Internet Engineering Task Force (IETF) A. Morton
Request for Comments: 6049 AT&T Labs
Category: Standards Track E. Stephan
ISSN: 2070-1721 France Telecom Orange
January 2011
Spatial Composition of Metrics
Abstract
This memo utilizes IP performance metrics that are applicable to both
complete paths and sub-paths, and it defines relationships to compose
a complete path metric from the sub-path metrics with some accuracy
with regard to the actual metrics. This is called "spatial
composition" in RFC 2330. The memo refers to the framework for
metric composition, and provides background and motivation for
combining metrics to derive others. The descriptions of several
composed metrics and statistics follow.
Status of This Memo
This is an Internet Standards Track document.
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). Further information on
Internet Standards is available in 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/rfc6049.
Morton & Stephan Standards Track [Page 1]
RFC 6049 Spatial Composition January 2011
Copyright Notice
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Table of Contents
1. Introduction ....................................................4
1.1. Motivation .................................................6
1.2. Requirements Language ......................................6
2. Scope and Application ...........................................6
2.1. Scope of Work ..............................................6
2.2. Application ................................................7
2.3. Incomplete Information .....................................7
3. Common Specifications for Composed Metrics ......................8
3.1. Name: Type-P ...............................................8
3.1.1. Metric Parameters ...................................8
3.1.2. Definition and Metric Units .........................9
3.1.3. Discussion and Other Details ........................9
3.1.4. Statistic ...........................................9
3.1.5. Composition Function ................................9
3.1.6. Statement of Conjecture and Assumptions ............10
3.1.7. Justification of the Composition Function ..........10
3.1.8. Sources of Deviation from the Ground Truth .........10
3.1.9. Specific Cases where the Conjecture Might Fail .....11
3.1.10. Application of Measurement Methodology ............12
4. One-Way Delay Composed Metrics and Statistics ..................12
4.1. Name: Type-P-Finite-One-way-Delay--Stream .........12
4.1.1. Metric Parameters ..................................12
4.1.2. Definition and Metric Units ........................12
4.1.3. Discussion and Other Details .......................13
4.1.4. Statistic ..........................................13
4.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean ..........13
4.2.1. Metric Parameters ..................................13
4.2.2. Definition and Metric Units of the Mean Statistic ..14
4.2.3. Discussion and Other Details .......................14
4.2.4. Statistic ..........................................14
4.2.5. Composition Function: Sum of Means .................14
4.2.6. Statement of Conjecture and Assumptions ............15
4.2.7. Justification of the Composition Function ..........15
4.2.8. Sources of Deviation from the Ground Truth .........15
4.2.9. Specific Cases where the Conjecture Might Fail .....15
4.2.10. Application of Measurement Methodology ............16
4.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum .......16
4.3.1. Metric Parameters ..................................16
4.3.2. Definition and Metric Units of the Minimum
Statistic ..........................................16
4.3.3. Discussion and Other Details .......................16
4.3.4. Statistic ..........................................16
4.3.5. Composition Function: Sum of Minima ................16
4.3.6. Statement of Conjecture and Assumptions ............17
4.3.7. Justification of the Composition Function ..........17
4.3.8. Sources of Deviation from the Ground Truth .........17
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4.3.9. Specific Cases where the Conjecture Might Fail .....17
4.3.10. Application of Measurement Methodology ............17
5. Loss Metrics and Statistics ....................................18
5.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 18
5.1.1. Metric Parameters ..................................18
5.1.2. Definition and Metric Units ........................18
5.1.3. Discussion and Other Details .......................18
5.1.4. Statistic:
Type-P-One-way-Packet-Loss-Empirical-Probability ...18
5.1.5. Composition Function: Composition of
Empirical Probabilities ............................18
5.1.6. Statement of Conjecture and Assumptions ............19
5.1.7. Justification of the Composition Function ..........19
5.1.8. Sources of Deviation from the Ground Truth .........19
5.1.9. Specific Cases where the Conjecture Might Fail .....19
5.1.10. Application of Measurement Methodology ............19
6. Delay Variation Metrics and Statistics .........................20
6.1. Name: Type-P-One-way-pdv-refmin--Stream ...........20
6.1.1. Metric Parameters ..................................20
6.1.2. Definition and Metric Units ........................20
6.1.3. Discussion and Other Details .......................21
6.1.4. Statistics: Mean, Variance, Skewness, Quantile .....21
6.1.5. Composition Functions ..............................22
6.1.6. Statement of Conjecture and Assumptions ............23
6.1.7. Justification of the Composition Function ..........23
6.1.8. Sources of Deviation from the Ground Truth .........23
6.1.9. Specific Cases where the Conjecture Might Fail .....24
6.1.10. Application of Measurement Methodology ............24
7. Security Considerations ........................................24
7.1. Denial-of-Service Attacks .................................24
7.2. User Data Confidentiality .................................24
7.3. Interference with the Metrics .............................24
8. IANA Considerations ............................................25
9. Contributors and Acknowledgements ..............................27
10. References ....................................................28
10.1. Normative References .....................................28
10.2. Informative References ...................................28
1. Introduction
The IP Performance Metrics (IPPM) framework [RFC2330] describes two
forms of metric composition: spatial and temporal. The composition
framework [RFC5835] expands and further qualifies these original
forms into three categories. This memo describes spatial
composition, one of the categories of metrics under the umbrella of
the composition framework.
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Spatial composition encompasses the definition of performance metrics
that are applicable to a complete path, based on metrics collected on
various sub-paths.
The main purpose of this memo is to define the deterministic
functions that yield the complete path metrics using metrics of the
sub-paths. The effectiveness of such metrics is dependent on their
usefulness in analysis and applicability with practical measurement
methods.
The relationships may involve conjecture, and [RFC2330] lists four
points that the metric definitions should include:
o the specific conjecture applied to the metric and assumptions of
the statistical model of the process being measured (if any; see
[RFC2330], Section 12),
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 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.
Also, [RFC2330] gives an example using the conjecture that the delay
of a path is very nearly the sum of the delays of the exchanges and
clouds of the corresponding path digest. This example is
particularly relevant to those who wish to assess the performance of
an inter-domain path without direct measurement, and the performance
estimate of the complete path is related to the measured results for
various sub-paths instead.
Approximate functions between the sub-path and complete path metrics
are useful, with knowledge of the circumstances where the
relationships are/are not applicable. For example, we would not
expect that delay singletons from each sub-path would sum to produce
an accurate estimate of a delay singleton for the complete path
(unless all the delays were essentially constant -- very unlikely).
However, other delay statistics (based on a reasonable sample size)
may have a sufficiently large set of circumstances where they are
applicable.
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1.1. Motivation
One-way metrics defined in other RFCs (such as [RFC2679] and
[RFC2680]) all assume that the measurement can be practically carried
out between the source and the destination of interest. Sometimes
there are reasons that the measurement cannot be executed from the
source to the destination. For instance, the measurement path may
cross several independent domains that have conflicting policies,
measurement tools and methods, and measurement time assignment. The
solution then may be the composition of several sub-path
measurements. This means each domain performs the one-way
measurement on a sub-path between two nodes that are involved in the
complete path, following its own policy, using its own measurement
tools and methods, and using its own measurement timing. Under the
appropriate conditions, one can combine the sub-path one-way metric
results to estimate the complete path one-way measurement metric with
some degree of accuracy.
1.2. 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].
In this memo, the characters "<=" should be read as "less than or
equal to" and ">=" as "greater than or equal to".
2. Scope and Application
2.1. Scope of Work
For the primary IP Performance Metrics RFCs for loss [RFC2680], delay
[RFC2679], and delay variation [RFC3393], this memo gives a set of
metrics that can be composed from the same or similar sub-path
metrics. This means that the composition function may utilize:
o the same metric for each sub-path;
o multiple metrics for each sub-path (possibly one that is the same
as the complete path metric);
o a single sub-path metric that is different from the complete path
metric;
o different measurement techniques like active [RFC2330], [RFC3432]
and passive [RFC5474].
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We note a possibility: using a complete path metric and all but one
sub-path metric to infer the performance of the missing sub-path,
especially when the "last" sub-path metric is missing. However, such
de-composition calculations, and the corresponding set of issues they
raise, are beyond the scope of this memo.
2.2. Application
The composition framework [RFC5835] requires the specification of the
applicable circumstances for each metric. In particular, each
section addresses whether the metric:
o Requires the same test packets to traverse all sub-paths or may
use similar packets sent and collected separately in each
sub-path.
o Requires homogeneity of measurement methodologies or can allow a
degree of flexibility (e.g., active, active spatial division
[RFC5644], 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 synchronized measurement start and stop times in all
sub-paths or largely overlapping measurement intervals, or no
timing requirements.
o Requires the assumption of sub-path independence with regard to
the metric being defined/composed or other assumptions.
o Has known sources of inaccuracy/error and identifies the sources.
2.3. Incomplete Information
In practice, when measurements cannot be initiated on a sub-path (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
entire test result SHOULD be recorded as "undefined". This case
should be distinguished from the case where the measurement system
continued to send packets throughout the test interval, but all were
declared lost.
When a composed metric requires measurements from sub-paths A, B, and
C, and one or more of the sub-path results are undefined, then the
composed metric SHOULD also be recorded as undefined.
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3. Common Specifications for Composed Metrics
To reduce the redundant information presented in the detailed metrics
sections that follow, this section presents the specifications that
are common to two or more metrics. The section is organized using
the same subsections as the individual metrics, to simplify
comparisons.
Also, the index variables are represented as follows:
o m = index for packets sent.
o n = index for packets received.
o s = index for involved sub-paths.
3.1. Name: Type-P
All metrics use the "Type-P" convention as described in [RFC2330].
The rest of the name is unique to each metric.
3.1.1. Metric Parameters
o Src, the IP address of a host.
o Dst, the IP address of a host.
o T, a time (start of test interval).
o Tf, a time (end of test interval).
o lambda, a rate in reciprocal seconds (for Poisson Streams).
o incT, the nominal duration of inter-packet interval, first bit to
first bit (for Periodic Streams).
o dT, the duration of the allowed interval for Periodic Stream
sample start times.
o T0, a time that MUST be selected at random from the interval
[T, T + dT] to start generating packets and taking measurements
(for Periodic Streams).
o TstampSrc, the wire time of the packet as measured at MP(Src)
(measurement point at the source).
o TstampDst, the wire time of the packet as measured at MP(Dst),
assigned to packets that arrive within a "reasonable" time.
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o Tmax, a maximum waiting time for packets at the destination, set
sufficiently long to disambiguate packets with long delays from
packets that are discarded (lost); thus, the distribution of delay
is not truncated.
o M, the total number of packets sent between T0 and Tf.
o N, the total number of packets received at Dst (sent between T0
and Tf).
o S, the number of sub-paths involved in the complete Src-Dst path.
o Type-P, as defined in [RFC2330], which includes any field that may
affect a packet's treatment as it traverses the network.
In metric names, the term "" is intended to be replaced by
the name of the method used to define a sample of values of parameter
TstampSrc. This can be done in several ways, including:
1. Poisson: a pseudo-random Poisson process of rate lambda, whose
values fall between T and Tf. The time interval between
successive values of TstampSrc will then average 1/lambda, as per
[RFC2330].
2. Periodic: a Periodic stream process with pseudo-random start time
T0 between T and dT, and nominal inter-packet interval incT, as
per [RFC3432].
3.1.2. Definition and Metric Units
This section is unique for every metric.
3.1.3. Discussion and Other Details
This section is unique for every metric.
3.1.4. Statistic
This section is unique for every metric.
3.1.5. Composition Function
This section is unique for every metric.
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3.1.6. Statement of Conjecture and Assumptions
This section is unique for each metric. The term "ground truth" is
frequently used in these sections and is defined in Section 4.7 of
[RFC5835].
3.1.7. Justification of the Composition Function
It is sometimes impractical to conduct active measurements between
every Src-Dst pair. Since the full mesh of N measurement points
grows as N x N, the scope of measurement may be limited by testing
resources.
There may be varying limitations on active testing in different parts
of the network. For example, it may not be possible to collect the
desired sample size in each test interval when access link speed is
limited, because of the potential for measurement traffic to degrade
the user traffic performance. The conditions on a low-speed access
link may be understood well enough to permit use of a small sample
size/rate, while a larger sample size/rate may be used on other
sub-paths.
Also, since measurement operations have a real monetary cost, there
is value in re-using measurements where they are applicable, rather
than launching new measurements for every possible source-destination
pair.
3.1.8. Sources of Deviation from the Ground Truth
3.1.8.1. Sub-Path List Differs from Complete Path
The measurement packets, each having source and destination addresses
intended for collection at edges of the sub-path, may take a
different specific path through the network equipment and links when
compared to packets with the source and destination addresses of the
complete path. Example sources of parallel paths include Equal Cost
Multi-Path and parallel (or bundled) links. Therefore, the
performance estimated from the composition of sub-path measurements
may differ from the performance experienced by packets on the
complete path. Multiple measurements employing sufficient sub-path
address pairs might produce bounds on the extent of this error.
We also note the possibility of re-routing during a measurement
interval, as it may affect the correspondence between packets
traversing the complete path and the sub-paths that were "involved"
prior to the re-route.
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3.1.8.2. Sub-Path Contains Extra Network Elements
Related to the case of an alternate path described above is the case
where elements in the measured path are unique to measurement system
connectivity. For example, a measurement system may use a dedicated
link to a LAN switch, and packets on the complete path do not
traverse that link. The performance of such a dedicated link would
be measured continuously, and its contribution to the sub-path
metrics SHOULD be minimized as a source of error.
3.1.8.3. Sub-Paths Have Incomplete Coverage
Measurements of sub-path performance may not cover all the network
elements on the complete path. For example, the network exchange
points might be excluded unless a cooperative measurement is
conducted. In this example, test packets on the previous sub-path
are received just before the exchange point, and test packets on the
next sub-path are injected just after the same exchange point.
Clearly, the set of sub-path measurements SHOULD cover all critical
network elements in the complete path.
3.1.8.4. Absence of Route
At a specific point in time, no viable route exists between the
complete path source and destination. The routes selected for one or
more sub-paths therefore differ from the complete path.
Consequently, spatial composition may produce finite estimation of a
ground truth metric (see Section 4.7 of [RFC5835]) between a source
and a destination, even when the route between them is undefined.
3.1.9. Specific Cases where the Conjecture Might Fail
This section is unique for most metrics (see the metric-specific
sections).
For delay-related metrics, one-way delay always depends on packet
size and link capacity, since it is measured in [RFC2679] from first
bit to last bit. If the size of an IP packet changes on its route
(due to encapsulation), this can influence delay performance.
However, the main error source may be the additional processing
associated with encapsulation and encryption/decryption if not
experienced or accounted for in sub-path measurements.
Fragmentation is a major issue for composition accuracy, since all
metrics require all fragments to arrive before proceeding, and
fragmented complete path performance is likely to be different from
performance with non-fragmented packets and composed metrics based on
non-fragmented sub-path measurements.
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Highly manipulated routing can cause measurement error if not
expected and compensated for. For example, policy-based MPLS routing
could modify the class of service for the sub-paths and complete
path.
3.1.10. Application of Measurement Methodology
o The methodology SHOULD use similar packets sent and collected
separately in each sub-path, where "similar" in this case means
that Type-P contains as many equal attributes as possible, while
recognizing that there will be differences. Note that Type-P
includes stream characteristics (e.g., Poisson, Periodic).
o The methodology allows a degree of flexibility regarding test
stream generation (e.g., active or passive methods can produce an
equivalent result, but the lack of control over the source,
timing, and correlation of passive measurements is much more
challenging).
o Poisson and/or Periodic streams are RECOMMENDED.
o The methodology applies to both inter-domain and intra-domain
composition.
o The methodology SHOULD have synchronized measurement time
intervals in all sub-paths, but largely overlapping intervals MAY
suffice.
o Assumption of sub-path independence with regard to the metric
being defined/composed is REQUIRED.
4. One-Way Delay Composed Metrics and Statistics
4.1. Name: Type-P-Finite-One-way-Delay--Stream
This metric is a necessary element of delay composition metrics, and
its definition does not formally exist elsewhere in IPPM literature.
4.1.1. Metric Parameters
See the common parameters section (Section 3.1.1).
4.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of the Type-P-One-
way-Delay singleton as per [RFC2679].
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For each packet "[i]" that has a finite one-way delay (in other
words, excluding packets that have undefined one-way delay):
Type-P-Finite-One-way-Delay--Stream[i] =
FiniteDelay[i] = TstampDst - TstampSrc
This metric is measured in units of time in seconds, expressed in
sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
4.1.3. Discussion and Other Details
The "Type-P-Finite-One-way-Delay" metric permits calculation of the
sample mean statistic. This resolves the problem of including lost
packets in the sample (whose delay is undefined) and the issue with
the informal assignment of infinite delay to lost packets (practical
systems can only assign some very large value).
The Finite-One-way-Delay approach handles the problem of lost packets
by reducing the event space. We consider conditional statistics, and
estimate the mean one-way delay conditioned on the event that all
packets in the sample arrive at the destination (within the specified
waiting time, Tmax). This offers a way to make some valid statements
about one-way delay, at the same time avoiding events with undefined
outcomes. This approach is derived from the treatment of lost
packets in [RFC3393], and is similar to [Y.1540].
4.1.4. Statistic
All statistics defined in [RFC2679] are applicable to the finite one-
way delay, and additional metrics are possible, such as the mean (see
below).
4.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean
This section describes a statistic based on the Type-P-Finite-One-
way-Delay--Stream metric.
4.2.1. Metric Parameters
See the common parameters section (Section 3.1.1).
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4.2.2. Definition and Metric Units of the Mean Statistic
We define
Type-P-Finite-One-way-Delay-Mean =
N
---
1 \
MeanDelay = - * > (FiniteDelay [n])
N /
---
n = 1
where all packets n = 1 through N have finite singleton delays.
This metric is measured in units of time in seconds, expressed in
sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
4.2.3. Discussion and Other Details
The Type-P-Finite-One-way-Delay-Mean metric requires the conditional
delay distribution described in Section 4.1.3.
4.2.4. Statistic
This metric, a mean, does not require additional statistics.
4.2.5. Composition Function: Sum of Means
The Type-P-Finite-Composite-One-way-Delay-Mean, or CompMeanDelay, for
the complete source to destination path can be calculated from the
sum of the mean delays of all of its S constituent sub-paths.
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Then the
Type-P-Finite-Composite-One-way-Delay-Mean =
S
---
\
CompMeanDelay = > (MeanDelay [s])
/
---
s = 1
where sub-paths s = 1 to S are involved in the complete path.
4.2.6. Statement of Conjecture and Assumptions
The mean of a sufficiently large stream of packets measured on each
sub-path during the interval [T, Tf] will be representative of the
ground truth mean of the delay distribution (and the distributions
themselves are sufficiently independent), such that the means may be
added to produce an estimate of the complete path mean delay.
It is assumed that the one-way delay distributions of the sub-paths
and the complete path are continuous. The mean of multi-modal
distributions has the unfortunate property that such a value may
never occur.
4.2.7. Justification of the Composition Function
See the common section (Section 3).
4.2.8. Sources of Deviation from the Ground Truth
See the common section (Section 3).
4.2.9. Specific Cases where the Conjecture Might Fail
If any of the sub-path distributions are multi-modal, then the
measured means may not be stable, and in this case the mean will not
be a particularly useful statistic when describing the delay
distribution of the complete path.
The mean may not be a sufficiently robust statistic to produce a
reliable estimate, or to be useful even if it can be measured.
If a link contributing non-negligible delay is erroneously included
or excluded, the composition will be in error.
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4.2.10. Application of Measurement Methodology
The requirements of the common section (Section 3) apply here as
well.
4.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum
This section describes a statistic based on the Type-P-Finite-One-
way-Delay--Stream metric, and the composed metric based on
that statistic.
4.3.1. Metric Parameters
See the common parameters section (Section 3.1.1).
4.3.2. Definition and Metric Units of the Minimum Statistic
We define
Type-P-Finite-One-way-Delay-Minimum =
MinDelay = (FiniteDelay [j])
such that for some index, j, where 1 <= j <= N
FiniteDelay[j] <= FiniteDelay[n] for all n
where all packets n = 1 through N have finite singleton delays.
This metric is measured in units of time in seconds, expressed in
sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
4.3.3. Discussion and Other Details
The Type-P-Finite-One-way-Delay-Minimum metric requires the
conditional delay distribution described in Section 4.1.3.
4.3.4. Statistic
This metric, a minimum, does not require additional statistics.
4.3.5. Composition Function: Sum of Minima
The Type-P-Finite-Composite-One-way-Delay-Minimum, or CompMinDelay,
for the complete source to destination path can be calculated from
the sum of the minimum delays of all of its S constituent sub-paths.
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Then the
Type-P-Finite-Composite-One-way-Delay-Minimum =
S
---
\
CompMinDelay = > (MinDelay [s])
/
---
s = 1
4.3.6. Statement of Conjecture and Assumptions
The minimum of a sufficiently large stream of packets measured on
each sub-path during the interval [T, Tf] will be representative of
the ground truth minimum of the delay distribution (and the
distributions themselves are sufficiently independent), such that the
minima may be added to produce an estimate of the complete path
minimum delay.
It is assumed that the one-way delay distributions of the sub-paths
and the complete path are continuous.
4.3.7. Justification of the Composition Function
See the common section (Section 3).
4.3.8. Sources of Deviation from the Ground Truth
See the common section (Section 3).
4.3.9. Specific Cases where the Conjecture Might Fail
If the routing on any of the sub-paths is not stable, then the
measured minimum may not be stable. In this case the composite
minimum would tend to produce an estimate for the complete path that
may be too low for the current path.
4.3.10. Application of Measurement Methodology
The requirements of the common section (Section 3) apply here as
well.
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5. Loss Metrics and Statistics
5.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability
5.1.1. Metric Parameters
See the common parameters section (Section 3.1.1).
5.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of the Type-P-One-
way-Packet-Loss singleton and stream as per [RFC2680].
We obtain a sequence of pairs with elements as follows:
o TstampSrc, as above.
o L, either zero or one, where L = 1 indicates loss and L = 0
indicates arrival at the destination within TstampSrc + Tmax.
5.1.3. Discussion and Other Details
None.
5.1.4. Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability
Given the stream parameter M, the number of packets sent, we can
define the Empirical Probability of Loss Statistic (Ep), consistent
with average loss in [RFC2680], as follows:
Type-P-One-way-Packet-Loss-Empirical-Probability =
M
---
1 \
Ep = - * > (L[m])
M /
---
m = 1
where all packets m = 1 through M have a value for L.
5.1.5. Composition Function: Composition of Empirical Probabilities
The Type-P-One-way-Composite-Packet-Loss-Empirical-Probability, or
CompEp, for the complete source to destination path can be calculated
by combining the Ep of all of its constituent sub-paths (Ep1, Ep2,
Ep3, ... Epn) as
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Type-P-Composite-One-way-Packet-Loss-Empirical-Probability =
CompEp = 1 - {(1 - Ep1) x (1 - Ep2) x (1 - Ep3) x ... x (1 - EpS)}
If any Eps is undefined in a particular measurement interval,
possibly because a measurement system failed to report a value, then
any CompEp that uses sub-path s for that measurement interval is
undefined.
5.1.6. Statement of Conjecture and Assumptions
The empirical probability of loss calculated on a sufficiently large
stream of packets measured on each sub-path during the interval
[T, Tf] will be representative of the ground truth empirical loss
probability (and the probabilities themselves are sufficiently
independent), such that the sub-path probabilities may be combined to
produce an estimate of the complete path empirical loss probability.
5.1.7. Justification of the Composition Function
See the common section (Section 3).
5.1.8. Sources of Deviation from the Ground Truth
See the common section (Section 3).
5.1.9. Specific Cases where the Conjecture Might Fail
A concern for loss measurements combined in this way is that root
causes may be correlated to some degree.
For example, if the links of different networks follow the same
physical route, then a single catastrophic event like a fire in a
tunnel could cause an outage or congestion on remaining paths in
multiple networks. Here it is important to ensure that measurements
before the event and after the event are not combined to estimate the
composite performance.
Or, when traffic volumes rise due to the rapid spread of an email-
borne worm, loss due to queue overflow in one network may help
another network to carry its traffic without loss.
5.1.10. Application of Measurement Methodology
See the common section (Section 3).
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6. Delay Variation Metrics and Statistics
6.1. Name: Type-P-One-way-pdv-refmin--Stream
This packet delay variation (PDV) metric is a necessary element of
Composed Delay Variation metrics, and its definition does not
formally exist elsewhere in IPPM literature (with the exception of
[RFC5481]).
6.1.1. Metric Parameters
In addition to the parameters of Section 3.1.1:
o TstampSrc[i], the wire time of packet[i] as measured at MP(Src)
(measurement point at the source).
o TstampDst[i], the wire time of packet[i] as measured at MP(Dst),
assigned to packets that arrive within a "reasonable" time.
o B, a packet length in bits.
o F, a selection function unambiguously defining the packets from
the stream that are selected for the packet-pair computation of
this metric. F(current packet), the first packet of the pair,
MUST have a valid Type-P-Finite-One-way-Delay less than Tmax (in
other words, excluding packets that have undefined one-way delay)
and MUST have been transmitted during the interval [T, Tf]. The
second packet in the pair, F(min_delay packet) MUST be the packet
with the minimum valid value of Type-P-Finite-One-way-Delay for
the stream, in addition to the criteria for F(current packet). If
multiple packets have equal minimum Type-P-Finite-One-way-Delay
values, then the value for the earliest arriving packet SHOULD be
used.
o MinDelay, the Type-P-Finite-One-way-Delay value for F(min_delay
packet) given above.
o N, the number of packets received at the destination that meet the
F(current packet) criteria.
6.1.2. Definition and Metric Units
Using the definition above in Section 5.1.2, we obtain the value of
Type-P-Finite-One-way-Delay--Stream[n], the singleton for
each packet[i] in the stream (a.k.a. FiniteDelay[i]).
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For each packet[n] that meets the F(first packet) criteria given
above: Type-P-One-way-pdv-refmin--Stream[n] =
PDV[n] = FiniteDelay[n] - MinDelay
where PDV[i] is in units of time in seconds, expressed in
sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
6.1.3. Discussion and Other Details
This metric produces a sample of delay variation normalized to the
minimum delay of the sample. The resulting delay variation
distribution is independent of the sending sequence (although
specific FiniteDelay values within the distribution may be
correlated, depending on various stream parameters such as packet
spacing). This metric is equivalent to the IP Packet Delay Variation
parameter defined in [Y.1540].
6.1.4. Statistics: Mean, Variance, Skewness, Quantile
We define the mean PDV as follows (where all packets n = 1 through N
have a value for PDV[n]):
Type-P-One-way-pdv-refmin-Mean = MeanPDV =
N
---
1 \
- * > (PDV[n])
N /
---
n = 1
We define the variance of PDV as follows:
Type-P-One-way-pdv-refmin-Variance = VarPDV =
N
---
1 \ 2
------- > (PDV[n] - MeanPDV)
(N - 1) /
---
n = 1
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We define the skewness of PDV as follows:
Type-P-One-way-pdv-refmin-Skewness = SkewPDV =
N
--- 3
\ / \
> | PDV[n] - MeanPDV |
/ \ /
---
n = 1
-----------------------------------
/ \
| ( 3/2 ) |
\ (N - 1) * VarPDV /
(See Appendix X of [Y.1541] for additional background information.)
We define the quantile of the PDV sample as the value where the
specified fraction of singletons is less than the given value.
6.1.5. Composition Functions
This section gives two alternative composition functions. The
objective is to estimate a quantile of the complete path delay
variation distribution. The composed quantile will be estimated
using information from the sub-path delay variation distributions.
6.1.5.1. Approximate Convolution
The Type-P-Finite-One-way-Delay--Stream samples from each
sub-path are summarized as a histogram with 1-ms bins representing
the one-way delay distribution.
From [STATS], the distribution of the sum of independent random
variables can be derived using the relation:
Type-P-Composite-One-way-pdv-refmin-quantile-a =
. .
/ /
P(X + Y + Z <= a) = | | P(X <= a - y - z) * P(Y = y) * P(Z = z) dy dz
/ /
` `
z y
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Note that dy and dz indicate partial integration above, and that y
and z are the integration variables. Also, the probability of an
outcome is indicated by the symbol P(outcome), where X, Y, and Z are
random variables representing the delay variation distributions of
the sub-paths of the complete path (in this case, there are three
sub-paths), and "a" is the quantile of interest.
This relation can be used to compose a quantile of interest for the
complete path from the sub-path delay distributions. The histograms
with 1-ms bins are discrete approximations of the delay
distributions.
6.1.5.2. Normal Power Approximation (NPA)
Type-P-One-way-Composite-pdv-refmin-NPA for the complete source to
destination path can be calculated by combining the statistics of all
the constituent sub-paths in the process described in [Y.1541],
Clause 8 and Appendix X.
6.1.6. Statement of Conjecture and Assumptions
The delay distribution of a sufficiently large stream of packets
measured on each sub-path during the interval [T, Tf] will be
sufficiently stationary, and the sub-path distributions themselves
are sufficiently independent, so that summary information describing
the sub-path distributions can be combined to estimate the delay
distribution of the complete path.
It is assumed that the one-way delay distributions of the sub-paths
and the complete path are continuous.
6.1.7. Justification of the Composition Function
See the common section (Section 3).
6.1.8. Sources of Deviation from the Ground Truth
In addition to the common deviations, a few additional sources exist
here. For one, very tight distributions with ranges on the order of
a few milliseconds are not accurately represented by a histogram with
1-ms bins. This size was chosen assuming an implicit requirement on
accuracy: errors of a few milliseconds are acceptable when assessing
a composed distribution quantile.
Also, summary statistics cannot describe the subtleties of an
empirical distribution exactly, especially when the distribution is
very different from a classical form. Any procedure that uses these
statistics alone may incur error.
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6.1.9. Specific Cases where the Conjecture Might Fail
If the delay distributions of the sub-paths are somehow correlated,
then neither of these composition functions will be reliable
estimators of the complete path distribution.
In practice, sub-path delay distributions with extreme outliers have
increased the error of the composed metric estimate.
6.1.10. Application of Measurement Methodology
See the common section (Section 3).
7. Security Considerations
7.1. Denial-of-Service Attacks
This metric requires a stream of packets sent from one host (source)
to another host (destination) through intervening networks. This
method could be abused for denial-of-service attacks directed at the
destination and/or the intervening network(s).
Administrators of source, destination, and intervening networks
should establish bilateral or multilateral agreements regarding the
timing, size, and frequency of collection of sample metrics. Use of
this method in excess of the terms agreed upon between the
participants may be cause for immediate rejection or discarding of
packets, or other escalation procedures defined between the affected
parties.
7.2. User Data Confidentiality
Active use of this method generates packets for a sample, rather than
taking samples based on user data, and does not threaten user data
confidentiality. Passive measurement MUST restrict attention to the
headers of interest. Since user payloads may be temporarily stored
for length analysis, suitable precautions MUST be taken to keep this
information safe and confidential. In most cases, a hashing function
will produce a value suitable for payload comparisons.
7.3. Interference with the Metrics
It may be possible to identify that a certain packet or stream of
packets is part of a sample. With that knowledge at the destination
and/or the intervening networks, it is possible to change the
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processing of the packets (e.g., increasing or decreasing delay),
which may distort the measured performance. It may also be possible
to generate additional packets that appear to be part of the sample
metric. These additional packets are likely to perturb the results
of the sample measurement.
To discourage the kind of interference mentioned above, packet
interference checks, such as cryptographic hash, may be used.
8. IANA Considerations
Metrics defined in the IETF are typically registered in the IANA IPPM
Metrics Registry as described in the initial version of the registry
[RFC4148].
IANA has registered the following metrics in the
IANA-IPPM-METRICS-REGISTRY-MIB:
ietfFiniteOneWayDelayStream OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Finite-One-way-Delay-Stream"
REFERENCE "RFC 6049, Section 4.1."
::= { ianaIppmMetrics 71 }
ietfFiniteOneWayDelayMean OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Finite-One-way-Delay-Mean"
REFERENCE "RFC 6049, Section 4.2."
::= { ianaIppmMetrics 72 }
ietfCompositeOneWayDelayMean OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Finite-Composite-One-way-Delay-Mean"
REFERENCE "RFC 6049, Section 4.2.5."
::= { ianaIppmMetrics 73 }
ietfFiniteOneWayDelayMinimum OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Finite-One-way-Delay-Minimum"
REFERENCE "RFC 6049, Section 4.3.2."
::= { ianaIppmMetrics 74 }
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ietfCompositeOneWayDelayMinimum OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Finite-Composite-One-way-Delay-Minimum"
REFERENCE "RFC 6049, Section 4.3."
::= { ianaIppmMetrics 75 }
ietfOneWayPktLossEmpiricProb OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-One-way-Packet-Loss-Empirical-Probability"
REFERENCE "RFC 6049, Section 5.1.4"
::= { ianaIppmMetrics 76 }
ietfCompositeOneWayPktLossEmpiricProb OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Composite-One-way-Packet-Loss-Empirical-Probability"
REFERENCE "RFC 6049, Section 5.1."
::= { ianaIppmMetrics 77 }
ietfOneWayPdvRefminStream OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-One-way-pdv-refmin-Stream"
REFERENCE "RFC 6049, Section 6.1."
::= { ianaIppmMetrics 78 }
ietfOneWayPdvRefminMean OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-One-way-pdv-refmin-Mean"
REFERENCE "RFC 6049, Section 6.1.4."
::= { ianaIppmMetrics 79 }
ietfOneWayPdvRefminVariance OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-One-way-pdv-refmin-Variance"
REFERENCE "RFC 6049, Section 6.1.4."
::= { ianaIppmMetrics 80 }
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ietfOneWayPdvRefminSkewness OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-One-way-pdv-refmin-Skewness"
REFERENCE "RFC 6049, Section 6.1.4."
::= { ianaIppmMetrics 81 }
ietfCompositeOneWayPdvRefminQtil OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-Composite-One-way-pdv-refmin-quantile-a"
REFERENCE "RFC 6049, Section 6.1.5.1."
::= { ianaIppmMetrics 82 }
ietfCompositeOneWayPdvRefminNPA OBJECT-IDENTITY
STATUS current
DESCRIPTION
"Type-P-One-way-Composite-pdv-refmin-NPA"
REFERENCE "RFC 6049, Section 6.1.5.2."
::= { ianaIppmMetrics 83 }
9. Contributors and Acknowledgements
The following people have contributed useful ideas, suggestions, or
the text of sections that have been incorporated into this memo:
- Phil Chimento
- Reza Fardid
- Roman Krzanowski
- Maurizio Molina
- Lei Liang
- Dave Hoeflin
A long time ago, in a galaxy far, far away (Minneapolis), Will Leland
suggested the simple and elegant Type-P-Finite-One-way-Delay concept.
Thanks Will.
Yaakov Stein and Donald McLachlan also provided useful comments along
the way.
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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.
[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.
[RFC3393] Demichelis, C. and P. Chimento, "IP Packet Delay Variation
Metric for IP Performance Metrics (IPPM)", RFC 3393,
November 2002.
[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network
performance measurement with periodic streams", RFC 3432,
November 2002.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005.
[RFC5835] Morton, A. and S. Van den Berghe, "Framework for Metric
Composition", RFC 5835, April 2010.
10.2. Informative References
[RFC5474] Duffield, N., Chiou, D., Claise, B., Greenberg, A.,
Grossglauser, M., and J. Rexford, "A Framework for Packet
Selection and Reporting", RFC 5474, March 2009.
[RFC5481] Morton, A. and B. Claise, "Packet Delay Variation
Applicability Statement", RFC 5481, March 2009.
[RFC5644] Stephan, E., Liang, L., and A. Morton, "IP Performance
Metrics (IPPM): Spatial and Multicast", RFC 5644,
October 2009.
[STATS] Mood, A., Graybill, F., and D. Boes, "Introduction to the
Theory of Statistics, 3rd Edition", McGraw-Hill, New York,
NY, 1974.
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RFC 6049 Spatial Composition January 2011
[Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data
communication service - IP packet transfer and
availability performance parameters", November 2007.
[Y.1541] ITU-T Recommendation Y.1541, "Network Performance
Objectives for IP-based Services", February 2006.
Authors' Addresses
Al Morton
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/
Stephan Emile
France Telecom Orange
2 avenue Pierre Marzin
Lannion, F-22307
France
EMail: emile.stephan@orange-ftgroup.com
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