<pre>Network Working Group                                         E. Stephan
Request for Comments: 5644                                France Telecom
Category: Standards Track                                       L. Liang
                                                    University of Surrey
                                                               A. Morton
                                                               AT&amp;T Labs
                                                            October 2009


          <span class="h1">IP Performance Metrics (IPPM): Spatial and Multicast</span>

Abstract

   The IETF has standardized IP Performance Metrics (IPPM) for measuring
   end-to-end performance between two points.  This memo defines two new
   categories of metrics that extend the coverage to multiple
   measurement points.  It defines spatial metrics for measuring the
   performance of segments of a source to destination path, and metrics
   for measuring the performance between a source and many destinations
   in multiparty communications (e.g., a multicast tree).

Status of This Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (c) 2009 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to <a href="https://www.rfc-editor.org/bcp/bcp78">BCP 78</a> and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (<a href="http://trustee.ietf.org/license-info">http://trustee.ietf.org/license-info</a>) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the BSD License.

   This document may contain material from IETF Documents or IETF
   Contributions published or made publicly available before November
   10, 2008.  The person(s) controlling the copyright in some of this
   material may not have granted the IETF Trust the right to allow



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   modifications of such material outside the IETF Standards Process.
   Without obtaining an adequate license from the person(s) controlling
   the copyright in such materials, this document may not be modified
   outside the IETF Standards Process, and derivative works of it may
   not be created outside the IETF Standards Process, except to format
   it for publication as an RFC or to translate it into languages other
   than English.

Table of Contents

   <a href="#section-1">1</a>. Introduction and Scope ..........................................<a href="#page-3">3</a>
   <a href="#section-2">2</a>. Terminology .....................................................<a href="#page-4">4</a>
   <a href="#section-3">3</a>. Brief Metric Descriptions .......................................<a href="#page-7">7</a>
   <a href="#section-4">4</a>. Motivations ....................................................<a href="#page-10">10</a>
   <a href="#section-5">5</a>. Spatial Vector Metrics Definitions .............................<a href="#page-12">12</a>
   <a href="#section-6">6</a>. Spatial Segment Metrics Definitions ............................<a href="#page-19">19</a>
   <a href="#section-7">7</a>. One-to-Group Metrics Definitions ...............................<a href="#page-27">27</a>
   <a href="#section-8">8</a>. One-to-Group Sample Statistics .................................<a href="#page-30">30</a>
   <a href="#section-9">9</a>. Measurement Methods: Scalability and Reporting .................<a href="#page-40">40</a>
   <a href="#section-10">10</a>. Manageability Considerations ..................................<a href="#page-44">44</a>
   <a href="#section-11">11</a>. Security Considerations .......................................<a href="#page-49">49</a>
   <a href="#section-12">12</a>. Acknowledgments ...............................................<a href="#page-50">50</a>
   <a href="#section-13">13</a>. IANA Considerations ...........................................<a href="#page-50">50</a>
   <a href="#section-14">14</a>. References ....................................................<a href="#page-56">56</a>
      <a href="#section-14.1">14.1</a>. Normative References .....................................<a href="#page-56">56</a>
      <a href="#section-14.2">14.2</a>. Informative References ...................................<a href="#page-57">57</a>

























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<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>.  Introduction and Scope</span>

   IETF has standardized IP Performance Metrics (IPPM) for measuring
   end-to-end performance between two points.  This memo defines two new
   categories of metrics that extend the coverage to multiple
   measurement points.  It defines spatial metrics for measuring the
   performance of segments of a source to destination path, and metrics
   for measuring the performance between a source and many destinations
   in multiparty communications (e.g., a multicast tree).

   The purpose of this memo is to define metrics to fulfill the new
   requirements of measurement involving multiple measurement points.
   Spatial metrics measure the performance of each segment along a path.
   One-to-group metrics measure the performance for a group of users.
   These metrics are derived from one-way end-to-end metrics, all of
   which follow the IPPM framework [<a href="./rfc2330" title="&quot;Framework for IP Performance Metrics&quot;">RFC2330</a>].

   This memo is organized as follows: <a href="#section-2">Section 2</a> introduces new terms
   that extend the original IPPM framework [<a href="./rfc2330" title="&quot;Framework for IP Performance Metrics&quot;">RFC2330</a>].  <a href="#section-3">Section 3</a> briefly
   introduces the new metrics, and <a href="#section-4">Section 4</a> motivates each metric
   category.  Sections <a href="#section-5">5</a> through <a href="#section-8">8</a> develop each category of metrics with
   definitions and statistics.  Then the memo discusses the impact of
   the measurement methods on the scalability and proposes an
   information model for reporting the measurements.  Finally, the memo
   discusses security aspects related to measurement and registers the
   metrics in the IANA IP Performance Metrics Registry [<a href="./rfc4148" title="&quot;IP Performance Metrics (IPPM) Metrics Registry&quot;">RFC4148</a>].

   The scope of this memo is limited to metrics using a single source
   packet or stream, and observations of corresponding packets along the
   path (spatial), at one or more destinations (one-to-group), or both.
   Note that all the metrics defined herein are based on observations of
   packets dedicated to testing, a process that is called active
   measurement.  Passive measurement (for example, a spatial metric
   based on the observation of user traffic) is beyond the scope of this
   memo.

<span class="h3"><a class="selflink" id="section-1.1" href="#section-1.1">1.1</a>.  Requirements Language</span>

   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 <a href="./rfc2119">RFC 2119</a> [<a href="./rfc2119" title="&quot;Key words for use in RFCs to Indicate Requirement Levels&quot;">RFC2119</a>].










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<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>.  Terminology</span>

<span class="h3"><a class="selflink" id="section-2.1" href="#section-2.1">2.1</a>.  Naming of the Metrics</span>

   The names of the metrics, including capitalized letters, are as close
   as possible of the names of the one-way end-to-end metrics they are
   derived from.

<span class="h3"><a class="selflink" id="section-2.2" href="#section-2.2">2.2</a>.  Terms Defined Elsewhere</span>

   host: <a href="./rfc2330#section-5">section&nbsp;5 of RFC 2330</a>

   router: <a href="./rfc2330#section-5">section&nbsp;5 of RFC 2330</a>

   loss threshold: <a href="./rfc2680#section-2.8.2">section&nbsp;2.8.2 of RFC 2680</a>

   path: <a href="./rfc2330#section-5">section&nbsp;5 of RFC 2330</a>

   sample: <a href="./rfc2330#section-11">section&nbsp;11 of RFC 2330</a>

   singleton: <a href="./rfc2330#section-11">section&nbsp;11 of RFC 2330</a>

<span class="h3"><a class="selflink" id="section-2.3" href="#section-2.3">2.3</a>.  Routers Digest</span>

   The list of the routers on the path from the source to the
   destination that act as points of interest, also referred to as the
   routers digest.

<span class="h3"><a class="selflink" id="section-2.4" href="#section-2.4">2.4</a>.  Multiparty Metric</span>

   A metric is said to be multiparty if the topology involves more than
   one measurement collection point.  All multiparty metrics designate a
   set of hosts as "points of interest", where one host is the source
   and other hosts are the measurement collection points.  For example,
   if the set of points of interest is &lt; ha, hb, hc, ..., hn &gt;, where ha
   is the source and &lt; hb, hc, ..., hn &gt; are the destinations, then
   measurements may be conducted between &lt; ha, hb&gt;, &lt; ha, hc&gt;, ..., &lt;ha,
   hn &gt;.

   For the purposes of this memo (reflecting the scope of a single
   source), the only multiparty metrics are one-to-group metrics.

<span class="h3"><a class="selflink" id="section-2.5" href="#section-2.5">2.5</a>.  Spatial Metric</span>

   A metric is said to be spatial if one of the hosts (measurement
   collection points) involved is neither the source nor a destination
   of the measured packet(s).  Such measurement hosts will usually be
   routers that are members of the routers digest.



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<span class="h3"><a class="selflink" id="section-2.6" href="#section-2.6">2.6</a>.  One-to-Group Metric</span>

   A metric is said to be one-to-group if the measured packet is sent by
   one source and (potentially) received by more than one destination.
   Thus, the topology of the communication group can be viewed as a
   center-distributed or server-client topology with the source as the
   center/server in the topology.

<span class="h3"><a class="selflink" id="section-2.7" href="#section-2.7">2.7</a>.  Points of Interest</span>

   Points of interest are the hosts (as per the <a href="./rfc2330">RFC 2330</a> definition,
   "hosts" include routing nodes) that are measurement collection
   points, which are a sub-set of the set of hosts involved in the
   delivery of the packets (in addition to the source itself).

   For spatial metrics, points of interest are a (possibly arbitrary)
   sub-set of all the routers involved in the path.

   Points of interest of one-to-group metrics are the intended
   destination hosts for packets from the source (in addition to the
   source itself).

                         Src                   Dst
                         `.          ,-.
                           `.      ,'   `...... <a href="#page-1">1</a>
                             `.   ;       :
                               `. ;       :
                                 ;         :... <a href="#page-2">2</a>
                                 |         |
                                 :         ;
                                  :       ;.... <a href="#page-3">3</a>
                                  :       ;
                                   `.   ,'
                                     `-'....... <a href="#page-I">I</a>

                 Figure 1: One-to-Group Points of Interest

   A candidate point of interest for spatial metrics is a router from
   the set of routers involved in the delivery of the packets from
   source to destination.











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                         Src ------.           Hosts
                                    \
                                     `---X   --- 1
                                         \
                                          x
                                         /
                              .---------X   ---- 2
                            /
                           x
                            ...
                            `---X           ---- ...
                                   \
                                    \
                                     \
                                      X     ---- J
                                       \
                                        \
                                         \
                                          `---- Dst

                Note: 'X' are nodes that are points of interest,
                      'x' are nodes that are not points of interest

                   Figure 2: Spatial Points of Interest

<span class="h3"><a class="selflink" id="section-2.8" href="#section-2.8">2.8</a>.  Reference Point</span>

   A reference point is defined as the server where the statistical
   calculations will be carried out.  It is usually a centralized server
   in the measurement architecture that is controlled by a network
   operator, where measurement data can be collected for further
   processing.  The reference point is distinctly different from hosts
   at measurement collection points, where the actual measurements are
   carried out (e.g., points of interest).

<span class="h3"><a class="selflink" id="section-2.9" href="#section-2.9">2.9</a>.  Vector</span>

   A vector is a set of singletons (single atomic results) comprised of
   observations corresponding to a single source packet at different
   hosts in a network.  For instance, if the one-way delay singletons
   observed at N receivers for Packet P sent by the source Src are dT1,
   dT2,..., dTN, then a vector V with N elements can be organized as
   {dT1, dT2,..., dTN}.  The element dT1 is distinct from all others as
   the singleton at receiver 1 in response to a packet sent from the
   source at a specific time.  The complete vector gives information
   over the dimension of space, a set of N receivers in this example.





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   The singleton elements of any vector are distinctly different from
   each other in terms of their measurement collection point.  Different
   vectors for common measurement points of interest are distinguished
   by the source packet sending time.

<span class="h3"><a class="selflink" id="section-2.10" href="#section-2.10">2.10</a>.  Matrix</span>

   Several vectors form a matrix, which contains results observed over a
   sampling interval at different places in a network at different
   times.  For example, the one-way delay vectors V1={dT11, dT12,...,
   dT1N}, V2={dT21, dT22,..., dT2N},..., Vm={dTm1, dTm2,..., dTmN} for
   Packet P1, P2,...,Pm, form a one-way delay Matrix {V1, V2,...,Vm}.
   The matrix organizes the vector information to present network
   performance in both space and time.

   A one-dimensional matrix (row) corresponds to a sample in simple
   point-to-point measurement.

   The relationship among singleton, sample, vector, and matrix is
   illustrated in Figure 3.

                 points of        singleton
                 interest           /       samples(time)
                  ,----.    ^      /
                 /   R1.....|  / R1dT1   R1dT2   R1dT3 ... R3dTk \
                /         \ | |                                   |
               ;  R2........| |  R2dT1   R2dT2   R2dT3 ... R3dTk  |
          Src  |           || |                                   |
               |      R3....| |  R3dT1   R3dT2   R3dT3 ... R3dTk  |
               |           || |                                   |
               :           ;| |                                   |
                \         / | |                                   |
                 \  Rn......|  \ RndT1   RndT2   RndT3 ... RndTk /
                  `-----'   +-------------------------------------&gt; time

                                vector           matrix
                               (space)      (time and space)

     Figure 3: Relationship between Singletons, Samples, Vectors, and
                                  Matrix

<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>.  Brief Metric Descriptions</span>

   The metrics for spatial and one-to-group measurement are based on the
   source-to-destination, or end-to-end metrics defined by IETF in
   [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>], [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>], [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>], and [<a href="./rfc3432" title="&quot;Network performance measurement with periodic streams&quot;">RFC3432</a>].





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   This memo defines seven new spatial metrics using the [<a href="./rfc2330" title="&quot;Framework for IP Performance Metrics&quot;">RFC2330</a>]
   framework of parameters, units of measure, and measurement
   methodologies.  Each definition includes a section that describes
   measurement constraints and issues, and provides guidance to increase
   the accuracy of the results.

   The spatial metrics are:

   o  Type-P-Spatial-One-way-Delay-Vector divides the end-to-end Type-P-
      One-way-Delay [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] into a spatial vector of one-way delay
      singletons.

   o  Type-P-Spatial-One-way-Packet-Loss-Vector divides an end-to-end
      Type-P-One-way-Packet-Loss [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] into a spatial vector of
      packet loss singletons.

   o  Type-P-Spatial-One-way-ipdv-Vector divides an end-to-end Type-P-
      One-way-ipdv into a spatial vector of ipdv (IP Packet Delay
      Variation) singletons.

   o  Using elements of the Type-P-Spatial-One-way-Delay-Vector metric,
      a sample called Type-P-Segment-One-way-Delay-Stream collects one-
      way delay metrics between two points of interest on the path over
      time.

   o  Likewise, using elements of the Type-P-Spatial-Packet-Loss-Vector
      metric, a sample called Type-P-Segment-Packet-Loss-Stream collects
      one-way delay metrics between two points of interest on the path
      over time.

   o  Using the Type-P-Spatial-One-way-Delay-Vector metric, a sample
      called Type-P-Segment-ipdv-prev-Stream will be introduced to
      compute ipdv metrics (using the previous packet selection
      function) between two points of interest on the path over time.

   o  Again using the Type-P-Spatial-One-way-Delay-Vector metric, a
      sample called Type-P-Segment-ipdv-min-Stream will define another
      set of ipdv metrics (using the minimum delay packet selection
      function) between two points of interest on the path over time.

   The memo also defines three one-to-group metrics to measure the one-
   way performance between a source and a group of receivers.  They are:

   o  Type-P-One-to-group-Delay-Vector which collects the set of Type-P-
      One-way-Delay singletons between one sender and N receivers;






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   o  Type-P-One-to-group-Packet-Loss-Vector which collects the set of
      Type-P-One-way-Packet-Loss singletons between one sender and N
      receivers; and

   o  Type-P-One-to-group-ipdv-Vector which collects the set of Type-P-
      One-way-ipdv singletons between one sender and N receivers.

   Finally, based on the one-to-group vector metrics listed above,
   statistics are defined to capture single receiver performance, group
   performance, and the relative performance for a multiparty
   communication:

   o  Using the Type-P-One-to-group-Delay-Vector, a metric called Type-
      P-One-to-group-Receiver-n-Mean-Delay, or RnMD, presents the mean
      of delays between one sender and a single receiver 'n'.  From this
      metric, three additional metrics are defined to characterize the
      mean delay over the entire group of receivers during the same time
      interval:

      *  Type-P-One-to-group-Mean-Delay, or GMD, presents the mean of
         delays;

      *  Type-P-One-to-group-Range-Mean-Delay, or GRMD, presents the
         range of mean delays; and

      *  Type-P-One-to-group-Max-Mean-Delay, or GMMD, presents the
         maximum of mean delays.

   o  Using the Type-P-One-to-group-Packet-Loss-Vector, a metric called
      Type-P-One-to-group-Receiver-n-Loss-Ratio, or RnLR, captures the
      packet loss ratio between one sender and a single receiver 'n'.
      Based on this definition, two more metrics are defined to
      characterize packet loss over the entire group during the same
      time interval:

      *  Type-P-One-to-group-Loss-Ratio, or GLR, captures the overall
         packet loss ratio for the entire group of receivers; and

      *  Type-P-One-to-group-Range-Loss-Ratio, or GRLR, presents the
         comparative packet loss ratio during the test interval between
         one sender and N receivers.

   o  Using the Type-P-One-to-group-Packet-Loss-Vector, a metric called
      Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio, or RnCLR, computes
      a packet loss ratio using the maximum number of packets received
      at any receiver.





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   o  Using Type-P-One-to-group-ipdv-Vector, a metric called Type-P-One-
      to-group-Range-Delay-Variation, or GRDV, presents the range of
      delay variation between one sender and a group of receivers.

<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>.  Motivations</span>

   All existing IPPM metrics are defined for end-to-end (source-to-
   destination) measurement of point-to-point paths.  It is logical to
   extend them to multiparty situations such as one-to-one trajectory
   metrics and one-to-multipoint metrics.

<span class="h3"><a class="selflink" id="section-4.1" href="#section-4.1">4.1</a>.  Motivations for Spatial Metrics</span>

   Spatial metrics are needed for:

   o  Decomposing the performance of an inter-domain path to quantify
      the per-AS (Autonomous System) contribution to the end-to-end
      performance.

   o  Traffic engineering and troubleshooting, which benefit from
      spatial views of one-way delay and ipdv consumption, or
      identification of the path segment where packets were lost.

   o  Monitoring the decomposed performance of a multicast tree based on
      MPLS point-to-multipoint communications.

   o  Dividing end-to-end metrics, so that some segment measurements can
      be re-used and help measurement systems reach large-scale
      coverage.  Spatial measures could characterize the performance of
      an intra-domain segment and provide an elementary piece of
      information needed to estimate inter-domain performance to another
      destination using Spatial Composition metrics [<a href="#ref-SPATIAL" title="&quot;Spatial Composition of Metrics&quot;">SPATIAL</a>].

<span class="h3"><a class="selflink" id="section-4.2" href="#section-4.2">4.2</a>.  Motivations for One-to-group Metrics</span>

   While the node-to-node-based spatial measures can provide very useful
   data in the view of each connection, we also need measures to present
   the performance of a multiparty communication topology.  A simple
   point-to-point metric cannot completely describe the multiparty
   situation.  New one-to-group metrics assess performance of the
   multiple paths for further statistical analysis.  The new metrics are
   named one-to-group performance metrics, and they are based on the
   unicast metrics defined in IPPM RFCs.  One-to-group metrics are one-
   way metrics from one source to a group of destinations or receivers.
   The metrics are helpful for judging the overall performance of a
   multiparty communications network and for describing the performance
   variation across a group of destinations.




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   One-to-group performance metrics are needed for:

   o  Designing and engineering multicast trees and MPLS point-to-
      multipoint Label Switched Paths (LSPs).

   o  Evaluating and controlling the quality of multicast services,
      including inter-domain multicast.

   o  Presenting and evaluating the performance requirements for
      multiparty communications and overlay multicast.

   To understand the packet transfer performance between one source and
   any one receiver in the multiparty communication group, we need to
   collect instantaneous end-to-end metrics, or singletons.  This gives
   a very detailed view into the performance of each branch of the
   multicast tree, and can provide clear and helpful information for
   engineers to identify the branch with problems in a complex
   multiparty routing tree.

   The one-to-group metrics described in this memo introduce the
   multiparty topology into the IPPM framework, and they describe the
   performance delivered to a group receiving packets from the same
   source.  The concept extends the "path" of the point-to-point
   measurement to "path tree" to cover one-to-many topologies.  If
   applied to one-to-one topology, the one-to-group metrics provide
   exactly the same results as the corresponding one-to-one metrics.

<span class="h3"><a class="selflink" id="section-4.3" href="#section-4.3">4.3</a>.  Discussion on Group-to-One and Group-to-Group Metrics</span>

   We note that points of interest can also be selected to define
   measurements on group-to-one and group-to-group topologies.  These
   topologies are beyond the scope of this memo, because they would
   involve multiple packets launched from different sources.  However,
   this section gives some insights on these two cases.

   The measurements for group-to-one topology can be easily derived from
   the one-to-group measurement.  The measurement point is the host that
   is acting as a receiver while all other hosts act as sources in this
   case.

   The group-to-group communication topology has no obvious focal point:
   the sources and the measurement collection points can be anywhere.
   However, it is possible to organize the problem by applying
   measurements in one-to-group or group-to-one topologies for each host
   in a uniform way (without taking account of how the real






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   communication might be carried out).  For example, one group of hosts
   &lt; ha, hb, hc, ..., hn &gt; might act as sources to send data to another
   group of hosts &lt; Ha, Hb, Hc, ..., Hm &gt;, and they can be organized
   into n sets of points of interest for one-to-group communications:

   &lt; ha, Ha, Hb, Hc, ..., Hm &gt;, &lt; hb, Ha, Hb, Hc, ..., Hm &gt;, &lt;hc, Ha,
   Hb, Hc, ..., Hm &gt;, ..., &lt; hn, Ha, Hb, Hc, ..., Hm &gt;.

<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>.  Spatial Vector Metrics Definitions</span>

   This section defines vectors for the spatial decomposition of end-to-
   end singleton metrics over a path.

   Spatial vector metrics are based on the decomposition of standard
   end-to-end metrics defined by the IPPM WG in [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>], [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>],
   [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>], and [<a href="./rfc3432" title="&quot;Network performance measurement with periodic streams&quot;">RFC3432</a>].

   The spatial vector definitions are coupled with the corresponding
   end-to-end metrics.  Measurement methodology aspects are common to
   all the vectors defined and are consequently discussed in a common
   section.

<span class="h3"><a class="selflink" id="section-5.1" href="#section-5.1">5.1</a>.  A Definition for Spatial One-Way Delay Vector</span>

   This section is coupled with the definition of Type-P-One-way-Delay
   in <a href="./rfc2679#section-3">section&nbsp;3 of [RFC2679]</a>.  When a parameter from the definition in
   [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] is re-used in this section, the first instance will be
   tagged with a trailing asterisk.

   Sections <a href="#section-3.5">3.5</a> to <a href="#section-3.8">3.8</a> of [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] give requirements and applicability
   statements for end-to-end one-way delay measurements.  They are
   applicable to each point of interest, Hi, involved in the measure.
   Spatial one-way delay measurements MUST respect them, especially
   those related to methodology, clock, uncertainties, and reporting.

<span class="h4"><a class="selflink" id="section-5.1.1" href="#section-5.1.1">5.1.1</a>.  Metric Name</span>

   Type-P-Spatial-One-way-Delay-Vector

<span class="h4"><a class="selflink" id="section-5.1.2" href="#section-5.1.2">5.1.2</a>.  Metric Parameters</span>

   o  Src*, the IP address of the sender.

   o  Dst*, the IP address of the receiver.

   o  i, an integer in the ordered list &lt;1,2,...,n&gt; of routers in the
      path.




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   o  Hi, a router of the routers digest.

   o  T*, a time, the sending (or initial observation) time for a
      measured packet.

   o  dT*, a delay, the one-way delay for a measured packet.

   o  dTi, a delay, the one-way delay for a measured packet from the
      source to router Hi.

   o  &lt;dT1,... dTi,... dTn&gt; a list of n delay singletons.

   o  Type-P*, the specification of the packet type.

   o  &lt;H1, H2,..., Hn&gt; the routers digest.

<span class="h4"><a class="selflink" id="section-5.1.3" href="#section-5.1.3">5.1.3</a>.  Metric Units</span>

   The value of Type-P-Spatial-One-way-Delay-Vector is a sequence of
   times (a real number in the dimension of seconds with sufficient
   resolution to convey the results).

<span class="h4"><a class="selflink" id="section-5.1.4" href="#section-5.1.4">5.1.4</a>.  Definition</span>

   Given a Type-P packet sent by the Src at wire-time (first bit) T to
   the receiver Dst on the path &lt;H1, H2,..., Hn&gt;.  There is a sequence
   of values &lt;T+dT1,T+dT2,...,T+dTn,T+dT&gt; such that dT is the Type-P-
   One-way-Delay from Src to Dst, and for each Hi of the path, T+dTi is
   either a real number corresponding to the wire-time the packet passes
   (last bit received) Hi, or undefined if the packet does not pass Hi
   within a specified loss threshold* time.

   Type-P-Spatial-One-way-Delay-Vector metric is defined for the path
   &lt;Src, H1, H2,..., Hn, Dst&gt; as the sequence of values
   &lt;T,dT1,dT2,...,dTn,dT&gt;.

<span class="h4"><a class="selflink" id="section-5.1.5" href="#section-5.1.5">5.1.5</a>.  Discussion</span>

   Some specific issues that may occur are as follows:

   o  the delay singletons "appear" to decrease: dTi &gt; dTi+1.  This may
      occur despite being physically impossible with the definition
      used.








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      *  This is frequently due to a measurement clock synchronization
         issue.  This point is discussed in <a href="#section-3.7.1">section 3.7.1</a> "Errors or
         uncertainties related to Clocks" of [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>].  Consequently,
         the values of delays measured at multiple routers may not match
         the order of those routers on the path.

      *  The actual order of routers on the path may change due to
         reconvergence (e.g., recovery from a link failure).

      *  The location of the measurement collection point in the device
         influences the result.  If the packet is not observed directly
         on the input interface, the delay includes buffering time and
         consequently an uncertainty due to the difference between
         'wire-time' and 'host time'.

<span class="h3"><a class="selflink" id="section-5.2" href="#section-5.2">5.2</a>.  A Definition for Spatial Packet Loss Vector</span>

   This section is coupled with the definition of Type-P-One-way-Packet-
   Loss.  When a parameter from <a href="./rfc2680#section-2">section&nbsp;2 of [RFC2680]</a> is used in this
   section, the first instance will be tagged with a trailing asterisk.

   Sections <a href="#section-2.5">2.5</a> to <a href="#section-2.8">2.8</a> of [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] give requirements and applicability
   statements for end-to-end one-way packet loss measurements.  They are
   applicable to each point of interest, Hi, involved in the measure.
   Spatial packet loss measurement MUST respect them, especially those
   related to methodology, clock, uncertainties, and reporting.

   The following sections define the spatial loss vector, adapt some of
   the points above, and introduce points specific to spatial loss
   measurement.

<span class="h4"><a class="selflink" id="section-5.2.1" href="#section-5.2.1">5.2.1</a>.  Metric Name</span>

   Type-P-Spatial-Packet-Loss-Vector

<span class="h4"><a class="selflink" id="section-5.2.2" href="#section-5.2.2">5.2.2</a>.  Metric Parameters</span>

   o  Src*, the IP address of the sender.

   o  Dst*, the IP address of the receiver.

   o  i, an integer in the ordered list &lt;1,2,...,n&gt; of routers in the
      path.

   o  Hi, a router of the routers digest.

   o  T*, a time, the sending time for a measured packet.




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   o  dTi, a delay, the one-way delay for a measured packet from the
      source to host Hi.

   o  &lt;dT1,..., dTn&gt;, list of n delay singletons.

   o  Type-P*, the specification of packet type.

   o  &lt;H1, H2,..., Hn&gt;, the routers digest.

   o  &lt;L1, L2, ...,Ln&gt;, a list of Boolean values.

<span class="h4"><a class="selflink" id="section-5.2.3" href="#section-5.2.3">5.2.3</a>.  Metric Units</span>

   The value of Type-P-Spatial-Packet-Loss-Vector is a sequence of
   Boolean values.

<span class="h4"><a class="selflink" id="section-5.2.4" href="#section-5.2.4">5.2.4</a>.  Definition</span>

   Given a Type-P packet sent by the Src at time T to the receiver Dst
   on the path &lt;H1, H2, ..., Hn&gt;.  For the sequence of times &lt;T+dT1,T+
   dT2,..., T+dTi, ...,T+dTn&gt; the packet passes in &lt;H1, H2, ..., Hi,
   ..., Hn&gt;, define the Type-P-Packet-Loss-Vector metric as the sequence
   of values &lt;T, L1, L2, ..., Ln&gt; such that for each Hi of the path, a
   value of 0 for Li means that dTi is a finite value, and a value of 1
   means that dTi is undefined.

<span class="h4"><a class="selflink" id="section-5.2.5" href="#section-5.2.5">5.2.5</a>.  Discussion</span>

   Some specific issues that may occur are as follows:

   o  The result might include the sequence of values 1,0.  Although
      this appears physically impossible (a packet is lost, then re-
      appears later on the path):

      *  The actual routers on the path may change due to reconvergence
         (e.g., recovery from a link failure).

      *  The order of routers on the path may change due to
         reconvergence.

      *  A packet may not be observed in a router due to some buffer or
         CPU overflow at the measurement collection point.

<span class="h3"><a class="selflink" id="section-5.3" href="#section-5.3">5.3</a>.  A Definition for Spatial One-Way ipdv Vector</span>

   When a parameter from <a href="./rfc3393#section-2">section&nbsp;2 of [RFC3393]</a> (the definition of Type-
   P-One-way-ipdv) is used in this section, the first instance will be
   tagged with a trailing asterisk.



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   The following sections define the spatial ipdv vector, adapt some of
   the points above, and introduce points specific to spatial ipdv
   measurement.

<span class="h4"><a class="selflink" id="section-5.3.1" href="#section-5.3.1">5.3.1</a>.  Metric Name</span>

   Type-P-Spatial-One-way-ipdv-Vector

<span class="h4"><a class="selflink" id="section-5.3.2" href="#section-5.3.2">5.3.2</a>.  Metric Parameters</span>

   o  Src*, the IP address of the sender.

   o  Dst*, the IP address of the receiver.

   o  i, an integer in the ordered list &lt;1,2,...,n&gt; of routers in the
      path.

   o  Hi, a router of the routers digest.

   o  T1*, a time, the sending time for a first measured packet.

   o  T2*, a time, the sending time for a second measured packet.

   o  dT*, a delay, the one-way delay for a measured packet.

   o  dTi, a delay, the one-way delay for a measured packet from the
      source to router Hi.

   o  Type-P*, the specification of the packet type.

   o  P1, the first packet sent at time T1.

   o  P2, the second packet sent at time T2.

   o  &lt;H1, H2,..., Hn&gt;, the routers digest.

   o  &lt;T1,dT1.1, dT1.2,..., dT1.n,dT1&gt;, the Type-P-Spatial-One-way-
      Delay-Vector for a packet sent at time T1.

   o  &lt;T2,dT2.1, dT2.2,..., dT2.n,dT2&gt;, the Type-P-Spatial-One-way-
      Delay-Vector for a packet sent at time T2.

   o  L*, a packet length in bits.  The packets of a Type-P packet
      stream from which the Type-P-Spatial-One-way-Delay-Vector metric
      is taken MUST all be of the same length.






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<span class="h4"><a class="selflink" id="section-5.3.3" href="#section-5.3.3">5.3.3</a>.  Metric Units</span>

   The value of Type-P-Spatial-One-way-ipdv-Vector is a sequence of
   times (a real number in the dimension of seconds with sufficient
   resolution to convey the results).

<span class="h4"><a class="selflink" id="section-5.3.4" href="#section-5.3.4">5.3.4</a>.  Definition</span>

   Given P1 the Type-P packet sent by the sender Src at wire-time (first
   bit) T1 to the receiver Dst. Given &lt;T1, dT1.1, dT1.2,..., dT1.n, dT1&gt;
   the Type-P-Spatial-One-way-Delay-Vector of P1 over the sequence of
   routers &lt;H1, H2,..., Hn&gt;.

   Given P2 the Type-P packet sent by the sender Src at wire-time (first
   bit) T2 to the receiver Dst. Given &lt;T2, dT2.1, dT2.2,..., dT2.n, dT2&gt;
   the Type-P-Spatial-One-way-Delay-Vector of P2 over the same path.

   The Type-P-Spatial-One-way-ipdv-Vector metric is defined as the
   sequence of values &lt;T1, T2, dT2.1-dT1.1, dT2.2-dT1.2 ,..., dT2.n-
   dT1.n, dT2-dT1&gt; such that for each Hi of the sequence of routers &lt;H1,
   H2,..., Hn&gt;, dT2.i-dT1.i is either a real number if the packets P1
   and P2 pass Hi at wire-time (last bit) dT1.i and dT2.i respectively,
   or undefined if at least one of them never passes Hi (and the
   respective one-way delay is undefined).  The T1,T2* pair indicates
   the inter-packet emission interval and dT2-dT1 is ddT* the Type-P-
   One-way-ipdv.

<span class="h3"><a class="selflink" id="section-5.4" href="#section-5.4">5.4</a>.  Spatial Methodology</span>

   The methodology, reporting specifications, and uncertainties
   specified in <a href="./rfc2679#section-3">section&nbsp;3 of [RFC2679]</a> apply to each point of interest
   (or measurement collection point), Hi, measuring an element of a
   spatial delay vector.

   Likewise, the methodology, reporting specifications, and
   uncertainties specified in <a href="./rfc2680#section-2">section&nbsp;2 of [RFC2680]</a> apply to each point
   of interest, Hi, measuring an element of a spatial packet loss
   vector.

   Sections <a href="#section-3.5">3.5</a> to <a href="#section-3.7">3.7</a> of [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>] give requirements and applicability
   statements for end-to-end One-way ipdv measurements.  They are
   applicable to each point of interest, Hi, involved in the measure.
   Spatial One-way ipdv measurement MUST respect the methodology, clock,
   uncertainties, and reporting aspects given there.







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   Generally, for a given Type-P packet of length L at a specific Hi,
   the methodology for spatial vector metrics may proceed as follows:

   o  At each Hi, points of interest/measurement collection points
      prepare to capture the packet sent at time T, record a timestamp
      Ti', and determine the internal delay correction dTi' (see <a href="#section-3.7.1">section</a>
      <a href="#section-3.7.1">3.7.1</a>.  "Errors or uncertainties related to Clocks" of [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>]);

   o  Each Hi extracts the path ordering information from the packet
      (e.g., time-to-live (TTL));

   o  Each Hi computes the corrected wire-time from Src to Hi: Ti = Ti'
      - dTi'.  This arrival time is undefined if the packet is not
      detected after the 'loss threshold' duration;

   o  Each Hi extracts the timestamp T from the packet;

   o  Each Hi computes the one-way delay from Src to Hi: dTi = Ti - T;

   o  The reference point gathers the result of each Hi and arranges
      them according to the path ordering information received to build
      the Type-P spatial one-way vector (e.g., Type-P-Spatial-One-way-
      Delay-Vector metric &lt;T, dT1, dT2,..., dTn, dT&gt;) over the path
      &lt;Src, H1, H2,..., Hn, Dst&gt; at time T.

<span class="h4"><a class="selflink" id="section-5.4.1" href="#section-5.4.1">5.4.1</a>.  Packet Loss Detection</span>

   In a pure end-to-end measurement, packet losses are detected by the
   receiver only.  A packet is lost when Type-P-One-way-Delay is
   undefined or very large (see sections <a href="#section-2.4">2.4</a> and <a href="#section-2.5">2.5</a> of [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] and
   <a href="./rfc2680#section-3.5">section&nbsp;3.5 of [RFC2680]</a>).  A packet is deemed lost by the receiver
   after a duration that starts at the time the packet is sent.  This
   timeout value is chosen by a measurement process.  It determines the
   threshold between recording a long packet transfer time as a finite
   value or an undefined value.

   In a spatial measurement, packet losses may be detected at several
   measurement collection points.  Depending on the consistency of the
   packet loss detections among the points of interest, a packet may be
   considered as lost at one point despite having a finite delay at
   another, or it may be observed by the last measurement collection
   point of the path but considered lost by Dst.

   There is a risk of misinterpreting such results: has the path
   changed?  Did the packet arrive at the destination or was it lost on
   the very last link?





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   The same concern applies to one-way delay measures: a delay measured
   may be computed as infinite by one observation point but as a real
   value by another one, or may be measured as a real value by the last
   observation point of the path but designated as undefined by Dst.

   The observation/measurement collection points and the destination
   SHOULD use consistent methods to detect packets losses.  The methods
   and parameters must be systematically reported to permit careful
   comparison and to avoid introducing any confounding factors in the
   analysis.

<span class="h4"><a class="selflink" id="section-5.4.2" href="#section-5.4.2">5.4.2</a>.  Routers Digest</span>

   The methodology given above relies on knowing the order of the
   router/measurement collection points on the path [<a href="./rfc2330" title="&quot;Framework for IP Performance Metrics&quot;">RFC2330</a>].

   Path instability might cause a test packet to be observed more than
   once by the same router, resulting in the repetition of one or more
   routers in the routers digest.

   For example, repeated observations may occur during rerouting phases
   that introduce temporary micro loops.  During such an event, the
   routers digest for a packet crossing Ha and Hb may include the
   pattern &lt;Hb, Ha, Hb, Ha, Hb&gt;, meaning that Ha ended the computation
   of the new path before Hb and that the initial path was from Ha to
   Hb, and that the new path is from Hb to Ha.

   Consequently, duplication of routers in the routers digest of a
   vector MUST be identified before computation of statistics to avoid
   producing corrupted information.

<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>.  Spatial Segment Metrics Definitions</span>

   This section defines samples to measure the performance of a segment
   of a path over time.  The definitions rely on the matrix of the
   spatial vector metrics defined above.

   First, this section defines a sample of one-way delay, Type-P-
   Segment-One-way-Delay-Stream, and a sample of packet loss, Type-P-
   Segment-Packet-Loss-Stream.

   Then, it defines two different samples of ipdv: Type-P-Segment-ipdv-
   prev-Stream uses the current and previous packets as the selection
   function, and Type-P-Segment-ipdv-min-Stream uses the minimum delay
   as one of the selected packets in every pair.






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<span class="h3"><a class="selflink" id="section-6.1" href="#section-6.1">6.1</a>.  A Definition of a Sample of One-Way Delay of a Segment of the Path</span>

   This metric defines a sample of one-way delays over time between a
   pair of routers on a path.  Since it is very close semantically to
   the metric Type-P-One-way-Delay-Poisson-Stream defined in <a href="./rfc2679#section-4">section&nbsp;4
   of [RFC2679]</a>, sections <a href="#section-4.5">4.5</a> to <a href="#section-4.8">4.8</a> of [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] are integral parts of
   the definition text below.

<span class="h4"><a class="selflink" id="section-6.1.1" href="#section-6.1.1">6.1.1</a>.  Metric Name</span>

   Type-P-Segment-One-way-Delay-Stream

<span class="h4"><a class="selflink" id="section-6.1.2" href="#section-6.1.2">6.1.2</a>.  Metric Parameters</span>

   o  Src, the IP address of the sender.

   o  Dst, the IP address of the receiver.

   o  Type-P, the specification of the packet type.

   o  i, an integer in the ordered list &lt;1,2,...,n&gt; of routers in the
      path.

   o  k, an integer that orders the packets sent.

   o  a and b, two integers where b &gt; a.

   o  Hi, a router of the routers digest.

   o  &lt;H1,..., Ha, ..., Hb, ...., Hn&gt;, the routers digest.

   o  &lt;T1, T2, ..., Tm&gt;, a list of times.

<span class="h4"><a class="selflink" id="section-6.1.3" href="#section-6.1.3">6.1.3</a>.  Metric Units</span>

   The value of a Type-P-Segment-One-way-Delay-Stream is a pair of:

      A list of times &lt;T1, T2, ..., Tm&gt;; and

      A sequence of delays.

<span class="h4"><a class="selflink" id="section-6.1.4" href="#section-6.1.4">6.1.4</a>.  Definition</span>

   Given two routers, Ha and Hb, of the path &lt;H1, H2,..., Ha, ..., Hb,
   ..., Hn&gt;, and the matrix of Type-P-Spatial-One-way-Delay-Vector for
   the packets sent from Src to Dst at times &lt;T1, T2, ..., Tm-1, Tm&gt; :





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      &lt;T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1&gt;;

      &lt;T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2&gt;;

      ...

      &lt;Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm&gt;.

   We define the sample Type-P-Segment-One-way-Delay-Stream as the
   sequence &lt;dT1.ab, dT2.ab, ..., dTk.ab, ..., dTm.ab&gt; such that for
   each time Tk, 'dTk.ab' is either the real number 'dTk.b - dTk.a', if
   the packet sent at the time Tk passes Ha and Hb, or is undefined if
   this packet never passes Ha or (inclusive) never passes Hb.

<span class="h4"><a class="selflink" id="section-6.1.5" href="#section-6.1.5">6.1.5</a>.  Discussion</span>

   Some specific issues that may occur are as follows:

   o  the delay singletons "appear" to decrease: dTi &gt; DTi+1, and is
      discussed in <a href="#section-5.1.5">section 5.1.5</a>.

      *  This could also occur when the clock resolution of one
         measurement collection point is larger than the minimum delay
         of a path.  For example, the minimum delay of a 500 km path
         through optical fiber facilities is 2.5 ms, but the measurement
         collection point has a clock resolution of 8 ms.

   The metric SHALL be invalid for times &lt; T1 , T2, ..., Tm-1, Tm&gt; if
   the following conditions occur:

   o  Ha or Hb disappears from the path due to some routing change.

   o  The order of Ha and Hb changes in the path.

<span class="h3"><a class="selflink" id="section-6.2" href="#section-6.2">6.2</a>.  A Definition of a Sample of Packet Loss of a Segment of the Path</span>

   This metric defines a sample of packet loss over time between a pair
   of routers of a path.  Since it is very close semantically to the
   metric Type-P-Packet-loss-Stream defined in <a href="./rfc2680#section-3">section&nbsp;3 of [RFC2680]</a>,
   sections <a href="#section-3.5">3.5</a> to <a href="#section-3.8">3.8</a> of [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] are integral parts of the definition
   text below.

<span class="h4"><a class="selflink" id="section-6.2.1" href="#section-6.2.1">6.2.1</a>.  Metric Name</span>

   Type-P-Segment-Packet-Loss-Stream






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<span class="h4"><a class="selflink" id="section-6.2.2" href="#section-6.2.2">6.2.2</a>.  Metric Parameters</span>

   o  Src, the IP address of the sender.

   o  Dst, the IP address of the receiver.

   o  Type-P, the specification of the packet type.

   o  k, an integer that orders the packets sent.

   o  n, an integer that orders the routers on the path.

   o  a and b, two integers where b &gt; a.

   o  &lt;H1, H2, ..., Ha, ..., Hb, ...,Hn&gt;, the routers digest.

   o  Hi, a router of the routers digest.

   o  &lt;T1, T2, ..., Tm&gt;, a list of times.

   o  &lt;L1, L2, ..., Ln&gt;, a list of Boolean values.

<span class="h4"><a class="selflink" id="section-6.2.3" href="#section-6.2.3">6.2.3</a>.  Metric Units</span>

   The value of a Type-P-Segment-Packet-Loss-Stream is a pair of:

      The list of times &lt;T1, T2, ..., Tm&gt;; and

      A sequence of Boolean values.

<span class="h4"><a class="selflink" id="section-6.2.4" href="#section-6.2.4">6.2.4</a>.  Definition</span>

   Given two routers, Ha and Hb, of the path &lt;H1, H2,..., Ha, ..., Hb,
   ..., Hn&gt; and the matrix of Type-P-Spatial-Packet-Loss-Vector for the
   packets sent from Src to Dst at times &lt;T1, T2, ..., Tm-1, Tm&gt; :

      &lt;T1, L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L&gt;,

      &lt;T2, L2.1, L2.2,..., L2.a, ..., L2.b, ..., L2.n, L&gt;,

      ...,

      &lt;Tm, Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L&gt;.

   We define the value of the sample Type-P-Segment-Packet-Loss-Stream
   from Ha to Hb as the sequence of Booleans &lt;L1.ab, L2.ab,..., Lk.ab,
   ..., Lm.ab&gt; such that for each Tk:




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   o  A value of Lk of 0 means that Ha and Hb observed the packet sent
      at time Tk (both Lk.a and Lk.b have a value of 0).

   o  A value of Lk of 1 means that Ha observed the packet sent at time
      Tk (Lk.a has a value of 0) and that Hb did not observe the packet
      sent at time Tk (Lk.b has a value of 1).

   o  The value of Lk is undefined when neither Ha nor Hb observed the
      packet (both Lk.a and Lk.b have a value of 1).

<span class="h4"><a class="selflink" id="section-6.2.5" href="#section-6.2.5">6.2.5</a>.  Discussion</span>

   Unlike Type-P-Packet-loss-Stream, Type-P-Segment-Packet-Loss-Stream
   relies on the stability of the routers digest.  The metric SHALL be
   invalid for times &lt; T1 , T2, ..., Tm-1, Tm&gt; if the following
   conditions occur:

   o  Ha or Hb disappears from the path due to some routing change.

   o  The order of Ha and Hb changes in the path.

   o  Lk.a or Lk.b is undefined.

   o  Lk.a has the value 1 (not observed) and Lk.b has the value 0
      (observed).

   o  L has the value 0 (the packet was received by Dst) and Lk.ab has
      the value 1 (the packet was lost between Ha and Hb).

<span class="h3"><a class="selflink" id="section-6.3" href="#section-6.3">6.3</a>.  A Definition of a Sample of ipdv of a Segment Using the Previous</span>
<span class="h3">      Packet Selection Function</span>

   This metric defines a sample of ipdv [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>] over time between a
   pair of routers using the previous packet as the selection function.

<span class="h4"><a class="selflink" id="section-6.3.1" href="#section-6.3.1">6.3.1</a>.  Metric Name</span>

   Type-P-Segment-ipdv-prev-Stream

<span class="h4"><a class="selflink" id="section-6.3.2" href="#section-6.3.2">6.3.2</a>.  Metric Parameters</span>

   o  Src, the IP address of the sender.

   o  Dst, the IP address of the receiver.

   o  Type-P, the specification of the packet type.

   o  k, an integer that orders the packets sent.



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   o  n, an integer that orders the routers on the path.

   o  a and b, two integers where b &gt; a.

   o  &lt;H1, H2, ..., Ha, ..., Hb, ...,Hn&gt;, the routers digest.

   o  &lt;T1, T2, ..., Tm-1, Tm&gt;, a list of times.

   o  &lt;Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk&gt;, a
      Type-P-Spatial-One-way-Delay-Vector.

<span class="h4"><a class="selflink" id="section-6.3.3" href="#section-6.3.3">6.3.3</a>.  Metric Units</span>

   The value of a Type-P-Segment-ipdv-prev-Stream is a pair of:

      The list of &lt;T1, T2, ..., Tm-1, Tm&gt;; and

      A list of pairs of interval of times and delays;

<span class="h4"><a class="selflink" id="section-6.3.4" href="#section-6.3.4">6.3.4</a>.  Definition</span>

   Given two routers, Ha and Hb, of the path &lt;H1, H2,..., Ha, ..., Hb,
   ..., Hn&gt; and the matrix of Type-P-Spatial-One-way-Delay-Vector for
   the packets sent from Src to Dst at times &lt;T1, T2, ..., Tm-1, Tm&gt; :

      &lt;T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1&gt;,

      &lt;T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2&gt;,

      ...

      &lt;Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm&gt;.

   We define the Type-P-Segment-ipdv-prev-Stream as the sequence of
   packet time pairs and delay variations

   &lt;(T1, T2 , dT2.ab - dT1.ab) ,...,

   (Tk-1, Tk, dTk.ab - dTk-1.ab), ...,

   (Tm-1, Tm, dTm.ab - dTm-1.ab)&gt;

   For any pair, Tk, Tk-1 in k=1 through m, the difference dTk.ab - dTk-
   1.ab is undefined if:

   o  the delay dTk.a or the delay dTk-1.a is undefined, OR

   o  the delay dTk.b or the delay dTk-1.b is undefined.



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<span class="h4"><a class="selflink" id="section-6.3.5" href="#section-6.3.5">6.3.5</a>.  Discussion</span>

   This metric belongs to the family of inter-packet delay variation
   metrics (IPDV in uppercase) whose results are extremely sensitive to
   the inter-packet interval in practice.

   The inter-packet interval of an end-to-end IPDV metric is under the
   control of the source (ingress point of interest).  In contrast, the
   inter-packet interval of a segment IPDV metric is not under the
   control the ingress point of interest of the measure, Ha.  The
   interval will certainly vary if there is delay variation between the
   Source and Ha.  Therefore, the ingress inter-packet interval must be
   known at Ha in order to fully comprehend the delay variation between
   Ha and Hb.

<span class="h3"><a class="selflink" id="section-6.4" href="#section-6.4">6.4</a>.  A Definition of a Sample of ipdv of a Segment Using the Minimum</span>
<span class="h3">      Delay Selection Function</span>

   This metric defines a sample of ipdv [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>] over time between a
   pair of routers on a path using the minimum delay as one of the
   selected packets in every pair.

<span class="h4"><a class="selflink" id="section-6.4.1" href="#section-6.4.1">6.4.1</a>.  Metric Name</span>

   Type-P-Segment-One-way-ipdv-min-Stream

<span class="h4"><a class="selflink" id="section-6.4.2" href="#section-6.4.2">6.4.2</a>.  Metric Parameters</span>

   o  Src, the IP address of the sender.

   o  Dst, the IP address of the receiver.

   o  Type-P, the specification of the packet type.

   o  k, an integer that orders the packets sent.

   o  i, an integer that identifies a packet sent.

   o  n, an integer that orders the routers on the path.

   o  a and b, two integers where b &gt; a.

   o  &lt;H1, H2, ..., Ha, ..., Hb, ...,Hn&gt;, the routers digest.

   o  &lt;T1, T2, ..., Tm-1, Tm&gt;, a list of times.

   o  &lt;Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk&gt;, a
      Type-P-Spatial-One-way-Delay-Vector.



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<span class="h4"><a class="selflink" id="section-6.4.3" href="#section-6.4.3">6.4.3</a>.  Metric Units</span>

   The value of a Type-P-Segment-One-way-ipdv-min-Stream is a pair of:

      The list of &lt;T1, T2, ..., Tm-1, Tm&gt;; and

      A list of times.

<span class="h4"><a class="selflink" id="section-6.4.4" href="#section-6.4.4">6.4.4</a>.  Definition</span>

   Given two routers, Ha and Hb, of the path &lt;H1, H2,..., Ha, ..., Hb,
   ..., Hn&gt; and the matrix of Type-P-Spatial-One-way-Delay-Vector for
   the packets sent from Src to Dst at times &lt;T1, T2, ..., Tm-1, Tm&gt; :

      &lt;T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1&gt;,

      &lt;T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2&gt;,

      ...

      &lt;Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm&gt;.

   We define the Type-P-Segment-One-way-ipdv-min-Stream as the sequence
   of times &lt;dT1.ab - min(dTi.ab) ,..., dTk.ab - min(dTi.ab), ...,
   dTm.ab - min(dTi.ab)&gt; where:

   o  min(dTi.ab) is the minimum value of the tuples (dTk.b - dTk.a);

   o  for each time Tk, dTk.ab is undefined if dTk.a or (inclusive)
      dTk.b is undefined, or the real number (dTk.b - dTk.a) is
      undefined.

<span class="h4"><a class="selflink" id="section-6.4.5" href="#section-6.4.5">6.4.5</a>.  Discussion</span>

   This metric belongs to the family of packet delay variation metrics
   (PDV).  PDV distributions have less sensitivity to inter-packet
   interval variations than IPDV values, as discussed above.

   In principle, the PDV distribution reflects the variation over many
   different inter-packet intervals, from the smallest inter-packet
   interval, up to the length of the evaluation interval, Tm - T1.
   Therefore, when delay variation occurs and disturbs the packet
   spacing observed at Ha, the PDV results will likely compare favorably
   to a PDV measurement where the source is Ha and the destination is
   Hb, because a wide range of spacings are reflected in any PDV
   distribution.





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<span class="h2"><a class="selflink" id="section-7" href="#section-7">7</a>.  One-to-Group Metrics Definitions</span>

   This section defines performance metrics between a source and a group
   of receivers.

<span class="h3"><a class="selflink" id="section-7.1" href="#section-7.1">7.1</a>.  A Definition for One-to-Group Delay</span>

   This section defines a metric for one-way delay between a source and
   a group of receivers.

<span class="h4"><a class="selflink" id="section-7.1.1" href="#section-7.1.1">7.1.1</a>.  Metric Name</span>

   Type-P-One-to-group-Delay-Vector

<span class="h4"><a class="selflink" id="section-7.1.2" href="#section-7.1.2">7.1.2</a>.  Metric Parameters</span>

   o  Src, the IP address of a host acting as the source.

   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as
      receivers.

   o  T, a time.

   o  dT1,...,dTn a list of times.

   o  Type-P, the specification of the packet type.

   o  Gr, the receiving group identifier.  The parameter Gr is the
      multicast group address if the measured packets are transmitted
      over IP multicast.  This parameter is to differentiate the
      measured traffic from other unicast and multicast traffic.  It is
      OPTIONAL for this metric to avoid losing any generality, i.e., to
      make the metric also applicable to unicast measurement where there
      is only one receiver.

<span class="h4"><a class="selflink" id="section-7.1.3" href="#section-7.1.3">7.1.3</a>.  Metric Units</span>

   The value of a Type-P-One-to-group-Delay-Vector is a set of Type-P-
   One-way-Delay singletons [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>], that is a sequence of times (a
   real number in the dimension of seconds with sufficient resolution to
   convey the results).

<span class="h4"><a class="selflink" id="section-7.1.4" href="#section-7.1.4">7.1.4</a>.  Definition</span>

   Given a Type-P packet sent by the source Src at time T, and the N
   hosts { Recv1,...,RecvN } which receive the packet at the time {
   T+dT1,...,T+dTn }, or the packet does not pass a receiver within a
   specified loss threshold time, then the Type-P-One-to-group-Delay-



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   Vector is defined as the set of the Type-P-One-way-Delay singletons
   between Src and each receiver with value of { dT1, dT2,...,dTn },
   where any of the singletons may be undefined if the packet did not
   pass the corresponding receiver within a specified loss threshold
   time.

<span class="h3"><a class="selflink" id="section-7.2" href="#section-7.2">7.2</a>.  A Definition for One-to-Group Packet Loss</span>

<span class="h4"><a class="selflink" id="section-7.2.1" href="#section-7.2.1">7.2.1</a>.  Metric Name</span>

   Type-P-One-to-group-Packet-Loss-Vector

<span class="h4"><a class="selflink" id="section-7.2.2" href="#section-7.2.2">7.2.2</a>.  Metric Parameters</span>

   o  Src, the IP address of a host acting as the source.

   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as
      receivers.

   o  T, a time.

   o  Type-P, the specification of the packet type.

   o  Gr, the receiving group identifier, OPTIONAL.

<span class="h4"><a class="selflink" id="section-7.2.3" href="#section-7.2.3">7.2.3</a>.  Metric Units</span>

   The value of a Type-P-One-to-group-Packet-Loss-Vector is a set of
   Type-P-One-way-Packet-Loss singletons [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>].

   o  T, time the source packet was sent.

   o  L1,...,LN a list of Boolean values.

<span class="h4"><a class="selflink" id="section-7.2.4" href="#section-7.2.4">7.2.4</a>.  Definition</span>

   Given a Type-P packet sent by the source Src at T and the N hosts,
   Recv1,...,RecvN, the Type-P-One-to-group-Packet-Loss-Vector is
   defined as a set of the Type-P-One-way-Packet-Loss singletons between
   Src and each of the receivers:

   {T, &lt;L1=0|1&gt;,&lt;L2=0|1&gt;,..., &lt;LN=0|1&gt;},

   where the Boolean value 0|1 depends on receiving the packet at a
   particular receiver within a loss threshold time.






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<span class="h3"><a class="selflink" id="section-7.3" href="#section-7.3">7.3</a>.  A Definition for One-to-Group ipdv</span>

<span class="h4"><a class="selflink" id="section-7.3.1" href="#section-7.3.1">7.3.1</a>.  Metric Name</span>

   Type-P-One-to-group-ipdv-Vector

<span class="h4"><a class="selflink" id="section-7.3.2" href="#section-7.3.2">7.3.2</a>.  Metric Parameters</span>

   o  Src, the IP address of a host acting as the source.

   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as
      receivers.

   o  T1, a time.

   o  T2, a time.

   o  ddT1, ...,ddTn, a list of times.

   o  Type-P, the specification of the packet type.

   o  F, a selection function non-ambiguously defining the two packets
      from the stream selected for the metric.

   o  Gr, the receiving group identifier.  The parameter Gr is the
      multicast group address if the measured packets are transmitted
      over IP multicast.  This parameter is to differentiate the
      measured traffic from other unicast and multicast traffic.  It is
      OPTIONAL in the metric to avoid losing any generality, i.e., to
      make the metric also applicable to unicast measurement where there
      is only one receiver.

<span class="h4"><a class="selflink" id="section-7.3.3" href="#section-7.3.3">7.3.3</a>.  Metric Units</span>

   The value of a Type-P-One-to-group-ipdv-Vector is a set of Type-P-
   One-way-ipdv singletons [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>].

<span class="h4"><a class="selflink" id="section-7.3.4" href="#section-7.3.4">7.3.4</a>.  Definition</span>

   Given a Type-P packet stream, Type-P-One-to-group-ipdv-Vector is
   defined for two packets transferred from the source Src to the N
   hosts {Recv1,...,RecvN }, which are selected by the selection
   function F as the difference between the value of the Type-P-One-to-
   group-Delay-Vector from Src to { Recv1,..., RecvN } at time T1 and
   the value of the Type-P-One-to-group-Delay-Vector from Src to {
   Recv1,...,RecvN } at time T2.  T1 is the wire-time at which Src sent





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   the first bit of the first packet, and T2 is the wire-time at which
   Src sent the first bit of the second packet.  This metric is derived
   from the Type-P-One-to-group-Delay-Vector metric.

   For a set of real numbers {ddT1,...,ddTn}, the Type-P-One-to-group-
   ipdv-Vector from Src to { Recv1,...,RecvN } at T1, T2 is
   {ddT1,...,ddTn} means that Src sent two packets, the first at wire-
   time T1 (first bit), and the second at wire-time T2 (first bit) and
   the packets were received by { Recv1,...,RecvN } at wire-time {dT1+
   T1,...,dTn+T1}(last bit of the first packet), and at wire-time {dT'1+
   T2,...,dT'n+T2} (last bit of the second packet), and that {dT'1-
   dT1,...,dT'n-dTn} ={ddT1,...,ddTn}.

   For any pair of selected packets, the difference dT'n-dTn is
   undefined if:

   o  the delay dTn to Receiver n is undefined, OR

   o  the delay dT'n to Receiver n is undefined.

<span class="h2"><a class="selflink" id="section-8" href="#section-8">8</a>.  One-to-Group Sample Statistics</span>

   The one-to-group metrics defined above are directly achieved by
   collecting relevant unicast one-way metrics measurements results and
   by gathering them per group of receivers.  They produce network
   performance information that guides engineers toward potential
   problems that may have happened on any branch of a multicast routing
   tree.

   The results of these metrics are not directly usable to present the
   performance of a group because each result is made of a huge number
   of singletons that are difficult to read and analyze.  As an example,
   delays are not comparable because the distance between receiver and
   sender differs.  Furthermore, they don't capture relative performance
   situations in a multiparty communication.

   From the performance point of view, the multiparty communication
   services not only require the support of absolute performance
   information but also information on "relative performance".
   "Relative performance" means the difference between absolute
   performance of all users.  Directly using the one-way metrics cannot
   present the relative performance situation.  However, if we use the
   variations of all users' one-way parameters, we can have new metrics
   to measure the difference of the absolute performance and hence
   provide the threshold value of relative performance that a multiparty
   service might demand.  A very good example of the high relative
   performance requirement is online gaming.  A very small difference in
   delay might result in failure in the game.  We have to use multicast-



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   specific statistic metrics to define the relative delay required by
   online gaming.  There are many other services, e.g., online biding,
   online stock market, etc., that require multicast metrics in order to
   evaluate the network against their requirements.  Therefore, we can
   see the importance of new, multicast specific, statistic metrics to
   feed this need.

   We might also use some one-to-group statistic conceptions to present
   and report the group performance and relative performance to save the
   report transmission bandwidth.  Statistics have been defined for One-
   way metrics in corresponding RFCs.  They provide the foundation of
   definition for performance statistics.  For instance, there are
   definitions for minimum and maximum one-way delay in [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>].
   However, there is a dramatic difference between the statistics for
   one-to-one communications and for one-to-many communications.  The
   former one only has statistics over the time dimension while the
   later one can have statistics over both time and space dimensions.
   This space dimension is introduced by the Matrix concept as
   illustrated in Figure 4.  For a Matrix M, each row is a set of one-
   way singletons spreading over the time dimension and each column is
   another set of One-way singletons spreading over the space dimension.

            Receivers
             Space
               ^
             1 |    / R1dT1   R1dT2     R1dT3 ... R1dTk \
               |   |                                     |
             2 |   |  R2dT1   R2dT2     R2dT3 ... R2dTk  |
               |   |                                     |
             3 |   |  R3dT1   R3dT2     R3dT3 ... R3dTk  |
             . |   |                                     |
             . |   |                                     |
             . |   |                                     |
             n |    \ RndT1   RndT2     RndT3 ... RndTk /
               +--------------------------------------------&gt; time
              T0

                         Figure 4: Matrix M (n*m)

   In Matrix M, each element is a one-way delay singleton.  Each column
   is a delay vector.  It contains the one-way delays of the same packet
   observed at n points of interest.  It implies the geographical factor
   of the performance within a group.  Each row is a set of one-way
   delays observed during a sampling interval at one of the points of
   interest.  It presents the delay performance at a receiver over the
   time dimension.





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   Therefore, one can either calculate statistics by rows over the space
   dimension or by columns over the time dimension.  It's up to the
   operators or service providers in which dimension they are
   interested.  For example, a TV broadcast service provider might want
   to know the statistical performance of each user in a long-term run
   to make sure their services are acceptable and stable.  While for an
   online gaming service provider, he might be more interested in
   knowing if all users are served fairly by calculating the statistics
   over the space dimension.  This memo does not intend to recommend
   which of the statistics are better than the others.

   To save the report transmission bandwidth, each point of interest can
   send statistics in a pre-defined time interval to the reference point
   rather than sending every one-way singleton it observed.  As long as
   an appropriate time interval is decided, appropriate statistics can
   represent the performance in a certain accurate scale.  How to decide
   the time interval and how to bootstrap all points of interest and the
   reference point depend on applications.  For instance, applications
   with a lower transmission rate can have the time interval be longer,
   and ones with higher transmission rate can have the time interval be
   shorter.  However, this is out of the scope of this memo.

   Moreover, after knowing the statistics over the time dimension, one
   might want to know how these statistics are distributed over the
   space dimension.  For instance, a TV broadcast service provider had
   the performance Matrix M and calculated the one-way delay mean over
   the time dimension to obtain a delay Vector as {V1,V2,..., VN}.  He
   then calculated the mean of all the elements in the Vector to see
   what level of delay he has served to all N users.  This new delay
   mean gives information on how well the service has been delivered to
   a group of users during a sampling interval in terms of delay.  It
   requires twice as much calculation to have this statistic over both
   time and space dimensions.  These kinds of statistics are referred to
   as 2-level statistics to distinguish them from 1-level statistics
   calculated over either space or time dimension.  It can be easily
   proven that no matter over which dimension a 2-level statistic is
   calculated first, the results are the same.  That is, one can
   calculate the 2-level delay mean using the Matrix M by having the
   1-level delay mean over the time dimension first and then calculate
   the mean of the obtained vector to find out the 2-level delay mean.
   Or, he can do the 1-level statistic calculation over the space
   dimension first and then have the 2-level delay mean.  Both results
   will be exactly the same.  Therefore, when defining a 2-level
   statistic, there is no need to specify the order in which the
   calculation is executed.






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   Many statistics can be defined for the proposed one-to-group metrics
   over the space dimension, the time dimension, or both.  This memo
   treats the case where a stream of packets from the Source results in
   a sample at each of the Receivers in the Group, and these samples are
   each summarized with the usual statistics employed in one-to-one
   communication.  New statistic definitions are presented, which
   summarize the one-to-one statistics over all the Receivers in the
   Group.

<span class="h3"><a class="selflink" id="section-8.1" href="#section-8.1">8.1</a>.  Discussion on the Impact of Packet Loss on Statistics</span>

   Packet loss does have effects on one-way metrics and their
   statistics.  For example, a lost packet can result in an infinite
   one-way delay.  It is easy to handle the problem by simply ignoring
   the infinite value in the metrics and in the calculation of the
   corresponding statistics.  However, the packet loss has such a strong
   impact on the statistics calculation for the one-to-group metrics
   that it can not be solved by the same method used for one-way

   metrics.  This is due to the complexity of building a matrix, which
   is needed for calculation of the statistics proposed in this memo.

   The situation is that measurement results obtained by different end
   users might have different packet loss pattern.  For example, for
   User1, packet A was observed to be lost.  And for User2, packet A was
   successfully received, but packet B was lost.  If the method to
   overcome the packet loss for one-way metrics is applied, the two
   singleton sets reported by User1 and User2 will be different in terms
   of the transmitted packets.  Moreover, if User1 and User2 have a
   different number of lost packets, the size of the results will be
   different.  Therefore, for the centralized calculation, the reference
   point will not be able to use these two results to build up the group
   Matrix and cannot calculate the statistics.  The extreme situation
   being the case when no packets arrive at any user.  One of the
   possible solutions is to replace the infinite/undefined delay value
   by the average of the two adjacent values.  For example, if the
   result reported by User1 is { R1dT1 R1dT2 R1dT3 ...  R1dTK-1 UNDEF
   R1dTK+1...  R1MD } where "UNDEF" is an undefined value, the reference
   point can replace it by R1dTK = {(R1dTK-1)+( R1dTK+1)}/2.  Therefore,
   this result can be used to build up the group Matrix with an
   estimated value R1dTK.  There are other possible solutions, such as
   using the overall mean of the whole result to replace the infinite/
   undefined value, and so on.  However, this is out of the scope of
   this memo.

   For the distributed calculation, the reported statistics might have
   different "weight" to present the group performance, which is
   especially true for delay and ipdv relevant metrics.  For example,



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   User1 calculates the Type-P-Finite-One-way-Delay-Mean R1MD as shown
   in Figure 7 without any packet loss, and User2 calculates the R2MD
   with N-2 packet loss.  The R1MD and R2MD should not be treated with
   equal weight because R2MD was calculated only based on two delay
   values in the whole sample interval.  One possible solution is to use
   a weight factor to mark every statistic value sent by users and use
   this factor for further statistic calculation.

<span class="h3"><a class="selflink" id="section-8.2" href="#section-8.2">8.2</a>.  General Metric Parameters</span>

   o  Src, the IP address of a host.

   o  G, the receiving group identifier.

   o  N, the number of Receivers (Recv1, Recv2, ...  RecvN).

   o  T, a time (start of test interval).

   o  Tf, a time (end of test interval).

   o  K, the number of packets sent from the source during the test
      interval.

   o  J[n], the number of packets received at a particular Receiver, n,
      where 1&lt;=n&lt;=N.

   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+I] to start generating packets and taking measurements (for
      Periodic Streams).

   o  TstampSrc, the wire-time of the packet as measured at MP(Src) (the
      Source Measurement Point).

   o  TstampRecv, the wire-time of the packet as measured at MP(Recv),
      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  dT, shorthand notation for a one-way delay singleton value.




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   o  L, shorthand notation for a one-way loss singleton value, either
      zero or one, where L=1 indicates loss and L=0 indicates arrival at
      the destination within TstampSrc + Tmax, may be indexed over n
      Receivers.

   o  DV, shorthand notation for a one-way delay variation singleton
      value.

<span class="h3"><a class="selflink" id="section-8.3" href="#section-8.3">8.3</a>.  One-to-Group Delay Statistics</span>

   This section defines the overall one-way delay statistics for a
   receiver and for an entire group as illustrated by the matrix below.

      Recv    /----------- Sample -------------\   Stats      Group Stat

       1      R1dT1   R1dT2     R1dT3 ... R1dTk    R1MD  \
                                                          |
       2      R2dT1   R2dT2     R2dT3 ... R2dTk    R2MD   |
                                                          |
       3      R3dT1   R3dT2     R3dT3 ... R3dTk    R3MD    &gt; Group Delay
       .                                                  |
       .                                                  |
       .                                                  |
       n      RndT1   RndT2     RndT3 ... RndTk    RnMD  /

                                                 Receiver-n
                                                   Delay

                     Figure 5: One-to-Group Mean Delay

   Statistics are computed on the finite one-way delays of the matrix
   above.

   All one-to-group delay statistics are expressed in seconds with
   sufficient resolution to convey three significant digits.

<span class="h4"><a class="selflink" id="section-8.3.1" href="#section-8.3.1">8.3.1</a>.  Type-P-One-to-group-Receiver-n-Mean-Delay</span>

   This section defines Type-P-One-to-group-Receiver-n-Mean-Delay, the
   Delay Mean, at each Receiver N, also named RnMD.

   We obtain the value of Type-P-One-way-Delay singleton for all packets
   sent during the test interval at each Receiver (Destination), as per
   [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>].  For each packet that arrives within Tmax of its sending
   time, TstampSrc, the one-way delay singleton (dT) will be the finite
   value TstampRecv[i] - TstampSrc[i] in units of seconds.  Otherwise,
   the value of the singleton is Undefined.




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                           J[n]
                           ---
                      1    \
           RnMD =    --- *  &gt;  TstampRecv[i] - TstampSrc[i]
                     J[n]  /
                           ---
                           i = 1

           Note:  RnMD value is Undefined when J[n] = 0 for all n.

            Figure 6: Type-P-One-to-group-Receiver-n-Mean-Delay

   where all packets i= 1 through J[n] have finite singleton delays.

<span class="h4"><a class="selflink" id="section-8.3.2" href="#section-8.3.2">8.3.2</a>.  Type-P-One-to-group-Mean-Delay</span>

   This section defines Type-P-One-to-group-Mean-Delay, the Mean one-way
   Delay calculated over the entire Group, also named GMD.

                                         N
                                        ---
                                   1    \
                            GMD =  - *   &gt;   RnMD
                                   N    /
                                        ---
                                        n = 1

                 Figure 7: Type-P-One-to-group-Mean-Delay

   Note that the Group Mean Delay can also be calculated by summing the
   finite one-way delay singletons in the matrix, and dividing by the
   number of finite one-way delay singletons.

<span class="h4"><a class="selflink" id="section-8.3.3" href="#section-8.3.3">8.3.3</a>.   Type-P-One-to-group-Range-Mean-Delay</span>

   This section defines a metric for the Range of Mean Delays over all N
   receivers in the Group (R1MD, R2MD...RnMD).

   Type-P-One-to-group-Range-Mean-Delay = GRMD = max(RnMD) - min(RnMD)

<span class="h4"><a class="selflink" id="section-8.3.4" href="#section-8.3.4">8.3.4</a>.  Type-P-One-to-group-Max-Mean-Delay</span>

   This section defines a metric for the Maximum of Mean Delays over all
   N receivers in the Group (R1MD, R2MD,...RnMD).

   Type-P-One-to-group-Max-Mean-Delay = GMMD = max(RnMD)





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<span class="h3"><a class="selflink" id="section-8.4" href="#section-8.4">8.4</a>.  One-to-Group Packet Loss Statistics</span>

   This section defines the overall one-way loss statistics for a
   receiver and for an entire group as illustrated by the matrix below.

    Recv    /----------- Sample ----------\   Stats     Group Stat

      1      R1L1   R1L2     R1L3 ... R1Lk     R1LR \
                                                     |
      2      R2L1   R2L2     R2L3 ... R2Lk     R2LR  |
                                                     |
      3      R3L1   R3L2     R3L3 ... R3Lk     R3LR   &gt; Group Loss Ratio
      .                                              |
      .                                              |
      .                                              |
      n      RnL1   RnL2     RnL3 ... RnLk     RnLR /

                                           Receiver-n
                                           Loss Ratio

                     Figure 8: One-to-Group Loss Ratio

   Statistics are computed on the sample of Type-P-One-way-Packet-Loss
   [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] of the matrix above.

   All loss ratios are expressed in units of packets lost to total
   packets sent.

<span class="h4"><a class="selflink" id="section-8.4.1" href="#section-8.4.1">8.4.1</a>.  Type-P-One-to-group-Receiver-n-Loss-Ratio</span>

   Given a Matrix of loss singletons as illustrated above, determine the
   Type-P-One-way-Packet-Loss-Average for the sample at each receiver,
   according to the definitions and method of [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>].  The Type-P-
   One-way-Packet-Loss-Average and the Type-P-One-to-group-Receiver-n-
   Loss-Ratio, also named RnLR, are equivalent metrics.  In terms of the
   parameters used here, these metrics definitions can be expressed as

                                           K
                                          ---
                                     1    \
                             RnLR =  - *   &gt;   RnLk
                                     K    /
                                          ---
                                         k = 1

            Figure 9: Type-P-One-to-group-Receiver-n-Loss-Ratio





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<span class="h4"><a class="selflink" id="section-8.4.2" href="#section-8.4.2">8.4.2</a>.  Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio</span>

   Usually, the number of packets sent is used in the denominator of
   packet loss ratio metrics.  For the comparative metrics defined here,
   the denominator is the maximum number of packets received at any
   receiver for the sample and test interval of interest.  The numerator
   is the sum of the losses at receiver n.

   The Comparative Loss Ratio, also named, RnCLR, is defined as

                                  K
                                 ---
                                 \
                                  &gt;   Ln(k)
                                 /
                                 ---
                                 k=1
            RnCLR =  -----------------------------
                              /    K         \
                              |   ---        |
                              |   \          |
                      K - Min |    &gt;   Ln(k) |
                              |   /          |
                              |   ---        |
                              \   k=1        / N


            Note: Ln is a set of one-way loss values at receiver n.
                  There is one value for each of the K packets sent.

         Figure 10: Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio

<span class="h4"><a class="selflink" id="section-8.4.3" href="#section-8.4.3">8.4.3</a>.  Type-P-One-to-group-Loss-Ratio</span>

   Type-P-One-to-group-Loss-Ratio, the overall Group Loss Ratio, also
   named GLR, is defined as:

                                         K,N
                                         ---
                                   1     \
                            GLR = --- *   &gt;   Ln(k)
                                  K*N    /
                                         ---
                                        k,n = 1

                 Figure 11: Type-P-One-to-group-Loss-Ratio





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   Where the sum includes all of the Loss singletons, Ln(k), over the N
   receivers and K packets sent, in a ratio with the total packets over
   all receivers.

<span class="h4"><a class="selflink" id="section-8.4.4" href="#section-8.4.4">8.4.4</a>.  Type-P-One-to-group-Range-Loss-Ratio</span>

   The One-to-group Loss Ratio Range is defined as:

   Type-P-One-to-group-Range-Loss-Ratio = max(RnLR) - min(RnLR)

   It is most effective to indicate the range by giving both the maximum
   and minimum loss ratios for the Group, rather than only reporting the
   difference between them.

<span class="h3"><a class="selflink" id="section-8.5" href="#section-8.5">8.5</a>.  One-to-group Delay Variation Statistics</span>

   This section defines one-way delay variation (DV) statistics for an
   entire group as illustrated by the matrix below.

    Recv    /------------- Sample --------------\   Stats

     1      R1ddT1   R1ddT2     R1ddT3 ... R1ddTk   R1DV  \
                                                           |
     2      R2ddT1   R2ddT2     R2ddT3 ... R2ddTk   R2DV   |
                                                           |
     3      R3ddT1   R3ddT2     R3ddT3 ... R3ddTk   R3DV    &gt; Group Stat
     .                                                     |
     .                                                     |
     .                                                     |
     n      RnddT1   RnddT2     RnddT3 ... RnddTk   RnDV  /

           Figure 12: One-to-group Delay Variation Matrix (DVMa)

   Statistics are computed on the sample of Type-P-One-way-ipdv
   singletons of the group delay variation matrix above where RnddTk is
   the Type-P-One-way-ipdv singleton evaluated at Receiver n for the
   packet k and where RnDV is the point-to-point one-way packet delay
   variation for Receiver n.

   All One-to-group delay variation statistics are expressed in seconds
   with sufficient resolution to convey three significant digits.

<span class="h4"><a class="selflink" id="section-8.5.1" href="#section-8.5.1">8.5.1</a>.  Type-P-One-to-group-Range-Delay-Variation</span>

   This section defines a metric for the Range of Delay Variation over
   all N receivers in the Group.





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   Maximum DV and minimum DV over all receivers summarize the
   performance over the Group (where DV is a point-to-point metric).
   For each receiver, the DV is usually expressed as the 1-10^(-3)
   quantile of one-way delay minus the minimum one-way delay.

   Type-P-One-to-group-Range-Delay-Variation = GRDV =

   = max(RnDV) - min(RnDV) for all n receivers

   This range is determined from the minimum and maximum values of the
   point-to-point one-way IP Packet Delay Variation for the set of
   Destinations in the group and a population of interest, using the
   Packet Delay Variation expressed as the 1-10^-3 quantile of one-way
   delay minus the minimum one-way delay.  If a more demanding service
   is considered, one alternative is to use the 1-10^-5 quantile, and in
   either case, the quantile used should be recorded with the results.
   Both the minimum and the maximum delay variation are recorded, and
   both values are given to indicate the location of the range.

<span class="h2"><a class="selflink" id="section-9" href="#section-9">9</a>.  Measurement Methods: Scalability and Reporting</span>

   Virtually all the guidance on measurement processes supplied by the
   earlier IPPM RFCs (such as [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] and [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>]) for one-to-one
   scenarios is applicable here in the spatial and multiparty
   measurement scenario.  The main difference is that the spatial and
   multiparty configurations require multiple points of interest where a
   stream of singletons will be collected.  The amount of information
   requiring storage grows with both the number of metrics and the
   points of interest, so the scale of the measurement architecture
   multiplies the number of singleton results that must be collected and
   processed.

   It is possible that the architecture for results collection involves
   a single reference point with connectivity to all the points of
   interest.  In this case, the number of points of interest determines
   both storage capacity and packet transfer capacity of the host acting
   as the reference point.  However, both the storage and transfer
   capacity can be reduced if the points of interest are capable of
   computing the summary statistics that describe each measurement
   interval.  This is consistent with many operational monitoring
   architectures today, where even the individual singletons may not be
   stored at each point of interest.

   In recognition of the likely need to minimize the form of the results
   for storage and communication, the Group metrics above have been
   constructed to allow some computations on a per-Receiver basis.  This





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   means that each Receiver's statistics would normally have an equal
   weight with all other Receivers in the Group (regardless of the
   number of packets received).

<span class="h3"><a class="selflink" id="section-9.1" href="#section-9.1">9.1</a>.  Computation Methods</span>

   The scalability issue can be raised when there are thousands of
   points of interest in a group who are trying to send back the
   measurement results to the reference point for further processing and
   analysis.  The points of interest can send either the whole measured
   sample or only the calculated statistics.  The former is a
   centralized statistic calculation method and the latter is a
   distributed statistic calculation method.  The sample should include
   all metrics parameters, the values, and the corresponding sequence
   numbers.  The transmission of the whole sample can cost much more
   bandwidth than the transmission of the statistics that should include
   all statistic parameters specified by policies and the additional
   information about the whole sample, such as the size of the sample,
   the group address, the address of the point of interest, the ID of
   the sample session, and so on.  Apparently, the centralized
   calculation method can require much more bandwidth than the
   distributed calculation method when the sample size is big.  This is
   especially true when the measurement has a very large number of the
   points of interest.  It can lead to a scalability issue at the
   reference point by overloading the network resources.

   The distributed calculation method can save much more bandwidth and
   mitigate issues arising from scalability at the reference point side.

   However, it may result in a loss of information.  As not all measured
   singletons are available for building up the group matrix, the real
   performance over time can be hidden from the result.  For example,
   the loss pattern can be missed by simply accepting the loss ratio.
   This tradeoff between bandwidth consumption and information
   acquisition has to be taken into account when designing the
   measurement approach.

   One possible solution could be to transmit the statistic parameters
   to the reference point first to obtain the general information of the
   group performance.  If detailed results are required, the reference
   point should send the requests to the points of interest, which could
   be particular ones or the whole group.  This procedure can happen in
   the off peak time and can be well scheduled to avoid delivery of too
   many points of interest at the same time.  Compression techniques can
   also be used to minimize the bandwidth required by the transmission.
   This could be a measurement protocol to report the measurement
   results.  However, this is out of the scope of this memo.




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<span class="h3"><a class="selflink" id="section-9.2" href="#section-9.2">9.2</a>.  Measurement</span>

   To prevent any bias in the result, the configuration of a one-to-many
   measure must take into consideration that more packets will be routed
   than sent (copies of a packet sent are expected to arrive at many
   destination points) and select a test packet rate that will not
   impact the network performance.

<span class="h3"><a class="selflink" id="section-9.3" href="#section-9.3">9.3</a>.  Effect of Time and Space Aggregation Order on Stats</span>

   This section presents the impact of the aggregation order on the
   scalability of the reporting and of the computation.  It makes the
   hypothesis that receivers are not co-located and that results are
   gathered in a point of reference for further usages.

   Multimetric samples are represented in a matrix as illustrated below

      Point of
      Interest
        1      R1S1   R1S1     R1S1 ... R1Sk    \
                                                 |
        2      R2S1   R2S2     R2S3 ... R2Sk     |
                                                 |
        3      R3S1   R3S2     R3S3 ... R3Sk      &gt;  Sample over Space
        .                                        |
        .                                        |
        .                                        |
        n      RnS1   RnS2     RnS3 ... RnSk    /

               S1M    S2M      S3M  ... SnM     Stats over Space

               \-------------  ------------/
                             \/
                 Stats over Space and Time

       Figure 13: Impact of Space Aggregation on Multimetrics Stats

   Two methods are available to compute statistics on a matrix:

   o  Method 1: The statistic metric is computed over time and then over
      space; or

   o  Method 2: The statistic metric is computed over space and then
      over time.







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   These two methods differ only by the order of the aggregation.  The
   order does not impact the computation resources required.  It does
   not change the value of the result.  However, it impacts severely the
   minimal volume of data to report:

   o  Method 1: Each point of interest periodically computes statistics
      over time to lower the volume of data to report.  They are
      reported to the reference point for subsequent computations over
      the spatial dimension.  This volume no longer depends on the
      number of samples.  It is only proportional to the computation
      period.

   o  Method 2: The volume of data to report is proportional to the
      number of samples.  Each sample, RiSi, must be reported to the
      reference point for computing statistic over space and statistic
      over time.  The volume increases with the number of samples.  It
      is proportional to the number of test packets;

   Method 2 has severe drawbacks in terms of security and dimensioning:

   o  Increasing the rate of the test packets may result in a Denial of
      Service (DoS) toward the points of reference;

   o  The dimensioning of a measurement system is quite impossible to
      validate because any increase of the rate of the test packets will
      increase the bandwidth requested to collect the raw results.

   The computation period over time period (commonly named the
   aggregation period) provides the reporting side with a control of
   various collecting aspects such as bandwidth, computation, and
   storage capacities.  So this document defines metrics based on method
   1.

<span class="h4"><a class="selflink" id="section-9.3.1" href="#section-9.3.1">9.3.1</a>.  Impact on Spatial Statistics</span>

   Two methods are available to compute spatial statistics:

   o  Method 1: Spatial segment metrics and statistics are preferably
      computed over time for each points of interest;

   o  Method 2: Vectors metrics are intrinsically instantaneous space
      metrics, which must be reported using Method 2 whenever
      instantaneous metrics information is needed.








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<span class="h4"><a class="selflink" id="section-9.3.2" href="#section-9.3.2">9.3.2</a>.  Impact on One-to-Group Statistics</span>

   Two methods are available to compute group statistics:

   o  Method 1: Figure 5 and Figure 8 illustrate the method.  The one-
      to-one statistic is computed per interval of time before the
      computation of the mean over the group of receivers.

   o  Method 2: Figure 13 presents the second method.  The metric is
      computed over space and then over time.

<span class="h2"><a class="selflink" id="section-10" href="#section-10">10</a>.  Manageability Considerations</span>

   This section defines the reporting of all the metrics introduced in
   the document.

   Information models of spatial metrics and of one-to-group metrics are
   similar except that points of interests of spatial vectors MUST be
   ordered.

   The complexity of the reporting relies on the number of points of
   interest.

<span class="h3"><a class="selflink" id="section-10.1" href="#section-10.1">10.1</a>.  Reporting Spatial Metric</span>

   The reporting of spatial metrics shares a lot of aspects with <a href="./rfc2679">RFC</a>
   <a href="./rfc2679">2679</a> and <a href="./rfc2680">RFC 2680</a>.  New ones are common to all the definitions and
   are mostly related to the reporting of the path and of methodology
   parameters that may bias raw results analysis.  This section presents
   these specific parameters and then lists exhaustively the parameters
   that SHOULD be reported.

<span class="h4"><a class="selflink" id="section-10.1.1" href="#section-10.1.1">10.1.1</a>.  Path</span>

   End-to-end metrics can't determine the path of the measure despite
   the fact that IPPM RFCs recommend it be reported (see <a href="./rfc2679#section-3.8.4">section&nbsp;3.8.4
   of [RFC2679]</a>).  Spatial metrics vectors provide this path.  The
   report of a spatial vector MUST include the points of interests
   involved: the sub-set of the routers of the path participating to the
   instantaneous measure.

<span class="h4"><a class="selflink" id="section-10.1.2" href="#section-10.1.2">10.1.2</a>.  Host Order</span>

   A spatial vector MUST order the points of interest according to their
   order in the path.  The ordering MAY be based on information from the
   TTL in IPv4, the Hop Limit in IPv6, or the corresponding information
   in MPLS.




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   The report of a spatial vector MUST include the ordered list of the
   hosts involved in the instantaneous measure.

<span class="h4"><a class="selflink" id="section-10.1.3" href="#section-10.1.3">10.1.3</a>.  Timestamping Bias</span>

   The location of the point of interest inside a node influences the
   timestamping skew and accuracy.  As an example, consider that some
   internal machinery delays the timestamping up to three milliseconds;
   then the minimal uncertainty reported be 3 ms if the internal delay
   is unknown at the time of the timestamping.

   The report of a spatial vector MUST include the uncertainty of the
   timestamping compared to wire-time.

<span class="h4"><a class="selflink" id="section-10.1.4" href="#section-10.1.4">10.1.4</a>.  Reporting Spatial One-Way Delay</span>

   The reporting includes information to report for one-way delay as
   <a href="./rfc2679#section-3.6">section&nbsp;3.6 of [RFC2679]</a>.  The same applies for packet loss and ipdv.

<span class="h3"><a class="selflink" id="section-10.2" href="#section-10.2">10.2</a>.  Reporting One-to-Group Metric</span>

   All reporting rules described in [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] and [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] apply to the
   corresponding One-to-group metrics.  The following are specific
   parameters that SHOULD be reported.

<span class="h4"><a class="selflink" id="section-10.2.1" href="#section-10.2.1">10.2.1</a>.  Path</span>

   As suggested by [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] and [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>], the path traversed by the
   packet SHOULD be reported, if possible.  For One-to-group metrics,
   the path tree between the source and the destinations or the set of
   paths between the source and each destination SHOULD be reported.

   The path tree might not be as valuable as individual paths because an
   incomplete path might be difficult to identify in the path tree.  For
   example, how many points of interest are reached by a packet
   traveling along an incomplete path?

<span class="h4"><a class="selflink" id="section-10.2.2" href="#section-10.2.2">10.2.2</a>.  Group Size</span>

   The group size SHOULD be reported as one of the critical management
   parameters.  One-to-group metrics, unlike spatial metrics, don't
   require the ordering of the points of interests because group members
   receive the packets in parallel.

<span class="h4"><a class="selflink" id="section-10.2.3" href="#section-10.2.3">10.2.3</a>.  Timestamping Bias</span>

   It is the same as described in <a href="#section-10.1.3">section 10.1.3</a>.




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<span class="h4"><a class="selflink" id="section-10.2.4" href="#section-10.2.4">10.2.4</a>.  Reporting One-to-group One-way Delay</span>

   It is the same as described in <a href="#section-10.1.4">section 10.1.4</a>.

<span class="h4"><a class="selflink" id="section-10.2.5" href="#section-10.2.5">10.2.5</a>.  Measurement Method</span>

   As explained in <a href="#section-9">section 9</a>, the measurement method will have impact on
   the analysis of the measurement result.  Therefore, it SHOULD be
   reported.

<span class="h3"><a class="selflink" id="section-10.3" href="#section-10.3">10.3</a>.  Metric Identification</span>

   IANA assigns each metric defined by the IPPM WG a unique identifier
   as per [<a href="./rfc4148" title="&quot;IP Performance Metrics (IPPM) Metrics Registry&quot;">RFC4148</a>] in the IANA-IPPM-METRICS-REGISTRY-MIB.

<span class="h3"><a class="selflink" id="section-10.4" href="#section-10.4">10.4</a>.  Information Model</span>

   This section presents the elements of information and the usage of
   the information reported for network performance analysis.  It is out
   of the scope of this section to define how the information is
   reported.

   The information model is built with pieces of information introduced
   and explained in the sections of [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>] , [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] , [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>],
   and [<a href="./rfc3432" title="&quot;Network performance measurement with periodic streams&quot;">RFC3432</a>] that define the IPPM metrics and from any of the
   sections named "Reporting the metric" , "Methodology", and "Errors
   and Uncertainties" whenever they exist in these documents.

   The following are the elements of information taken from end-to-end
   metrics definitions referred to in this memo and from spatial and
   multicast metrics it defines:

   o  Packet_type, the Type-P of test packets (Type-P).

   o  Packet_length, a packet length in bits (L).

   o  Src_host, the IP address of the sender.

   o  Dst_host, the IP address of the receiver.

   o  Hosts_series: &lt;H1, H2,..., Hn&gt;, a list of points of interest
      participating in the instantaneous measure.  They are routers in
      the case of spatial metrics or receivers in the case of one-to-
      group metrics.

   o  Loss_threshold, the threshold of infinite delay.





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   o  Systematic_error, constant delay between wire-time and
      timestamping.

   o  Calibration_error, maximal uncertainty.

   o  Src_time, the sending time for a measured packet.

   o  Dst_time, the receiving time for a measured packet.

   o  Result_status, an indicator of usability of a result 'Resource
      exhaustion' 'infinite', 'lost'.

   o  Delays_series, &lt;dT1,..., dTn&gt;, a list of delays.

   o  Losses_series, &lt;B1, B2, ..., Bi, ..., Bn&gt;, a list of Boolean
      values (spatial) or a set of Boolean values (one-to-group).

   o  Result_status_series, a list of results status.

   o  dT, a delay.

   o  Singleton_number, a number of singletons.

   o  Observation_duration, an observation duration.

   o  metric_identifier.

   The following is the information of each vector that SHOULD be
   available to compute samples:

   o  Packet_type;

   o  Packet_length;

   o  Src_host, the sender of the packet;

   o  Dst_host, the receiver of the packet, apply only for spatial
      vectors;

   o  Hosts_series, not ordered for one-to-group;

   o  Src_time, the sending time for the measured packet;

   o  dT, the end-to-end one-way delay for the measured packet, apply
      only for spatial vectors;

   o  Delays_series, apply only for delays and ipdv vector, not ordered
      for one-to-group;



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   o  Losses_series, apply only for packets loss vector, not ordered for
      one-to-group;

   o  Result_status_series;

   o  Observation_duration, the difference between the time of the last
      singleton and the time of the first singleton.

   Following is the context information (measure, points of interests)
   that SHOULD be available to compute samples:

   o  Loss threshold;

   o  Systematic error, constant delay between wire-time and
      timestamping;

   o  Calibration error, maximal uncertainty.

   A spatial or a one-to-group sample is a collection of singletons
   giving the performance from the sender to a single point of interest.

   The following is the information that SHOULD be available for each
   sample to compute statistics:

   o  Packet_type;

   o  Packet_length;

   o  Src_host, the sender of the packet;

   o  Dst_host, the receiver of the packet;

   o  Start_time, the sending time of the first packet;

   o  Delays_series, apply only for delays and ipdv samples;

   o  Losses_series, apply only for packets loss samples;

   o  Result_status_series;

   o  Observation_duration, the difference between the time of the last
      singleton of the last sample and the time of the first singleton
      of the first sample.

   The following is the context information (measure, points of
   interests) that SHOULD be available to compute statistics:

   o  Loss threshold;



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   o  Systematic error, constant delay between wire-time and
      timestamping;

   o  Calibration error, maximal uncertainty;

   The following is the information of each statistic that SHOULD be
   reported:

   o  Result;

   o  Start_time;

   o  Duration;

   o  Result_status;

   o  Singleton_number, the number of singletons on which the statistic
      is computed;

<span class="h2"><a class="selflink" id="section-11" href="#section-11">11</a>.  Security Considerations</span>

   Spatial and one-to-group metrics are defined on the top of end-to-end
   metrics.  Security considerations discussed in the one-way delay
   metrics definitions of [<a href="./rfc2679" title="&quot;A One-way Delay Metric for IPPM&quot;">RFC2679</a>], in packet loss metrics definitions
   of [<a href="./rfc2680" title="&quot;A One-way Packet Loss Metric for IPPM&quot;">RFC2680</a>] and in IPDV metrics definitions of [<a href="./rfc3393" title="&quot;IP Packet Delay Variation Metric for IP Performance Metrics (IPPM)&quot;">RFC3393</a>] and
   [<a href="./rfc3432" title="&quot;Network performance measurement with periodic streams&quot;">RFC3432</a>] apply to metrics defined in this memo.

   Someone may spoof the identity of a point of interest identity and
   intentionally send corrupt results in order to remotely orient the
   traffic engineering decisions.

   A point of interest could intentionally corrupt its results in order
   to remotely orient the traffic engineering decisions.

<span class="h3"><a class="selflink" id="section-11.1" href="#section-11.1">11.1</a>.  Spatial Metrics</span>

   Malicious generation of packets that systematically match the hash
   function used to detect the packets may lead to a DoS attack toward
   the point of reference.

   Spatial measurement results carry the performance of individual
   segments of the path and the identity of nodes.  An attacker may
   infer from this information the points of weakness of a network
   (e.g., congested node) that would require the least amount of
   additional attacking traffic to exploit.  Therefore, monitoring
   information should be carried in a way that prevents unintended





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   recipients from inspecting the measurement reports.  A
   straightforward solution is to restrict access to the reports using
   encrypted sessions or secured networks.

<span class="h3"><a class="selflink" id="section-11.2" href="#section-11.2">11.2</a>.  One-to-Group Metrics</span>

   Reporting of measurement results from a huge number of probes may
   overload reference point resources (network, network interfaces,
   computation capacities, etc.).

   The configuration of a measurement must take into consideration that
   implicitly more packets will be routed than sent and select a test
   packet rate accordingly.  Collecting statistics from a huge number of
   probes may overload any combination of the network to which the
   measurement controller is attached, measurement controller network
   interfaces, and measurement controller computation capacities.

   One-to-group metric measurements should consider using source
   authentication protocols, standardized in the MSEC group, to avoid
   fraud packet in the sampling interval.  The test packet rate could be
   negotiated before any measurement session to avoid denial-of-service
   attacks.

   A point of interest could intentionally degrade its results in order
   to remotely increase the quality of the network on the branches of
   the multicast tree to which it is connected.

<span class="h2"><a class="selflink" id="section-12" href="#section-12">12</a>.  Acknowledgments</span>

   Lei would like to acknowledge Professor Zhili Sun from CCSR,
   University of Surrey, for his instruction and helpful comments on
   this work.

<span class="h2"><a class="selflink" id="section-13" href="#section-13">13</a>.  IANA Considerations</span>

   Metrics defined in this memo have been registered in the IANA IPPM
   METRICS REGISTRY as described in the initial version of the registry
   [<a href="./rfc4148" title="&quot;IP Performance Metrics (IPPM) Metrics Registry&quot;">RFC4148</a>]:

   IANA has registered the following metrics in the IANA-IPPM-METRICS-
   REGISTRY-MIB:

   ietfSpatialOneWayDelayVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION




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         "Type-P-Spatial-One-way-Delay-Vector"

      REFERENCE

         "<a href="./rfc5644#section-5.1">RFC 5644, section&nbsp;5.1</a>."

      := { ianaIppmMetrics 52 }

   ietfSpatialPacketLossVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Spatial-Packet-Loss-Vector"

      REFERENCE

         "<a href="./rfc5644#section-5.2">RFC 5644, section&nbsp;5.2</a>."

      := { ianaIppmMetrics 53 }

   ietfSpatialOneWayIpdvVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Spatial-One-way-ipdv-Vector"

      REFERENCE

         "<a href="./rfc5644#section-5.3">RFC 5644, section&nbsp;5.3</a>."

      := { ianaIppmMetrics 54 }

   ietfSegmentOneWayDelayStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Segment-One-way-Delay-Stream"

      REFERENCE

         "<a href="./rfc5644#section-6.1">RFC 5644, section&nbsp;6.1</a>."




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      := { ianaIppmMetrics 55 }

   ietfSegmentPacketLossStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Segment-Packet-Loss-Stream"

      REFERENCE

         "<a href="./rfc5644#section-6.2">RFC 5644, section&nbsp;6.2</a>."

      := { ianaIppmMetrics 56 }

   ietfSegmentIpdvPrevStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Segment-ipdv-prev-Stream"

      REFERENCE

         "<a href="./rfc5644#section-6.3">RFC 5644, section&nbsp;6.3</a>."

      := { ianaIppmMetrics 57 }

   ietfSegmentIpdvMinStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Segment-ipdv-min-Stream"

      REFERENCE

         "<a href="./rfc5644#section-6.4">RFC 5644, section&nbsp;6.4</a>."

      := { ianaIppmMetrics 58 }

   -- One-to-group metrics

   ietfOneToGroupDelayVector OBJECT-IDENTITY




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      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Delay-Vector"

      REFERENCE

         "<a href="./rfc5644#section-7.1">RFC 5644, section&nbsp;7.1</a>."

      := { ianaIppmMetrics 59 }

   ietfOneToGroupPacketLossVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Packet-Loss-Vector"

      REFERENCE

         "<a href="./rfc5644#section-7.2">RFC 5644, section&nbsp;7.2</a>."

      := { ianaIppmMetrics 60 }

   ietfOneToGroupIpdvVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-ipdv-Vector"

      REFERENCE

         "<a href="./rfc5644#section-7.3">RFC 5644, section&nbsp;7.3</a>."

      := { ianaIppmMetrics 61 }

   -- One to group statistics

   --

   ietfOnetoGroupReceiverNMeanDelay OBJECT-IDENTITY

      STATUS current




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      DESCRIPTION

         "Type-P-One-to-group-Receiver-n-Mean-Delay"

      REFERENCE

         "<a href="./rfc5644#section-8.3.1">RFC 5644, section&nbsp;8.3.1</a>."

      := { ianaIppmMetrics 62 }

   ietfOneToGroupMeanDelay OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Mean-Delay"

      REFERENCE

         "<a href="./rfc5644#section-8.3.2">RFC 5644, section&nbsp;8.3.2</a>."

      := { ianaIppmMetrics 63 }

   ietfOneToGroupRangeMeanDelay OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Range-Mean-Delay"

      REFERENCE

         "<a href="./rfc5644#section-8.3.3">RFC 5644, section&nbsp;8.3.3</a>."

      := { ianaIppmMetrics 64 }

   ietfOneToGroupMaxMeanDelay OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Max-Mean-Delay"


      REFERENCE



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         "<a href="./rfc5644#section-8.3.4">RFC 5644, section&nbsp;8.3.4</a>."

      := { ianaIppmMetrics 65 }

   ietfOneToGroupReceiverNLossRatio OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Receiver-n-Loss-Ratio"

      REFERENCE

         "<a href="./rfc5644#section-8.4.1">RFC 5644, section&nbsp;8.4.1</a>."

      := { ianaIppmMetrics 66 }

   --

   ietfOneToGroupReceiverNCompLossRatio OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio"

      REFERENCE

         "<a href="./rfc5644#section-8.4.2">RFC 5644, section&nbsp;8.4.2</a>."

      := { ianaIppmMetrics 67 }

   ietfOneToGroupLossRatio OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Loss-Ratio"

      REFERENCE

         "<a href="./rfc5644#section-8.4.3">RFC 5644, section&nbsp;8.4.3</a>."


      := { ianaIppmMetrics 68 }



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   --

   ietfOneToGroupRangeLossRatio OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Range-Loss-Ratio"

      REFERENCE

         "<a href="./rfc5644#section-8.4.4">RFC 5644, section&nbsp;8.4.4</a>."

      := { ianaIppmMetrics 69 }

   ietfOneToGroupRangeDelayVariation OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-group-Range-Delay-Variation"

      REFERENCE

         "<a href="./rfc5644#section-8.5.1">RFC 5644, section&nbsp;8.5.1</a>."

      := { ianaIppmMetrics 70 }

   --

<span class="h2"><a class="selflink" id="section-14" href="#section-14">14</a>.  References</span>

<span class="h3"><a class="selflink" id="section-14.1" href="#section-14.1">14.1</a>.  Normative References</span>

   [<a id="ref-RFC2119">RFC2119</a>]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", <a href="https://www.rfc-editor.org/bcp/bcp14">BCP 14</a>, <a href="./rfc2119">RFC 2119</a>, March 1997.

   [<a id="ref-RFC2679">RFC2679</a>]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Delay Metric for IPPM", <a href="./rfc2679">RFC 2679</a>, September 1999.

   [<a id="ref-RFC2680">RFC2680</a>]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Packet Loss Metric for IPPM", <a href="./rfc2680">RFC 2680</a>, September 1999.

   [<a id="ref-RFC3393">RFC3393</a>]  Demichelis, C. and P. Chimento, "IP Packet Delay Variation
              Metric for IP Performance Metrics (IPPM)", <a href="./rfc3393">RFC 3393</a>,
              November 2002.



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   [<a id="ref-RFC4148">RFC4148</a>]  Stephan, E., "IP Performance Metrics (IPPM) Metrics
              Registry", <a href="https://www.rfc-editor.org/bcp/bcp108">BCP 108</a>, <a href="./rfc4148">RFC 4148</a>, August 2005.

<span class="h3"><a class="selflink" id="section-14.2" href="#section-14.2">14.2</a>.  Informative References</span>

   [<a id="ref-RFC2330">RFC2330</a>]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
              "Framework for IP Performance Metrics", <a href="./rfc2330">RFC 2330</a>,
              May 1998.

   [<a id="ref-RFC3432">RFC3432</a>]  Raisanen, V., Grotefeld, G., and A. Morton, "Network
              performance measurement with periodic streams", <a href="./rfc3432">RFC 3432</a>,
              November 2002.

   [<a id="ref-SPATIAL">SPATIAL</a>]  Morton, A. and E. Stephan, "Spatial Composition of
              Metrics", Work in Progress, June 2009.

Authors' Addresses

   Stephan Emile
   France Telecom Division R&amp;D
   2 avenue Pierre Marzin
   Lannion  F-22307
   France

   Fax:   +33 2 96 05 18 52
   EMail: emile.stephan@orange-ftgroup.com


   Lei Liang
   CCSR, University of Surrey
   Guildford
   Surrey  GU2 7XH
   UK

   Fax:   +44 1483 683641
   EMail: L.Liang@surrey.ac.uk


   Al Morton
   200 Laurel Ave. South
   Middletown, NJ  07748
   USA

   Phone: +1 732 420 1571
   EMail: acmorton@att.com






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