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Copyright © The Internet Society (2006).
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.
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 (Bradner, S., “Key words for use in RFCs to Indicate Requirement Levels,” March 1997.) [RFC2119].
In this memo, the characters "<=" should be read as "less than or equal to" and ">=" as "greater than or equal to".
1.
Contributors
2.
Introduction
2.1.
Motivation
3.
Scope, Application, and Terminology
3.1.
Scope of work
3.2.
Application
3.3.
Terminology
4.
One-way Delay Composition Metrics and Statistics
4.1.
Name: Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream
4.1.1.
Metric Parameters:
4.1.2.
Definition and Metric Units
4.1.3.
Discussion and other details
4.1.4.
Mean Statistic
4.1.5.
Composition Relationship: Sum of Means
4.1.6.
Statement of Conjecture
4.1.7.
Justification of Composite Relationship
4.1.8.
Sources of Error
4.1.9.
Specific cases where the conjecture might fail
4.1.10.
Application of Measurement Methodology
5.
Loss Metrics and Statistics
5.1.
Name: Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream
5.1.1.
Metric Parameters:
5.1.2.
Definition and Metric Units
5.1.3.
Discussion and other details
5.1.4.
Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability
5.1.5.
Composition Relationship: Composition of Empirical Probabilities
5.1.6.
Statement of Conjecture
5.1.7.
Justification of Composite Relationship
5.1.8.
Sources of Error
5.1.9.
Specific cases where the conjecture might fail
5.1.10.
Application of Measurement Methodology
6.
Delay Variation Metrics and Statistics
6.1.
Name: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream
6.1.1.
Metric Parameters:
6.1.2.
Definition and Metric Units
6.1.3.
Discussion and other details
6.1.4.
Statistics: Mean, Variance, Skewness, Quanitle
6.1.5.
Composition Relationships:
6.1.6.
Statement of Conjecture
6.1.7.
Justification of Composite Relationship
6.1.8.
Sources of Error
6.1.9.
Specific cases where the conjecture might fail
6.1.10.
Application of Measurement Methodology
7.
Other Metrics and Statistics: One-way Combined Metric
7.1.
Metric Name:
7.1.1.
Metric Parameters:
7.1.2.
Definition and Metric Units
7.1.3.
Discussion and other details
7.1.4.
Type-P-One-way-Combo-subpathes-stream
7.1.5.
Type-P-One-way-composition
7.1.6.
Type-P-One-way-composition
7.1.7.
Statement of Conjecture
7.1.8.
Justification of Composite Relationship
7.1.9.
Sources of Error
7.1.10.
Specific cases where the conjecture might fail
7.1.11.
Application of Measurement Methodology
8.
Security Considerations
8.1.
Denial of Service Attacks
8.2.
User Data Confidentiality
8.3.
Interference with the metrics
9.
IANA Considerations
10.
Security Considerations
11.
Open Issues
12.
Acknowledgements
13.
References
13.1.
Normative References
13.2.
Informative References
§
Authors' Addresses
§
Intellectual Property and Copyright Statements
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Thus far, the following people have contributed useful ideas, suggestions, or the text of sections that have been incorporated into this memo:
- Phil Chimento <vze275m9@verizon.net>
- Reza Fardid <RFardid@Covad.COM>
- Roman Krzanowski <roman.krzanowski@verizon.com>
- Maurizio Molina <maurizio.molina@dante.org.uk>
- Al Morton <acmorton@att.com>
- Emile Stephan <emile.stephan@francetelecom.com>
- Lei Liang <L.Liang@surrey.ac.uk>
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The IPPM framework RFC 2330 (Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, “Framework for IP Performance Metrics,” May 1998.) [RFC2330] describes two forms of metric composition, spatial and temporal. The new composition framework [FRMWK] 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 purpose of this memo is to define relationships 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:
RFC 2330 also gives an example where a 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 relationships 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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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 slot assignment. The solution then may be the composition of several sub-path measurements. That 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 within its own measurement time slot. 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 accuracy.
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For the primary IPPM metrics (currently Loss, Delay, and Delay Variation), this memo gives a set of complete path metrics that can be composed from the same or similar sub-path metrics. This means that the complete path metric may be composed from:
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The new composition framework [FRMWK] requires the specification of the applicable circumstances for each metric. In particular, the application of Spatial Composition metrics are addressed as to 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.
Has known sources of inaccuracy/error, and identifies the sources.
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This section defines the terminology applicable to Spatial Composition metrics.
Measurement Points:
<there must be a suitable definition for this in IPPM’s literature>
Complete path:
The complete path is the true path that a packet would follow as it traverses from the packet’s Source to its Destination.
Complete path metric:
The complete path metric is the Source to Destination metric that a composed metric is estimating. A complete path metric represents the ground-truth for a composed metric.
Composite Metric (or Composed Metric):
A composite metric is type of metric that is derived from other metrics principally by applying a composition relationship.
Composition Relationship:
A composition relationship is a deterministic process applied to Sub-path metrics to derive another metric (such as a Composite metric).
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 this sub-path is “involved” in the complete path.
Sub-path metrics:
A sub-path path metric is an element of the process to derive a Composite metric, quantifying some aspect of the performance a particular sub-path from its Source to Destination.
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This metric is a necessary element of Delay Composition metrics, and its definition does not formally exist elsewhere in IPPM literature.
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Using the parameters above, we obtain the value of Type-P-One-way-Delay singleton as per RFC 2679 (Almes, G., Kalidindi, S., and M. Zekauskas, “A One-way Delay Metric for IPPM,” September 1999.) [RFC2679].
For each packet [i] that has a finite One-way Delay (in other words, excluding packets which have undefined, or infinite one-way delay):
Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i] =
FiniteDelay[i] = TstampDst - TstampSrc
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The “Type-P-Finite-One-way-Delay” metric allows calculation of the mean statistic. This avoids the need to include lost packets in the sample (whose delay is undefined), and the issue with the prescribed assignment of infinite delay to lost packets when practical systems can only assign some very large value.
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We add the following parameter:
and define
Type-P-Finite-One-way-Delay-Mean =
N
---
1 \
- * > (FiniteDelay [i])
N /
---
i = 1
where all packets i= 1 through N have finite singleton delays.
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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 =
CompMeanDelay = (1/S)Sum(from i=1 to S, MeanDelay[i])
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The mean of a sufficiently large stream of packets measured on each sub-path during the interval [T, Tf] will be representative of the true 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.
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It is sometimes impractical to conduct active measurements between every Src-Dst pair. 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.
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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 parallel exchanges than packets with the source and destination addresses of the complete path. Therefore, the 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.
others...
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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.
others...
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The methodology:
SHOULD use similar packets sent and collected separately in each sub-path.
Allows a degree of flexibility (e.g., active or passive methods can produce the "same" metric, but timing and correlation of passive measurements is much more challenging).
Poisson and/or Periodic streams are RECOMMENDED.
Applicable 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.
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Same as section 4.1.1.
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Using the parameters above, we obtain the value of Type-P-One-way-Packet-Loss singleton and stream as per RFC 2680 (Almes, G., Kalidindi, S., and M. Zekauskas, “A One-way Packet Loss Metric for IPPM,” September 1999.) [RFC2680].
We obtain a sequence of pairs with elements as follows:
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Given the following stream parameter
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 =
Ep = (1/N)Sum(from i=1 to N, L[i])
where all packets i= 1 through N have a value for L.
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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-One-way-Composite-Packet-Loss-Empirical-Probability = CompEp = 1 – {(1 - Ep1) x (1 – Ep2) x (1 – Ep3) x ... x (1 – Epn)}
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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 true 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 loss probability.
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It is sometimes impractical to conduct active measurements between every Src-Dst pair. 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.
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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 parallel exchanges than packets with the source and destination addresses of the complete path. Therefore, the 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.
others...
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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 event like a tunnel fire 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...
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The methodology:
SHOULD use similar packets sent and collected separately in each sub-path.
Allows a degree of flexibility (e.g., active or passive methods can produce the "same" metric, but timing and correlation of passive measurements is much more challenging).
Poisson and/or Periodic streams are RECOMMENDED.
Applicable 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.
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This metric is a necessary element of Composed Delay Variation metrics, and its definition does not formally exist elsewhere in IPPM literature.
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In addition to the parameters of section 4.1.1:
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Using the definition above in section 4.1.2, we obtain the value of Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream[i], the singleton for each packet[i] in the stream (a.k.a. FiniteDelay[i]).
For each packet[i] that meets the F(first packet) criteria given above: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream[i] =
IPDVRefMin[i] = FiniteDelay[i] – MinDelay
where IPDVRefMin[i] is in units of time (seconds, milliseconds).
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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].
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We define the mean IPDVRefMin as follows (where all packets i= 1 through N have a value for IPDVRefMin):
Type-P-One-way-ipdv-refmin-Mean = MeanIPDVRefMin =
N
---
1 \
- * > (IPDVRefMin [i])
N /
---
i = 1
We define the variance of IPDVRefMin as follows:
Type-P-One-way-ipdv-refmin-Variance = VarIPDVRefMin =
N
---
1 \ 2
------- > (IPDVRefMin [i] - MeanIPDVRefMin)
(N - 1) /
---
i = 1
We define the skewness of IPDVRefMin as follows:
Type-P-One-way-ipdv-refmin-Skewness = SkewIPDVRefMin =
N
--- 3
\ / \
> | IPDVRefMin[i]- MeanIPDVRefMin |
/ \ /
---
i = 1
-------------------------------------------
/ \
| ( 3/2 ) |
\ (N - 1) * VarIPDVRefMin /
We define the Quantile of the IPDVRefMin sample as the value where the specified fraction of points is less than the given value.
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The Type-P-One-way-Composite-ipdv-refmin-<something> for the complete Source to Destination path can be calculated by combining statistics of all the constituent sub-paths in the following process:
< to be provided >
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This definition may be the common part for the definition of "Loss Metrics/Statistics" and for the definition of "One-way Delay Composition Metrics and Statistics".
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Type-P-One-way-Combo-mean
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Editorial notes (ES): parameters list to be completed
<P1,T1,dt1>...<Pn,Tn,dtn>:
It is a stream of One-way delay corresponding either to an end to end measure of a sub-path, or to the spatial measure of the sub-path:
- Type-P-One-way-Delay-Poisson-Stream as per [RFC2679];
- Type-P-One-way-Delay-Periodic-Stream a per RFC 3432 (Raisanen, V., Grotefeld, G., and A. Morton, “Network performance measurement with periodic streams,” November 2002.) [RFC3432];
- Type-P-One-way-Composition-Stream as defined below;
- Type-P-subpath-One-way-Delay-Stream as per
I-D.stephan-ippm-multimetrics (Stephan, E., “IP Performance Metrics (IPPM) for spatial and multicast,” October 2005.) [I-D.stephan-ippm-multimetrics].
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Using the value <P1,T1,dt1>...<Pn,Tn,dtn> of one of the One-way delay Stream listed above, we define Type-P-One-way-Combo as the couple (D,L) where D is the mean of the delay of the packets that have a finite One-way, and where L is the average of lost of packets (which have undefined, or infinite one-way delay).
D corresponds to the Type-P-Finite-One-way-Delay-Mean defined above.
L corresponds to the Type-P-One-way-Packet-Loss-Empirical-Probability defined above.
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Parameters:
+ dT1,..., dTn a list of delay.
+ <Src, H1, H2,..., Hn, Dst>, the equivalent path.
Definition:
Using Type-P-One-way-Combo-mean of each sub-path in the equivalent path we define a Type-P-One-way-subpathes-stream as the list of couples (D,L) of the sub-path list;
Results: {<D0,L0>, <D1,L1>, <D2,L2>, … <Dn,Ln>}
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The composition over a path gives D and L which give an estimation of the end-to-end delay and end-to-end packet lost over this path.
Parameters:
+ <Src, H1, H2,..., Hn, Dst>, the complete path.
+ {<D0,L0>, <D1,L1>, <D2,L2>, … <Dn,Ln>}, the composition stream of the sub-paths of a path.
Definition:
Using Type-P-One-way-subpathes-stream we define Type-P-One-way-composition as the couple <D,L> where D is the mean of the delays Di and where L is the average of lost of Li.
Results: <D,L>, where D is a delay and L is the lost
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The sample of Type-P-One-way-composition is defined to permit the usage of the results of Type-P-One-way-composition measure in computation of Type-P-One-way-Combo-mean composition.
Parameters:
+ T1,..., Tn, a list of times;
+ <D,L>, the delay and the lost computed by composition.
Definition:
Using Type-P-One-way-composition we define Type-P-One-way-composition-stream as the stream of couples <D,L> over time.
Results: <T1,D1,L1>...<Tn,Dn,Ln>
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Combo metric is very easy to measure and to compose.
It gives the delay and the lost, so most of the need.
Combo metric may be performed on com metric too.
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Packets may cross different sub path than the equivalent end-to-end measure because Type-P differ.
Packets may experiment different behavior than the equivalent end-to-end measure because of access classification based on packet addresses.
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When
+ Sum of sub-path differ from the equivalent path.
+ Type-P differ.
+ Size differ.
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The methodology: Is applicable to Intra and interdomain;
SHOULD report the context of the measure;
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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.
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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.
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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.
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Metrics defined in this memo will be registered in the IANA IPPM METRICS REGISTRY as described in initial version of the registry RFC 4148 (Stephan, E., “IP Performance Metrics (IPPM) Metrics Registry,” August 2005.) [RFC4148].
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>>>>>>>>>>>>Open 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?
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>OPEN 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.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> OPEN Issue
How can we introduce multicast metrics here, without causing too much confusion? Should the multicast version of this draft wait until the Unicast concepts are stable (or maybe appear in a separate draft)?
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| [FRMWK] | Morton, A. and S.Van Den Berghe, “Framework for Metric Composition,” February 2006. |
| [RFC2119] | Bradner, S., “Key words for use in RFCs to Indicate Requirement Levels,” BCP 14, RFC 2119, March 1997 (TXT, HTML, XML). |
| [RFC2330] | Paxson, V., Almes, G., Mahdavi, J., and M. Mathis, “Framework for IP Performance Metrics,” RFC 2330, May 1998 (TXT, HTML, XML). |
| [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. |
| [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. |
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| [I-D.stephan-ippm-multimetrics] | Stephan, E., “IP Performance Metrics (IPPM) for spatial and multicast,” draft-stephan-ippm-multimetrics-02 (work in progress), October 2005. |
| [Y.1540] | ITU-T Recommendation Y.1540, “Internet protocol data communication service - IP packet transfer and availability performance parameters,” December 2002. |
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| 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@francetelecom.com |
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