Network Working Group                                     A. Morton, Ed.
Internet-Draft                                                 AT&T Labs
Expires: August 28, 2006                          S. Van den Berghe, Ed.
                                                 Ghent University - IBBT
                                                       February 24, 2006

                    Framework for Metric Composition

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Copyright Notice

   Copyright (C) The Internet Society (2006).


   This memo describes a framework for composing and aggregating metrics
   (both in time and in space) defined by RFC 2330 and developed by the
   IPPM working group.  The framework describes the generic composition
   and aggregation mechanisms.  It provides a basis for additional
   documents that implement this framework for detailed, and practically
   useful, compositions and aggregations of metrics.

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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 . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Motivation . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Purpose and Scope  . . . . . . . . . . . . . . . . . . . . . .  4
   3.  Description of Metric Types  . . . . . . . . . . . . . . . . .  4
     3.1.  Time Aggregation Description . . . . . . . . . . . . . . .  4
     3.2.  Spatial Aggregation Description  . . . . . . . . . . . . .  5
     3.3.  Spatial Composition Description  . . . . . . . . . . . . .  5
     3.4.  Help Metrics . . . . . . . . . . . . . . . . . . . . . . .  6
     3.5.  Higher Order Composition . . . . . . . . . . . . . . . . .  6
   4.  Requirements for Composed Metrics  . . . . . . . . . . . . . .  6
   5.  Guidelines for Defining Composed Metrics . . . . . . . . . . .  7
     5.1.  Ground Truth: Comparison with other IPPM Metrics . . . . .  7
     5.2.  Deviation from the Ground Truth  . . . . . . . . . . . . .  9
   6.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 10
   7.  Security Considerations  . . . . . . . . . . . . . . . . . . . 10
   8.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 10
   9.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     9.1.  Normative References . . . . . . . . . . . . . . . . . . . 10
     9.2.  Informative References . . . . . . . . . . . . . . . . . . 11
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 12
   Intellectual Property and Copyright Statements . . . . . . . . . . 13

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1.  Introduction

   The IPPM framework RFC 2330 [RFC2330] describes two forms of metric
   composition, spatial and temporal.  Also, the text 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 mentioned
   in the original IPPM framework.  The classes include temporal
   aggregation, spatial aggregation, and spatial composition.

1.1.  Motivation

   The deployment of a measurement infrastructure and the collection of
   elementary measurements are not enough to understand and keep under
   control the network's behaviour.  Network measurements need in
   general to be post-processed to be useful for the several tasks of
   network engineering and management.  The first step of this post
   processing is often a process of "composition" of single measurements
   or measurement sets into other ones.  The reasons for doing so are
   briefly introduced here.

   A first reason, mainly applicable to network engineering, is
   scaleability.  Due to the number of network elements in large
   networks, it is impossible to perform measurements from each element
   to all others.  It is necessary to select a set of links of special
   interest and to perform the measurements there.  Examples for this
   are active measurements of one-way delay, jitter, and loss.

   Another reason may be data reduction (opposite need with respect to
   the previous one, where more data is generated).  This is of interest
   for network planners and managers.  Let us assume that there is
   network domain in which delay measurements are performed among a
   subset of its elements.  A network manager might ask whether there is
   a problem with the network delay in general.  Therefore, it would be
   desirable to obtain a single value giving an indication of the
   general network delay.  This value has to be calculated from the
   elementary delay measurements, but it not obvious how: for example,
   it does not seem to be reasonable to average all delay measurements,
   as some links (e.g. having a higher bandwidth or more important
   customers) might be considered more important than others.

   Moreover, metric manipulation (or "composition") can be helpful to
   provide, from raw measurement data, some tangible, well-understood

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   and agreed upon information about the services guarantees provided by
   a network.  Such information can be used in the SLA/SLS contracts
   among a Provider and its Customers Finally, another important reason
   for composing measurements is to perform trend analysis.  For doing
   so, a single value for an hour, a day or, a month is computed from
   the basic measurements which are scheduled e.g. every five minutes.
   In doing so, trends can be more easily witnessed, like an increasing
   usage of a backbone link which might require the installation of
   alternative links or the rerouting of some network flows.

2.  Purpose and Scope

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

   This memo will retain the terminology of the IPPM Framework as much
   as possible, but will extend the terminology when necessary.

3.  Description of Metric Types

   This section defines the various classes of Composition.  There are
   two classes more accurately referred to as aggregation over time and
   space, and the third is simply composition in space.

3.1.  Time Aggregation Description

   Firstly, 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 One-Way
   Delay measurements on a certain network path obtained in 5-minute
   periods and averaging groups of 12 consecutive values, a time series
   measurement with a coarser resolution.  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

   Note that in RFC 2330, the term temporal composition is introduced,
   but with a different meaning than the one given here to aggregation
   in time.  The temporal composition considered there refers to

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   methodologies to predict future metrics on the basis of past
   observations, exploiting the time correlation that certain metrics
   can exhibit.  We do not consider this type of composition here.

3.2.  Spatial Aggregation Description

   Aggregation in space is defined as the composition of metrics of the
   same type but with different scope.  This composition may involve
   weighing the contributions of the several input metrics.  For
   example, if we want to compose together the average OWD of the
   several Origin- Destination pairs of a network domain (thus where the
   inputs are already "statistics" metrics) it makes sense to weight
   each metric according to the traffic carried on the relative OD pair:
   OWD_sum=f1*OWD_1+f2*OWD_2+...+fn*OWD_n where fi=load_OD_i/total_load.
   Another example of metric that could be "aggregated in space", is the
   maximum edge-to-edge delay across a single domain.  Assume that a
   Service Provider wants to advertise the maximum delay that transit
   traffic will experience while passing through his/her domain.  As
   there are multiple edge-to-edge paths across a domain, shown with
   different coloured arrows in the following figure, the Service
   Provider has to either advertise a list of delays each of them
   corresponding to a specific edge-to-edge path, or advertise a maximum
   value.  The latter approach is more scalable and simplifies the
   advertisement of measurement information via interdomain protocols,
   such as BGP.  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.

3.3.  Spatial Composition Description

   The concatenation in space is defined as the composition of metrics
   of same type and different (physical and non-overlapping) spatial
   scope, so that the resulting metric is representative of what the
   metric would be if directly 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 domain'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.

   Different from aggregation in space, all path's portions contribute

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   equally to the composed metric, independent of the traffic load

3.4.  Help Metrics

   Finally, note that in practice there is often the need of extracting
   a new metric making some computation over one or more metrics with
   the same spatial and time scope.  For example, the composed metric
   rtt_sample_variance may be composed from two different metrics: the
   help metric rtt_square_sum and the statistical metric rtt_sum.  This
   operation is however more a simple calculation and not an aggregation
   or a concatenation, and we'll not investigate it further in this

3.5.  Higher Order Composition

   Composed metrics might themselves be subject to further concatenation
   or aggregation.  An example would be a maximal domain obtained
   through the spatial composition of end-to-end delays, that are
   themselves obtained through spatial composition.  All requirements
   for first order composition metrics apply to higher order

4.  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;

   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.

   Each metric will require a relationship to determine the aggregated
   or composed metric.  The relationships may involve conjecture, and
   [RFC2330] lists four points that the metric definitions should

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   o  the specific conjecture applied to the metric,

   o  a justification of the practical utility of the composition, in
      terms of making accurate measurements of the metric on the path,

   o  a justification of the usefulness of the aggregation or
      composition in terms of making analysis of the path using A-frame
      concepts more effective, and

   o  an analysis of how the conjecture could be incorrect.

   For each metric, the applicable circumstances are 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 domain, or is applicable to Inter-domain 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.  Guidelines for Defining Composed Metrics

5.1.  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 Relationship that
   produces a Composed Metric.

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                    Sub-Path Metrics
           ++  M1   ++ ++  M2   ++ ++  M3   ++
       Src ||.......|| ||.......|| ||.......|| Dst
           ++   `.  ++ ++   |   ++ ++  .'   ++
                  `.        |       .-'
                    `-.     |     .'
                     ,-'         `-.
                   ,'               `.
                   |   Composition   |
                   \   Relationship  '
                    `._           _,'
           ++               |               ++
       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
   [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.

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                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.

5.2.  Deviation from the Ground Truth

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

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   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 active
      measurement results to obtain the end-to-end metric, the actual
      measured path will not be identical to the end-to-end path.  It is
      in general difficult to quantify this deviation, 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.  IANA Considerations

   This document makes no request of IANA.

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

7.  Security Considerations

8.  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 Emile Stephan and Lei

9.  References

9.1.  Normative References

              Stephan, E., "IP Performance Metrics (IPPM) for spatial
              and multicast", draft-ietf-ippm-multimetrics-00 (work in
              progress), January 2006.

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

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9.2.  Informative References

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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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