic load present.

4.4.  Help Metrics

   In practice there is often the need to compute a new metric using one
   or more metrics with the same spatial and time scope.  For example,
   the metric rtt_sample_variance may be computed from two different
   metrics: the help metrics rtt_square_sum and the rtt_sum.  The
   process of using help metrics is a simple calculation and not an
   aggregation or a concatenation, and will not be investigated further
   in this memo.

4.5.  Higher Order Composition

   Composed metrics might themselves be subject to further steps of
   composition or aggregation.  An example would be the delay of a
   maximal path obtained through the spatial composition of several
   composed delays for each Complete Path in the maximal path (obtained
   through spatial composition).  All requirements for first order
   composition metrics apply to higher order composition.

   An example using temporal aggregation: twelve 5-minute metrics are
   aggregated to estimate the performance over an hour.  The seconds second step
   of aggregation would take 24 hourly metrics and estimate the
   performance over a day.

5.  Requirements for Composed Metrics

   The definitions for all composed metrics MUST include sections to
   treat the following topics.

   The description of each metric will clearly state:

   1.  the definition (and statistic, where appropriate);

   2.  the composition or aggregation relationship;

   3.  the specific conjecture on which the relationship is based and
       assumptions of the statistical model of the process being
       measured, if any (see [RFC2330] section 12);

   4.  a justification of practical utility or usefulness for analysis
       using the A-frame concepts;

   5.  one or more examples of how the conjecture could be incorrect and
       lead to inaccuracy;

   6.  the information to be reported.

   For each metric, the applicable circumstances will be defined, in
   terms of whether the composition or aggregation:

   o  Requires homogeneity of measurement methodologies, or can allow a
      degree of flexibility (e.g., active or passive methods produce the
      "same" metric).  Also, the applicable sending streams will be
      specified, such as Poisson, Periodic, or both.

   o  Needs information or access that will only be available within an
      operator's network, or is applicable to Inter-network composition.

   o  Requires precisely synchronized measurement time intervals in all
      component metrics, or loosely synchronized, or no timing

   o  Requires assumption of component metric independence w.r.t. the
      metric being defined/composed, or other assumptions.

   o  Has known sources of inaccuracy/error, and identifies the sources.

5.1.  Note on IPR

   If one or more components of the composition process are encumbered
   by Intellectual Property Rights (IPR), then the resulting Composed
   Metrics may be encumbered as well.  See BCP 79 [RFC3979] for IETF
   policies on IPR disclosure.

6.  Guidelines for Defining Composed Metrics

6.1.  Ground Truth: Comparison with other IPPM Metrics

   Figure 1 illustrates the process to derive a metric using spatial
   composition, and compares the composed metric to other IPPM metrics.

   Metrics <M1, M2, M3> describe the performance of sub-paths between
   the Source and Destination of interest during time interval <T, Tf>.
   These metrics are the inputs for a Composition Function that produces
   a Composed Metric.

                               Sub-Path Metrics
                      ++  M1   ++ ++  M2   ++ ++  M3   ++
                  Src ||.......|| ||.......|| ||.......|| Dst
                      ++   `.  ++ ++   |   ++ ++  .'   ++
                             `.        |       .-'
                               `-.     |     .'
                                ,-'         `-.
                              ,'               `.
                              |   Composition   |
                              \     Function    '
                               `._           _,'
                      ++               |               ++
                  Src ||...............................|| Dst
                      ++        Composed Metric        ++

                      ++      Complete Path Metric     ++
                  Src ||...............................|| Dst
                      ++                               ++
                                Spatial Metric
                      ++   S1   ++   S2    ++    S3    ++
                  Src ||........||.........||..........|| Dst
                      ++        ++         ++          ++

               Figure 1: Comparison with other IPPM metrics

   The Composed Metric is an estimate of an actual metric collected over
   the complete Source to Destination path.  We say that the Complete
   Path Metric represents the "Ground Truth" for the Composed Metric.
   In other words, Composed Metrics seek to minimize error w.r.t. the
   Complete Path Metric.

   Further, we observe that a Spatial Metric
   [I-D.ietf-ippm-multimetrics] collected for packets traveling over the
   same set of sub-paths provide a basis for the Ground Truth of the
   individual Sub-Path metrics.  We note that mathematical operations
   may be necessary to isolate the performance of each sub-path.

   Next, we consider multiparty metrics as defined in [I-D.ietf-ippm-
   multimetrics], and their spatial composition.  Measurements to each
   of the Receivers produce an element of the one-to-group metric.
   These elements can be composed from sub-path metrics and the composed
   metrics can be combined to create a composed one-to-group metric.
   Figure 2 illustrates this process.

                             Sub-Path Metrics
                    ++  M1   ++ ++  M2   ++ ++  M3   ++
                Src ||.......|| ||.......|| ||.......||Rcvr1
                    ++       ++ ++`.     ++ ++       ++
                                     M4`.++ ++  M5   ++
                                         || ||.......||Rcvr2
                                         ++ ++`.     ++

                            One-to-Group Metric
                    ++        ++         ++          ++
                Src ||........||.........||..........||Rcvr1
                    ++        ++.        ++          ++
                                    `-.  ++          ++
                                         ++.         ++
                                               `-.   ++

               Figure 2: Composition of One-to-Group Metrics

   Here, Sub-path Metrics M1, M2, and M3 are combined using a
   relationship to compose the metric applicable to the Src-Rcvr1 path.
   Similarly, M1, M4, and M5 are used to compose the Src-Rcvr2 metric
   and M1, M4, and M6 compose the Src-Rcvr3 metric.

   The Composed One-to-Group Metric would list the Src-Rcvr metrics for
   each Receiver in the Group:

   (Composed-Rcvr1, Composed-Rcvr2, Composed-Rcvr3)

   The "Ground Truth" for this composed metric is of course an actual
   One-to-Group metric, where a single source packet has been measured
   after traversing the Complete Paths to the various receivers.

6.1.1.  Ground Truth for Temporal Aggregation

   Temporal Aggregation involves measurements made over sub-intervals of
   the desired test complete time interval between the same Source and Destination.
   Therefore, the "Ground Truth" is the metric measured over the desired

6.1.2.  Ground Truth for Spatial Aggregation

   Spatial Aggregation combines many measurements using a weighting
   function to provide the same emphasis as though the measurements were
   based on actual traffic, with inherent weights.  Therefore, the
   "Ground Truth" is the metric measured on the actual traffic instead
   of the active streams that sample the performance.

6.2.  Deviation from the Ground Truth

   A metric composition can deviate from the ground truth for several
   reasons.  Two main aspects are:

   o  The propagation of the inaccuracies of the underlying measurements
      when composing the metric.  As part of the composition function,
      errors of measurements might propagate.  Where possible, this
      analysis should be made and included with the description of each

   o  A difference in scope.  When concatenating hop-by-hop many active measurement
      results (from two or more sub-paths) to obtain the end-to-end complete path
      metric, the actual measured path will not be identical to the end-to-end
      complete path.  It is in general difficult to quantify this deviation,
      deviation with exactness, but a metric definition might identify
      guidelines for keeping the deviation as small as possible.

   The description of the metric composition MUST include an section
   identifying the deviation from the ground truth.

6.3.  Incomplete Information

   In practice, when measurements cannot be initiated on a sub-path or
   during a particular measurement interval (and perhaps the measurement
   system gives up during the test interval), then there will not be a
   value for the sub-path reported, and the result SHOULD be recorded as

6.4.  Time Varying Metrics

   The measured values of many metrics depend on time-variant factors,
   such as the level of network traffic on the source to destination
   path.  Traffic levels often exhibit diurnal (or daily) variation, but
   a 24 hour measurement interval would obscure it.  Temporal
   Aggregation of hourly results to estimate the daily metric would have
   the same effect, and so the same cautions are warranted.

   Some metrics are predominantly* time-invariant, such as the actual
   minimum one-way delay of fixed path, and therefore temporal
   aggregation does not obscure the results as long as the path is
   stable.  However, paths do vary, and sometimes on less predictable
   time intervals than traffic variations. (* Note - It is recognized
   that propagation delay on transmission facilities may have diurnal,
   seasonal, and even longer-term variations.)

7.  IANA Considerations

   This document makes no request of IANA.

   Note to RFC Editor: this section may be removed on publication as an

8.  Security Considerations

   The security considerations that apply to any active measurement of
   live networks are relevant here as well.  See [RFC4656]. [RFC4656], and

   The exchange of sub-path measurements among network providers may be
   a source of concern, and the information should be sufficiently
   anonymized to avoid revealing unnecessary operational details (e.g.,
   the network addresses of measurement devices).  However, the schema
   for measurement exchange is beyond the scope of this memo, and likely
   to be covered by bilateral agreements for some time to come.

9.  Acknowledgements

   The authors would like to thank Maurizio Molina, Andy Van Maele,
   Andreas Haneman, Igor Velimirovic, Andreas Solberg, Athanassios
   Liakopulos, David Schitz, Nicolas Simar and the Geant2 Project.  We
   also acknowledge comments and suggestions from Phil Chimento, Emile
   Stephan, Lei Liang, Stephen Wolff, Reza Fardid, Loki Jorgenson, and
   Alan Clark.

10.  References

10.1.  Normative References

              Stephan, E., Liang, L., and A. Morton, "IP Performance
              Metrics (IPPM) for spatial and multicast",
              draft-ietf-ippm-multimetrics-11 (work in progress),
              October 2008.
              April 2009.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2330]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
              "Framework for IP Performance Metrics", RFC 2330,
              May 1998.

   [RFC3979]  Bradner, S., "Intellectual Property Rights in IETF
              Technology", BCP 79, RFC 3979, March 2005.

   [RFC4656]  Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M.
              Zekauskas, "A One-way Active Measurement Protocol
              (OWAMP)", RFC 4656, September 2006.

   [RFC5357]  Hedayat, K., Krzanowski, R., Morton, A., Yum, K., and J.
              Babiarz, "A Two-Way Active Measurement Protocol (TWAMP)",
              RFC 5357, October 2008.

10.2.  Informative References

   [G.107]    ITU-T Recommendation G.107, ""The E-model, a computational
              model for use in transmission planning"", March 2005.

Authors' Addresses

   Al Morton (editor)
   AT&T Labs
   200 Laurel Avenue South
   Middletown,, NJ  07748

   Phone: +1 732 420 1571
   Fax:   +1 732 368 1192

   Steven Van den Berghe (editor)
   Ghent University - IBBT
   G. Crommenlaan 8 bus 201
   Gent  9050

   Phone: +32 9 331 49 73

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