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
draft-ietf-ippm-framework-compagg-00
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Copyright (C) The Internet Society (2006).
Abstract
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",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
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
circumstances.
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
characteristics.
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
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
document.
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
composition.
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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include:
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
requirements.
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
++ ++`. ++
`-.
M6`.++
||Rcvr3
++
One-to-Group Metric
++ ++ ++ ++
Src ||........||.........||..........||Rcvr1
++ ++. ++ ++
`-.
`-. ++ ++
`-||..........||Rcvr2
++. ++
`-.
`-. ++
`-.||Rcvr3
++
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
metric.
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
RFC.
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
Liang.
9. References
9.1. Normative References
[I-D.ietf-ippm-multimetrics]
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
USA
Phone: +1 732 420 1571
Fax: +1 732 368 1192
Email: acmorton@att.com
URI: http://home.comcast.net/~acmacm/
Steven Van den Berghe (editor)
Ghent University - IBBT
G. Crommenlaan 8 bus 201
Gent 9050
Belgium
Phone: +32 9 331 49 73
Email: steven.vandenberghe@intec.ugent.be
URI: http://www.ibcn.intec.ugent.be
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