Network Working Group                                     A. Morton, Ed.
Internet-Draft                                                 AT&T Labs
Expires: December 26, 2006                        S. Van den Berghe, Ed.
                                                 Ghent University - IBBT
                                                           June 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
       1.1.1.  Reducing Measurement Overhead  . . . . . . . . . . . .  3
       1.1.2.  Measurement Re-use . . . . . . . . . . . . . . . . . .  4
       1.1.3.  Data Reduction and Consolidation . . . . . . . . . . .  4
       1.1.4.  Implications on Measurement Design and Reporting . . .  5
   2.  Purpose and Scope  . . . . . . . . . . . . . . . . . . . . . .  5
   3.  Description of Metric Types  . . . . . . . . . . . . . . . . .  5
     3.1.  Temporal Aggregation Description . . . . . . . . . . . . .  5
     3.2.  Spatial Aggregation Description  . . . . . . . . . . . . .  6
     3.3.  Spatial Composition Description  . . . . . . . . . . . . .  7
     3.4.  Help Metrics . . . . . . . . . . . . . . . . . . . . . . .  7
     3.5.  Higher Order Composition . . . . . . . . . . . . . . . . .  7
   4.  Requirements for Composed Metrics  . . . . . . . . . . . . . .  7
   5.  Guidelines for Defining Composed Metrics . . . . . . . . . . .  9
     5.1.  Ground Truth: Comparison with other IPPM Metrics . . . . .  9
     5.2.  Deviation from the Ground Truth  . . . . . . . . . . . . . 11
   6.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 12
   7.  Security Considerations  . . . . . . . . . . . . . . . . . . . 12
   8.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 12
   9.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 12
     9.1.  Normative References . . . . . . . . . . . . . . . . . . . 12
     9.2.  Informative References . . . . . . . . . . . . . . . . . . 13
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 14
   Intellectual Property and Copyright Statements . . . . . . . . . . 15

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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

   Network operators have deployed measurement systems to serve many
   purposes, including performance monitoring, maintenance support,
   network engineering, and customer reporting.  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 opportunites 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 OA&M for 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 nodes when

   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

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   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
   domain 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.

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1.1.4.  Implications on Measurement Design and Reporting

   If a network operator can anticipate needing to aggregate or compose
   overall metrics in the future, it is more efficient to start by
   considering the tenants of these methods in the measurement design/
   sampling plan, and reporting the results.  The Summary Statistics of
   certain metrics are more conducive to composition than others.  This
   figures prominently in the design of measurements and the results

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 function.  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.

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

   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.  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 One-Way Delay
   measurements on a certain network path obtained in 5-minute periods
   and averaging groups of 12 consecutive values, we obtain a time
   series measurement with a coarser resolution (60 minutes).  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

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   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,
   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.

3.2.  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 domain.  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 domain (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 domain.  Assume that a Service
   Provider wants to advertise the maximum delay that transit traffic
   will experience while passing through his/her domain.  There can be
   multiple edge-to-edge paths across a domain, 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

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   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

   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 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.
   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.

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 steps of
   composition or aggregation.  An example would be a the delay of a
   maximal domain obtained through the spatial composition of several
   composed end-to-end delays (obtained through spatial composition).
   All requirements for first order composition metrics apply to higher
   order composition.

   >>>>> Comment Response: are more examples needed here?

4.  Requirements for Composed Metrics

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   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

   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

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   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 Function that produces
   a Composed Metric.

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                    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
   [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 Phil Chimento, Emile
   Stephan and Lei Liang.

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

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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