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Internet Engineering Task Force (IETF) A. Morton, Ed.
Request for Comments: 5835 AT&T Labs
Category: Informational S. Van den Berghe, Ed.
ISSN: 2070-1721 Alcatel-Lucent
April 2010
Framework for Metric Composition
Abstract
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 that are useful in practice.
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are a candidate for any level of Internet
Standard; see Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc5835.
Morton and Van den Berghe Informational [Page 1]
RFC 5835 Framework for Metric Composition April 2010
Copyright Notice
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not be created outside the IETF Standards Process, except to format
it for publication as an RFC or to translate it into languages other
than English.
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RFC 5835 Framework for Metric Composition April 2010
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. Requirements Language ...........................................6
3. Purpose and Scope ...............................................6
4. Terminology .....................................................7
4.1. Measurement Point ..........................................7
4.2. Complete Path ..............................................7
4.3. Complete Path Metric .......................................7
4.4. Complete Time Interval .....................................7
4.5. Composed Metric ............................................7
4.6. Composition Function .......................................7
4.7. Ground Truth ...............................................8
4.8. Interval ...................................................8
4.9. Sub-Interval ...............................................8
4.10. Sub-Path ..................................................8
4.11. Sub-Path Metrics ..........................................8
5. Description of Metric Types .....................................9
5.1. Temporal Aggregation Description ...........................9
5.2. Spatial Aggregation Description ............................9
5.3. Spatial Composition Description ...........................10
5.4. Help Metrics ..............................................10
5.5. Higher-Order Composition ..................................11
6. Requirements for Composed Metrics ..............................11
6.1. Note on Intellectual Property Rights (IPR) ................12
7. Guidelines for Defining Composed Metrics .......................12
7.1. Ground Truth: Comparison with Other IPPM Metrics ..........12
7.1.1. Ground Truth for Temporal Aggregation ..............14
7.1.2. Ground Truth for Spatial Aggregation ...............15
7.2. Deviation from the Ground Truth ...........................15
7.3. Incomplete Information ....................................15
7.4. Time-Varying Metrics ......................................15
8. Security Considerations ........................................16
9. Acknowledgements ...............................................16
10. References ....................................................16
10.1. Normative References .....................................16
10.2. Informative References ...................................17
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1. Introduction
The IP Performance Metrics (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 circumstances.
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.
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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
overhead.
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
needs?
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, which may also be useful
in trend analysis.
The overall value would be calculated from the elementary delay
measurements, but it is not obvious how: for example, it may not be
reasonable to average all delay measurements, as some paths (e.g.,
those having a higher bandwidth or more important customers) might be
considered more critical than others.
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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. 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].
3. Purpose and Scope
The purpose of this memo is to 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 is included, such as the assumptions under
which the relationship holds and possible sources of
error/circumstances where the composition may fail.
At this time, the scope of effort is limited to composed metrics for
packet loss, delay, and delay variation, as defined in [RFC2679],
[RFC2680], [RFC2681], [RFC3393], [RFC5481], and the comparable
metrics in [Y.1540]. Composition of packet reordering metrics
[RFC4737] and duplication metrics [RFC5560] are considered research
topics at the time this memo was prepared, and are beyond the scope
of this document.
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.
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4. Terminology
This section defines the terminology applicable to the processes of
metric composition and aggregation.
4.1. Measurement Point
A measurement point is 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.
4.2. 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.
4.3. 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.
4.4. 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.
4.5. 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.
4.6. Composition Function
A composition function is a deterministic process applied to
individual metrics to derive another metric (such as a composed
metric).
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4.7. 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.
4.8. Interval
An interval refers to a span of time.
4.9. Sub-Interval
A sub-interval is a time interval that is included in another
interval.
4.10. 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 such a sub-path is "involved" in the
complete path.
Since sub-paths terminate on hosts, it is important to describe how
sub-paths are considered to be joined. In practice, the Source and
Destination hosts may perform the function 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
concession).
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 constitute another sub-path that is involved
in the complete path, and should be characterized and included in the
composed metric.
4.11. Sub-Path Metrics
A sub-path path metric is an element of the process to derive a
composed metric, quantifying some aspect of the performance of a
particular sub-path from its Source to Destination.
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5. 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.
5.1. 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 (OWD) 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 maximum of 12 consecutive 5-minute maxima and the minimum 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.
5.2. 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:
OWD_sum=f1*OWD_1+f2*OWD_2+...+fn*OWD_n
where fi=load_OD_i/total_load.
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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 of
coarser aggregates in general. 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 referring to the same time window, or the time
window of each composed metric does not affect the aggregated metric.
5.3. Spatial Composition Description
Concatenation in space is defined as the composition of metrics of
same type with (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 mean OWDs of adjacent edge-
to-edge networks, 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.
5.4. 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.
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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.
5.5. 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 second step
of aggregation would take 24 hourly metrics and estimate the
performance over a day.
6. 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.
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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 perhaps only loosely synchronized time
intervals, or has no timing requirements at all.
o Requires assumption of component metric independence with regard
to the metric being defined/composed, or other assumptions.
o Has known sources of inaccuracy/error and identifies the sources.
6.1. Note on Intellectual Property Rights (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.
7. Guidelines for Defining Composed Metrics
7.1. 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 with regard to
the complete path metric.
Further, we observe that a spatial metric [RFC5644] collected for
packets traveling over the same set of sub-paths provides 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 [RFC5644]) 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.
7.1.1. Ground Truth for Temporal Aggregation
Temporal aggregation involves measurements made over sub-intervals of
the complete time interval between the same Source and Destination.
Therefore, the ground truth is the metric measured over the desired
interval.
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7.1.2. 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.
7.2. 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
metric.
o A difference in scope. When concatenating many active measurement
results (from two or more sub-paths) to obtain the complete path
metric, the actual measured path will not be identical to the
complete path. It is in general difficult to quantify this
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 a section
identifying the deviation from the ground truth.
7.3. 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
"undefined".
7.4. 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.
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Some metrics are predominantly* time-invariant, such as the actual
minimum one-way delay of a 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.)
8. Security Considerations
The security considerations that apply to any active measurement of
live networks are relevant here as well. See [RFC4656] and
[RFC5357].
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
[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., Ed., "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.
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[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
[RFC2679] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
Delay Metric for IPPM", RFC 2679, September 1999.
[RFC2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
Packet Loss Metric for IPPM", RFC 2680, September 1999.
[RFC2681] Almes, G., Kalidindi, S., and M. Zekauskas, "A Round-trip
Delay Metric for IPPM", RFC 2681, September 1999.
[RFC3393] Demichelis, C. and P. Chimento, "IP Packet Delay
Variation Metric for IP Performance Metrics (IPPM)",
RFC 3393, November 2002.
[RFC4737] Morton, A., Ciavattone, L., Ramachandran, G., Shalunov,
S., and J. Perser, "Packet Reordering Metrics", RFC 4737,
November 2006.
[RFC5481] Morton, A. and B. Claise, "Packet Delay Variation
Applicability Statement", RFC 5481, March 2009.
[RFC5560] Uijterwaal, H., "A One-Way Packet Duplication Metric",
RFC 5560, May 2009.
[RFC5644] Stephan, E., Liang, L., and A. Morton, "IP Performance
Metrics (IPPM): Spatial and Multicast", RFC 5644,
October 2009.
[Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data
communication service - IP packet transfer and
availability performance parameters", November 2007.
Morton and Van den Berghe Informational [Page 17]
RFC 5835 Framework for Metric Composition April 2010
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)
Alcatel-Lucent
Copernicuslaan 50
Antwerp 2018
Belgium
Phone: +32 3 240 3983
EMail: steven.van_den_berghe@alcatel-lucent.com
Morton and Van den Berghe Informational [Page 18]