Network Working Group A. Morton
Internet-Draft AT&T Labs
Intended status: Standards Track E. Stephan
Expires: April 21, 2010 France Telecom Division R&D
October 18, 2009
Spatial Composition of Metrics
draft-ietf-ippm-spatial-composition-10
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Abstract
This memo utilizes IPPM metrics that are applicable to both complete
paths and sub-paths, and defines relationships to compose a complete
path metric from the sub-path metrics with some accuracy w.r.t. 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.
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".
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Table of Contents
1. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . 6
3. Scope and Application . . . . . . . . . . . . . . . . . . . . 6
3.1. Scope of work . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Application . . . . . . . . . . . . . . . . . . . . . . . 7
3.3. Incomplete Information . . . . . . . . . . . . . . . . . . 8
4. Common Specifications for Composed Metrics . . . . . . . . . . 8
4.1. Name: Type-P . . . . . . . . . . . . . . . . . . . . . . . 8
4.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 8
4.1.2. Definition and Metric Units . . . . . . . . . . . . . 9
4.1.3. Discussion and other details . . . . . . . . . . . . . 9
4.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 9
4.1.5. Composition Function . . . . . . . . . . . . . . . . . 9
4.1.6. Statement of Conjecture and Assumptions . . . . . . . 9
4.1.7. Justification of the Composition Function . . . . . . 10
4.1.8. Sources of Deviation from the Ground Truth . . . . . . 10
4.1.9. Specific cases where the conjecture might fail . . . . 11
4.1.10. Application of Measurement Methodology . . . . . . . . 11
5. One-way Delay Composed Metrics and Statistics . . . . . . . . 12
5.1. Name:
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream . . . 12
5.1.1. Metric Parameters . . . . . . . . . . . . . . . . . . 12
5.1.2. Definition and Metric Units . . . . . . . . . . . . . 12
5.1.3. Discussion and other details . . . . . . . . . . . . . 12
5.1.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 13
5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean . . . . . 13
5.2.1. Metric Parameters . . . . . . . . . . . . . . . . . . 13
5.2.2. Definition and Metric Units of the Mean Statistic . . 13
5.2.3. Discussion and other details . . . . . . . . . . . . . 14
5.2.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 14
5.2.5. Composition Function: Sum of Means . . . . . . . . . . 14
5.2.6. Statement of Conjecture and Assumptions . . . . . . . 14
5.2.7. Justification of the Composition Function . . . . . . 14
5.2.8. Sources of Deviation from the Ground Truth . . . . . . 14
5.2.9. Specific cases where the conjecture might fail . . . . 15
5.2.10. Application of Measurement Methodology . . . . . . . . 15
5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum . . . 15
5.3.1. Metric Parameters . . . . . . . . . . . . . . . . . . 15
5.3.2. Definition and Metric Units of the Minimum
Statistic . . . . . . . . . . . . . . . . . . . . . . 15
5.3.3. Discussion and other details . . . . . . . . . . . . . 16
5.3.4. Statistic: . . . . . . . . . . . . . . . . . . . . . . 16
5.3.5. Composition Function: Sum of Minima . . . . . . . . . 16
5.3.6. Statement of Conjecture and Assumptions . . . . . . . 16
5.3.7. Justification of the Composition Function . . . . . . 16
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5.3.8. Sources of Deviation from the Ground Truth . . . . . . 16
5.3.9. Specific cases where the conjecture might fail . . . . 17
5.3.10. Application of Measurement Methodology . . . . . . . . 17
6. Loss Metrics and Statistics . . . . . . . . . . . . . . . . . 17
6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability 17
6.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 17
6.1.2. Definition and Metric Units . . . . . . . . . . . . . 17
6.1.3. Discussion and other details . . . . . . . . . . . . . 17
6.1.4. Statistic:
Type-P-One-way-Packet-Loss-Empirical-Probability . . . 17
6.1.5. Composition Function: Composition of Empirical
Probabilities . . . . . . . . . . . . . . . . . . . . 18
6.1.6. Statement of Conjecture and Assumptions . . . . . . . 18
6.1.7. Justification of the Composition Function . . . . . . 18
6.1.8. Sources of Deviation from the Ground Truth . . . . . . 18
6.1.9. Specific cases where the conjecture might fail . . . . 18
6.1.10. Application of Measurement Methodology . . . . . . . . 19
7. Delay Variation Metrics and Statistics . . . . . . . . . . . . 19
7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-Stream . 19
7.1.1. Metric Parameters: . . . . . . . . . . . . . . . . . . 19
7.1.2. Definition and Metric Units . . . . . . . . . . . . . 20
7.1.3. Discussion and other details . . . . . . . . . . . . . 20
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle . . . . 20
7.1.5. Composition Functions: . . . . . . . . . . . . . . . . 21
7.1.6. Statement of Conjecture and Assumptions . . . . . . . 22
7.1.7. Justification of the Composition Function . . . . . . 22
7.1.8. Sources of Deviation from the Ground Truth . . . . . . 23
7.1.9. Specific cases where the conjecture might fail . . . . 23
7.1.10. Application of Measurement Methodology . . . . . . . . 23
8. Security Considerations . . . . . . . . . . . . . . . . . . . 23
8.1. Denial of Service Attacks . . . . . . . . . . . . . . . . 23
8.2. User Data Confidentiality . . . . . . . . . . . . . . . . 23
8.3. Interference with the metrics . . . . . . . . . . . . . . 24
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24
10. Acknowlegements . . . . . . . . . . . . . . . . . . . . . . . 24
11. Issues (Open and Closed) . . . . . . . . . . . . . . . . . . . 24
12. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 26
13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 26
13.1. Normative References . . . . . . . . . . . . . . . . . . . 26
13.2. Informative References . . . . . . . . . . . . . . . . . . 26
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 27
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1. Contributors
Thus far, 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
2. Introduction
The IPPM framework [RFC2330] describes two forms of metric
composition, spatial and temporal. The new composition framework
[I-D.ietf-ippm-framework-compagg] 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.
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,
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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.
2.1. Motivation
One-way metrics defined in other IPPM RFCs all assume that the
measurement can be practically carried out between the source and the
destination of the interest. Sometimes there are reasons that the
measurement can not 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.
3. Scope and Application
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3.1. Scope of work
For the primary IPPM metrics of Loss, Delay, and Delay Variation,
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 and passive
(recognizing that PSAMP WG will define capabilities to sample
packets to support measurement).
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.
3.2. Application
The new composition framework [I-D.ietf-ippm-framework-compagg]
requires the specification of the applicable circumstances for each
metric. In particular, each section addresses whether the metric:
Requires the same test packets to traverse all sub-paths, or may use
similar packets sent and collected separately in each sub-path.
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.
Needs information or access that will only be available within an
operator's domain, or is applicable to Inter-domain composition.
Requires synchronized measurement time intervals in all sub-paths, or
largely overlapping, or no timing requirements.
Requires assumption of sub-path independence w.r.t. the metric being
defined/composed, or other assumptions.
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Has known sources of inaccuracy/error, and identifies the sources.
3.3. 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.
4. 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 following index variables represent the following:
o m = index for packets sent
o n = index for packets received
o s = index for involved sub-paths
4.1. Name: Type-P
All metrics use the Type-P convention as described in [RFC2330]. The
rest of the name is unique to each metric.
4.1.1. 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)
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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 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)
o TstampDst, the wire time of the packet as measured at MP(Dst),
assigned to packets that arrive within a "reasonable" time.
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
4.1.2. Definition and Metric Units
This section is unique for every metric.
4.1.3. Discussion and other details
This section is unique for every metric.
4.1.4. Statistic:
This section is unique for every metric.
4.1.5. Composition Function
This section is unique for every metric.
4.1.6. Statement of Conjecture and Assumptions
This section is unique for each metric.
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4.1.7. 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.
4.1.8. Sources of Deviation from the Ground Truth
4.1.8.1. 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. Examples 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.
4.1.8.2. 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
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be measured continuously, and its contribution to the sub-path
metrics SHOULD be minimized as a source of error.
4.1.8.3. 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.
4.1.8.4. 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 differs from the complete path.
Consequently, spatial composition may produce finite estimation of a
ground truth metric between a source and a destination, even when the
route between them is undefined.
4.1.9. 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 (due to
encapsulation for security reasons), this will influence delay
performance.
Fragmentation is a major issue for compostion 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.
4.1.10. Application of Measurement Methodology
The methodology:
SHOULD use similar packets sent and collected separately in each sub-
path.
Allows a degree of flexibility regarding test stream generation
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(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).
Poisson and/or Periodic streams are RECOMMENDED.
Applies to both Inter-domain and Intra-domain composition.
SHOULD have synchronized measurement time intervals in all sub-paths,
but largely overlapping intervals MAY suffice.
REQUIRES assumption of sub-path independence w.r.t. the metric being
defined/composed.
5. One-way Delay Composed Metrics and Statistics
5.1. Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream
This metric is a necessary element of Delay Composition metrics, and
its definition does not formally exist elsewhere in IPPM literature.
5.1.1. Metric Parameters
See the common parameters section above.
5.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of Type-P-One-way-
Delay singleton as per [RFC2679].
For each packet [i] that has a finite One-way Delay (in other words,
excluding packets which have undefined one-way delay):
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] =
FiniteDelay[i] = TstampDst - TstampSrc
The units of measure for this metric are time in seconds, expressed
in sufficiently low resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
5.1.3. 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
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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, and 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] .
5.1.4. 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).
5.2. Name: Type-P-Finite-Composite-One-way-Delay-Mean
This section describes a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric.
5.2.1. Metric Parameters
See the common parameters section above.
5.2.2. 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.
The units of measure for this metric are time in seconds, expressed
in sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
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5.2.3. Discussion and other details
The Type-P-Finite-One-way-Delay-Mean metric requires the conditional
delay distribution described in section 5.1.
5.2.4. Statistic:
This metric, a mean, does not require additional statistics.
5.2.5. 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
sum of the Mean Delays of all its S constituent sub-paths.
Then the
Type-P-Finite-Composite-One-way-Delay-Mean =
S
---
\
CompMeanDelay = > (MeanDelay [s])
/
---
s = 1
where sub-paths s = 1 to S are invloved in the complete path.
5.2.6. 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 bi-modal
distributions have the unfortunate property that such a value may
never occur.
5.2.7. Justification of the Composition Function
See the common section.
5.2.8. Sources of Deviation from the Ground Truth
See the common section.
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5.2.9. Specific cases where the conjecture might fail
If any of the sub-path distributions are bimodal, 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 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.
5.2.10. Application of Measurement Methodology
The requirements of the common section apply here as well.
5.3. Name: Type-P-Finite-Composite-One-way-Delay-Minimum
This section describes is a statistic based on the Type-P-Finite-One-
way-Delay-Poisson/Periodic-Stream metric, and the composed metric
based on that statistic.
5.3.1. Metric Parameters
See the common parameters section above.
5.3.2. 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.
The units of measure for this metric are time in seconds, expressed
in sufficiently fine resolution to convey meaningful quantitative
information. For example, resolution of microseconds is usually
sufficient.
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5.3.3. Discussion and other details
The Type-P-Finite-One-way-Delay-Minimum metric requires the
conditional delay distribution described in section 5.1.3.
5.3.4. Statistic:
This metric, a minimum, does not require additional statistics.
5.3.5. 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
sum of the Minimum Delays of all its S constituent sub-paths.
Then the
Type-P-Finite-Composite-One-way-Delay-Minimum =
S
---
\
CompMinDelay = > (MinDelay [s])
/
---
s = 1
5.3.6. 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.
5.3.7. Justification of the Composition Function
See the common section.
5.3.8. Sources of Deviation from the Ground Truth
See the common section.
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5.3.9. 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.
5.3.10. Application of Measurement Methodology
The requirements of the common section apply here as well.
6. Loss Metrics and Statistics
6.1. Type-P-Composite-One-way-Packet-Loss-Empirical-Probability
6.1.1. Metric Parameters:
Same as section 4.1.1.
6.1.2. Definition and Metric Units
Using the parameters above, we obtain the value of 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.
6.1.3. Discussion and other details
6.1.4. 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:
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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.
6.1.5. 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 Ep of all its constituent sub-paths (Ep1, Ep2, Ep3, ...
Epn) as
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.
6.1.6. 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.
6.1.7. Justification of the Composition Function
See the common section.
6.1.8. Sources of Deviation from the Ground Truth
See the common section.
6.1.9. 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.
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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-
born worm, loss due to queue overflow in one network may help another
network to carry its traffic without loss.
others...
6.1.10. Application of Measurement Methodology
See the common section.
7. Delay Variation Metrics and Statistics
7.1. Name: Type-P-One-way-pdv-refmin-Poisson/Periodic-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.
7.1.1. Metric Parameters:
In addition to the parameters of section 4.1.1:
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(first 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 which have undefined one-way delay) and
MUST have been transmitted during the interval T, Tf. The second
packet in the pair, F(second 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(first packet). If multiple
packets have equal minimum Type-P-Finite-One-way-Delay values,
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then the value for the earliest arriving packet SHOULD be used.
o MinDelay, the Type-P-Finite-One-way-Delay value for F(second
packet) given above.
o N, the number of packets received at the Destination meeting the
F(first packet) criteria.
7.1.2. Definition and Metric Units
Using the definition above in section 5.1.2, we obtain the value of
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[n], the singleton
for each packet[i] in the stream (a.k.a. FiniteDelay[i]).
For each packet[n] that meets the F(first packet) criteria given
above: Type-P-One-way-pdv-refmin-Poisson/Periodic-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.
7.1.3. 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].
7.1.4. Statistics: Mean, Variance, Skewness, Quanitle
We define the mean PDV as follows (where all packets n = 1 through N
have a value for PDV[n]):
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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
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 /
We define the Quantile of the IPDVRefMin sample as the value where
the specified fraction of singletons is less than the given value.
7.1.5. 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.
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7.1.5.1. Approximate Convolution
The Type-P-Finite-One-way-Delay-Poisson/Periodic-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
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. Note dy and dz indicate partial integration here.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.
7.1.5.2. Normal Power Approximation
Type-P-One-way-Composite-pdv-refmin-NPA for the complete Source to
Destination path can be calculated by combining statistics of all the
constituent sub-paths in the process described in [Y.1541] clause 8
and Appendix X.
7.1.6. 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 complete path.
It is assumed that the one-way delay distributions of the sub-paths
and the complete path are continuous.
7.1.7. Justification of the Composition Function
See the common section.
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7.1.8. 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 range 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.
7.1.9. 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.
7.1.10. Application of Measurement Methodology
See the common section.
8. Security Considerations
8.1. 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
destination and/or the intervening network(s).
Administrators of source, destination, and the intervening network(s)
should establish bilateral or multi-lateral agreements regarding the
timing, size, and frequency of collection of sample metrics. Use of
this method in excess of the terms agreed between the participants
may be cause for immediate rejection or discard of packets or other
escalation procedures defined between the affected parties.
8.2. 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
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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.
8.3. 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
processing of the packets (e.g. increasing or decreasing delay) that
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.
9. IANA Considerations
Metrics defined in this memo will be registered in the IANA IPPM
METRICS REGISTRY as described in initial version of the registry
[RFC4148].
10. Acknowlegements
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.
11. Issues (Open and Closed)
>>>>>>>>>>>>Issue:
Is Section 4.1.8.4 really describing a new error case, about
Alternate Routing? Or does Section 4.1.8.1 on sub-path differences
cover it all?
RESOLUTION: The section was re-worded in -10 version to make the
topic, Absence of a real Route between the Src and Dst, more clear.
>>>>>>>>>>>>
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>>>>>>>>>>>>Issue:
What is the relationship between the decomposition and composition
metrics? Should we put both kinds in one draft to make up a
framework? The motivation of decomposition is as follows:
The One-way measurement can provide result to show what the network
performance between two end hosts is and whether it meets operator
expectations or not. It cannot provide further information to
engineers where and how to improve the performance between the source
and the destination. For instance, if the network performance is not
acceptable in terms of the One-way measurement, in which part of the
network the engineers should put their efforts. This question can to
be answered by decompose the One-way measurement to sub-path
measurement to investigate the performance of different part of the
network.
Editor's Questions for clarification: What additional information
would be provided to the decomposition process, beyond the
measurement of the complete path?
Is the decomposition described above intended to estimate a metric
for some/all disjoint sub-paths involved in the complete path?
>>>>>>>>>>>>>>>>>>RESOLUTION: treat this topic in a separate memo
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>Issue
Section 7 defines a new type of metric, a "combination" of metrics
for one-way delay and packet loss. The purpose of this metric is to
link these two primary metrics in a convenient way.
Readers are asked to comment on the efficiency of the combination
metric.
>>>>>>>>>>>>>>>>>RESOLUTION: If a delay singleton is recorded as
having "undefined" delay when the packet does not arrive within the
waiting time Tmax, then this information is sufficient to determine
the fraction of lost packets in the sample, and the additional loss
indication of this combo is not needed.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Issue
Can we introduce multicast metrics here, without causing too much
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confusion? Should the multicast version of this draft wait until the
Unicast concepts are stable (or maybe appear in a separate draft)?
>>>>>>>>>>>>>>>>RESOLUTION: No and Yes.
12. Acknowledgements
13. References
13.1. Normative References
[I-D.ietf-ippm-framework-compagg]
Morton, A., "Framework for Metric Composition",
draft-ietf-ippm-framework-compagg-08 (work in progress),
June 2009.
[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.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005.
13.2. Informative References
[I-D.ietf-ippm-multimetrics]
Stephan, E., Liang, L., and A. Morton, "IP Performance
Metrics (IPPM) for spatial and multicast",
draft-ietf-ippm-multimetrics-12 (work in progress),
September 2009.
[Stats] McGraw-Hill NY NY, "Introduction to the Theory of
Statistics, 3rd Edition,", 1974.
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[Y.1540] ITU-T Recommendation Y.1540, "Internet protocol data
communication service - IP packet transfer and
availability performance parameters", December 2002.
[Y.1541] ITU-T Recommendation Y.1541, "Network Performance
Objectives for IP-based Services", February 2006.
Index
?
??? 14
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/
Emile Stephan
France Telecom Division R&D
2 avenue Pierre Marzin
Lannion, F-22307
France
Phone:
Fax: +33 2 96 05 18 52
Email: emile.stephan@orange-ftgroup.com
URI:
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