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Network Working Group                                          A. Morton
Internet-Draft                                                 AT&T Labs
Expires: August 30, 2006                                      E. Stephan
                                             France Telecom Division R&D
                                                       February 26, 2006


                     Spatial Composition of Metrics
                 draft-ietf-ippm-spatial-composition-00

Status of this Memo

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   This Internet-Draft will expire on August 30, 2006.

Copyright Notice

   Copyright (C) The Internet Society (2006).

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.



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Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].

   In this memo, the characters "<=" should be read as "less than or
   equal to" and ">=" as "greater than or equal to".


Table of Contents

   1.  Contributors . . . . . . . . . . . . . . . . . . . . . . . . .  4
   2.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
     2.1.  Motivation . . . . . . . . . . . . . . . . . . . . . . . .  5
   3.  Scope, Application, and Terminology  . . . . . . . . . . . . .  5
     3.1.  Scope of work  . . . . . . . . . . . . . . . . . . . . . .  5
     3.2.  Application  . . . . . . . . . . . . . . . . . . . . . . .  6
     3.3.  Terminology  . . . . . . . . . . . . . . . . . . . . . . .  6
   4.  One-way Delay Composition Metrics and Statistics . . . . . . .  7
     4.1.  Name:
           Type-P-Finite-One-way-Delay-Poisson/Periodic-Stream  . . .  7
       4.1.1.  Metric Parameters: . . . . . . . . . . . . . . . . . .  7
       4.1.2.  Definition and Metric Units  . . . . . . . . . . . . .  8
       4.1.3.  Discussion and other details . . . . . . . . . . . . .  8
       4.1.4.  Mean Statistic . . . . . . . . . . . . . . . . . . . .  8
       4.1.5.  Composition Relationship: Sum of Means . . . . . . . .  9
       4.1.6.  Statement of Conjecture  . . . . . . . . . . . . . . .  9
       4.1.7.  Justification of Composite Relationship  . . . . . . .  9
       4.1.8.  Sources of Error . . . . . . . . . . . . . . . . . . . 10
       4.1.9.  Specific cases where the conjecture might fail . . . . 10
       4.1.10. Application of Measurement Methodology . . . . . . . . 10
   5.  Loss Metrics and Statistics  . . . . . . . . . . . . . . . . . 11
     5.1.  Name:
           Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream . . . . 11
       5.1.1.  Metric Parameters: . . . . . . . . . . . . . . . . . . 11
       5.1.2.  Definition and Metric Units  . . . . . . . . . . . . . 11
       5.1.3.  Discussion and other details . . . . . . . . . . . . . 11
       5.1.4.  Statistic:
               Type-P-One-way-Packet-Loss-Empirical-Probability . . . 11
       5.1.5.  Composition Relationship: Composition of Empirical
               Probabilities  . . . . . . . . . . . . . . . . . . . . 11
       5.1.6.  Statement of Conjecture  . . . . . . . . . . . . . . . 12
       5.1.7.  Justification of Composite Relationship  . . . . . . . 12
       5.1.8.  Sources of Error . . . . . . . . . . . . . . . . . . . 12
       5.1.9.  Specific cases where the conjecture might fail . . . . 12
       5.1.10. Application of Measurement Methodology . . . . . . . . 13
   6.  Delay Variation Metrics and Statistics . . . . . . . . . . . . 13



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     6.1.  Name:
           Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream . . . . 13
       6.1.1.  Metric Parameters: . . . . . . . . . . . . . . . . . . 13
       6.1.2.  Definition and Metric Units  . . . . . . . . . . . . . 14
       6.1.3.  Discussion and other details . . . . . . . . . . . . . 14
       6.1.4.  Statistics: Mean, Variance, Skewness, Quanitle . . . . 14
       6.1.5.  Composition Relationships: . . . . . . . . . . . . . . 15
       6.1.6.  Statement of Conjecture  . . . . . . . . . . . . . . . 16
       6.1.7.  Justification of Composite Relationship  . . . . . . . 16
       6.1.8.  Sources of Error . . . . . . . . . . . . . . . . . . . 16
       6.1.9.  Specific cases where the conjecture might fail . . . . 16
       6.1.10. Application of Measurement Methodology . . . . . . . . 16
   7.  Other Metrics and Statistics: One-way Combined Metric  . . . . 16
     7.1.  Metric Name: . . . . . . . . . . . . . . . . . . . . . . . 16
       7.1.1.  Metric Parameters: . . . . . . . . . . . . . . . . . . 16
       7.1.2.  Definition and Metric Units  . . . . . . . . . . . . . 16
       7.1.3.  Discussion and other details . . . . . . . . . . . . . 17
       7.1.4.  Type-P-One-way-Combo-subpathes-stream  . . . . . . . . 17
       7.1.5.  Type-P-One-way-composition . . . . . . . . . . . . . . 17
       7.1.6.  Type-P-One-way-composition . . . . . . . . . . . . . . 17
       7.1.7.  Statement of Conjecture  . . . . . . . . . . . . . . . 18
       7.1.8.  Justification of Composite Relationship  . . . . . . . 18
       7.1.9.  Sources of Error . . . . . . . . . . . . . . . . . . . 18
       7.1.10. Specific cases where the conjecture might fail . . . . 18
       7.1.11. Application of Measurement Methodology . . . . . . . . 18
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 19
     8.1.  Denial of Service Attacks  . . . . . . . . . . . . . . . . 19
     8.2.  User Data Confidentiality  . . . . . . . . . . . . . . . . 19
     8.3.  Interference with the metrics  . . . . . . . . . . . . . . 19
   9.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 19
   10. Security Considerations  . . . . . . . . . . . . . . . . . . . 20
   11. Open Issues  . . . . . . . . . . . . . . . . . . . . . . . . . 20
   12. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 21
   13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 21
     13.1. Normative References . . . . . . . . . . . . . . . . . . . 21
     13.2. Informative References . . . . . . . . . . . . . . . . . . 21
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 22
   Intellectual Property and Copyright Statements . . . . . . . . . . 23













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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 <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>


2.  Introduction

   The IPPM framework RFC 2330 [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:

   o  the specific conjecture applied to the metric,

   o  a justification of the practical utility of the composition in
      terms of making accurate measurements of the metric on the path,





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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.

   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.

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 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.


3.  Scope, Application, and Terminology

3.1.  Scope of work

   For the primary IPPM metrics (currently Loss, Delay, and Delay
   Variation), this memo gives a set of complete path metrics that can



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   be composed from the same or similar sub-path metrics.  This means
   that the complete path metric may be composed from:

   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 metrics 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).

3.2.  Application

   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.

3.3.  Terminology

   This section defines the terminology applicable to Spatial
   Composition metrics.

   Measurement Points:




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   <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.


4.  One-way Delay Composition Metrics and Statistics

4.1.  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.

4.1.1.  Metric Parameters:

   o  Src, the IP address of a host + Dst, the IP address of a host





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   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  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.

4.1.2.  Definition and Metric Units

   Using the parameters above, we obtain the value of Type-P-One-way-
   Delay singleton as per RFC 2679 [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

4.1.3.  Discussion and other details

   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.

4.1.4.  Mean Statistic

   We add the following parameter:

   o  N, the total number of packets received at Dst (sent between T0
      and Tf)

   and define



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   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.

4.1.5.  Composition Relationship: 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.

   o  S, the number of sub-paths involved in the complete Src-Dst path.

   Then the

   Type-P-Finite-Composite-One-way-Delay-Mean =

   CompMeanDelay = (1/S)Sum(from i=1 to S, MeanDelay[i])

4.1.6.  Statement of Conjecture

   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.

4.1.7.  Justification of Composite Relationship

   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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4.1.8.  Sources of Error

   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...

4.1.9.  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.

   others...

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 (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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5.  Loss Metrics and Statistics

5.1.  Name: Type-P-One-way-Packet-Loss-Poisson/Periodic-Stream

5.1.1.  Metric Parameters:

   Same as section 4.1.1.

5.1.2.  Definition and Metric Units

   Using the parameters above, we obtain the value of Type-P-One-way-
   Packet-Loss singleton and stream as per RFC 2680 [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

5.1.4.  Statistic: Type-P-One-way-Packet-Loss-Empirical-Probability

   Given the following stream parameter

   o  N, the total number of packets sent between T0 and Tf

   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.

5.1.5.  Composition Relationship: 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-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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5.1.6.  Statement of Conjecture

   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.

5.1.7.  Justification of Composite Relationship

   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.

5.1.8.  Sources of Error

   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...

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 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



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   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...

5.1.10.  Application of Measurement Methodology

   The methodology:

   SHOULD use similar packets sent and collected separately in each sub-
   path.

   Allows a degree of flexibility (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.


6.  Delay Variation Metrics and Statistics

6.1.  Name: Type-P-One-way-ipdv-refmin-Poisson/Periodic-Stream

   This metric is a necessary element of Composed Delay Variation
   metrics, and its definition does not formally exist elsewhere in IPPM
   literature.

6.1.1.  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)

   o  TstampDst[i], the wire time of packet[i] as measured at MP(Dst),
      assigned to packets that arrive within a "reasonable" time.





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   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, or infinite one-way
      delay) and MUST have been transmitted during the interval T, Tf.
      The second packet in the pair 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, 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.

6.1.2.  Definition and Metric Units

   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).

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, Quanitle

   We define the mean IPDVRefMin as follows (where all packets i= 1
   through N have a value for IPDVRefMin):




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   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.

6.1.5.  Composition Relationships:

   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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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

   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".

7.1.  Metric Name:

   Type-P-One-way-Combo-mean

7.1.1.  Metric Parameters:

   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 [RFC3432];

   - Type-P-One-way-Composition-Stream as defined below;

   - Type-P-subpath-One-way-Delay-Stream as per

   I-D.stephan-ippm-multimetrics [I-D.stephan-ippm-multimetrics].

7.1.2.  Definition and Metric Units

   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).




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   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.

7.1.3.  Discussion and other details

7.1.4.  Type-P-One-way-Combo-subpathes-stream

   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>}

7.1.5.  Type-P-One-way-composition

   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

7.1.6.  Type-P-One-way-composition

   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.



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   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>

7.1.7.  Statement of Conjecture

7.1.8.  Justification of Composite Relationship

   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.

7.1.9.  Sources of Error

   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.

7.1.10.  Specific cases where the conjecture might fail

   When

   + Sum of sub-path differ from the equivalent path.

   + Type-P differ.

   + Size differ.

7.1.11.  Application of Measurement Methodology

   The methodology: Is applicable to Intra and interdomain;

   SHOULD report the context of the measure;




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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
   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 RFC
   4148 [RFC4148].





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10.  Security Considerations


11.  Open Issues

   >>>>>>>>>>>>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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12.  Acknowledgements


13.  References

13.1.  Normative References

   [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.

   [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.

   [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.

13.2.  Informative References

   [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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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@francetelecom.com
   URI:



























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