One document matched: draft-ietf-ippm-multimetrics-07.xml


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<rfc category="std" docName="draft-ietf-ippm-multimetrics-07" ipr="full3978">
  <front>
    <title abbrev="Spatial and Multicast Metrics">IP Performance Metrics
    (IPPM) for spatial and multicast</title>

    <author fullname="Stephan Emile" initials="E." surname="Stephan">
      <organization abbrev="France Telecom">France Telecom Division
      R&D</organization>

      <address>
        <postal>
          <street>2 avenue Pierre Marzin</street>

          <city>Lannion</city>

          <region></region>

          <code>F-22307</code>
        </postal>

        <facsimile>+33 2 96 05 18 52</facsimile>

        <email>emile.stephan@orange-ftgroup.com</email>
      </address>
    </author>

    <author fullname="Lei Liang" initials="L." surname="Liang">
      <organization abbrev="University of Surrey">CCSR, University of
      Surrey</organization>

      <address>
        <postal>
          <street>Guildford</street>

          <city>Surrey</city>

          <region></region>

          <code>GU2 7XH</code>
        </postal>

        <facsimile>+44 1483 683641</facsimile>

        <email>L.Liang@surrey.ac.uk</email>
      </address>
    </author>

    <author fullname="Al Morton" initials="A." surname="Morton">
      <organization abbrev="AT&T Labs"></organization>

      <address>
        <postal>
          <street>200 Laurel Ave. South</street>

          <city>Middletown</city>

          <region>NJ</region>

          <code>07748</code>

          <country>USA</country>
        </postal>

        <phone>+1 732 420 1571</phone>

        <email>acmorton@att.com</email>
      </address>
    </author>

    <date day="26" month="June" year="2008" />

    <abstract>
      <t>The IETF IP Performance Metrics (IPPM) working group has standardized
      metrics 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).</t>
    </abstract>

    <note title="Requirements Language">
      <t>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 <xref
      target="RFC2119">RFC 2119</xref>.</t>
    </note>
  </front>

  <middle>
    <section title="Introduction">
      <t>The IETF IP Performance Metrics (IPPM) working group has standardized
      metrics 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).</t>

      <t>The purpose of the memo is to define metrics to fulfill the new
      requirements of measurement involving multiple measurement points.
      Spatial metrics are defined to measure the performance of each segments
      along a path while the one-to-group metrics are aiming to provide a
      ruler to measure the performance of a group of users. These metrics are
      derived from one-way end-to-end metrics defined by IETF and follow the
      criteria described in the IPPM framework <xref
      target="RFC2330"></xref>.</t>

      <t>New terms are introduced to extend the terminology of the IPPM
      framework to spatial metrics and one-to-group metrics. Then a section
      motivates the need of defining each category of metrics. After, each
      category is defined in a separate section. Then the memo discusses the
      impact of the measurement methods on the scalability and proposes an
      information model for reporting the measurements. Finally the document
      discusses security aspects related to measurement and registers the
      metrics in the IANA IP Performance Metrics Registry <xref
      target="RFC4148"></xref>.</t>

      <t>Note that all these metrics are based on observations of packets
      dedicated to testing, a process which is called Active measurement.
      Purely passive spatial measurement (for example, a spatial metric based
      on the observation of user traffic) is beyond the scope of this
      memo.</t>

      <t>Following is a summary of the metrics defined.</t>

      <t>This memo firstly defines metrics for spatial measurement based on
      the decomposition of standard end-to-end metrics defined by IETF in
      [<xref target="RFC2679"></xref>, <xref target="RFC2680"></xref>, <xref
      target="RFC3393"></xref>, <xref target="RFC3432"></xref>. Seven metrics
      are defined including their names, parameters, units and measurement
      methodologies. Each definion includes a specific section discussing
      measurements constraints and issues, and proposing guidance to increase
      results accucacy. These spatial metrics are:<list style="symbols">
          <t>A 'Vector', called Type-P-Spatial-One-way-Delay-Vector, will be
          introduced to divide an end-to-end Type-P-One-way-Delay <xref
          target="RFC2679"></xref> into a spatial sequence of one-way delay
          metrics.</t>

          <t>A 'Vector', called Type-P-Spatial-One-way-Packet-Loss-Vector,
          will be introduced to divide an end-to-end
          Type-P-One-way-Packet-Loss <xref target="RFC2680"></xref> in a
          spatial sequence of packet loss metrics.</t>

          <t>Using the Type-P-Spatial-One-way-Delay-Vector metric, a 'vector',
          called Type-P-Spatial-One-way-ipdv-Vector, will be introduced to
          divide an end-to-end Type-P-One-way-ipdv in a spatial sequence of
          ipdv metrics.</t>

          <t>Using the Type-P-Spatial-One-way-Delay-Vector metric, a 'sample',
          called Type-P-Segment-One-way-Delay-Stream, will be introduced to
          collect one-way delay metrics over time between two points of
          interest of the path;</t>

          <t>Using the Type-P-Spatial-Packet-Loss-Vector metric, a 'sample',
          called Type-P-Segment-Packet-Loss-Stream, will be introduced to
          collect packet loss metrics over time between two points of interest
          of the path;</t>

          <t>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 over time between two points of interest of the
          path using the previous packet selection function;</t>

          <t>Using the Type-P-Spatial-One-way-Delay-Vector metric, a 'sample',
          called Type-P-Segment-ipdv-min-Stream, will be introduced to compute
          ipdv metrics over time between two points of interest of the path
          using the shortest delay selection function;</t>
        </list></t>

      <t>Then the memo defines one-to-group metrics and one-to-group
      statistics.</t>

      <t>Three one-to-group metrics are defined to measure the one-way
      performance between a source and a group of receivers. Definitions
      derive from one-way metrics definitions of RFCs in <xref
      target="RFC2679"></xref>, <xref target="RFC2680"></xref>, <xref
      target="RFC3393"></xref>, <xref target="RFC3432"></xref>: <list
          style="symbols">
          <t>A 'Vector', called Type-P-One-to-Group-One-way-Delay-Vector, will
          be introduced to collect the set of Type-P-one-way-delay singletons
          between one sender and N receivers;</t>

          <t>A 'Vector', called
          Type-P-One-to-Group-One-way-Packet-Loss-Vector, will be introduced
          to collect the set of Type-P-One-way-Packet-Loss singletons between
          one sender and N receivers;</t>

          <t>A 'Vector', called Type-P-One-to-Group-One-way-ipdv-Vector, will
          be introduced to collect the set of Type-P-One-way-ipdv singletons
          between one sender and N receivers.</t>
        </list></t>

      <t>Then, based on the One-to-group vector metrics listed above,
      statistics are defined to capture single receiver performance, group
      performance and relative performance situation inside a multiparty
      communication for each packet sent during the test interval between one
      sender and N receivers: <list style="symbols">
          <t>Using the Type-P-One-to-Group-One-way-Delay-Vector, a metric
          called Type-P-One-to-Group-Receiver-n-Mean-Delay will be introduced
          to present the mean of delays between one sender and a receiver 'n'.
          Then, based on this definition, 3 metrics will be defined to
          characterize the mean delay over the entire group during this
          interval:<list>
              <t>a metric called Type-P-One-to-Group-Mean-Delay, will be
              introduced to present the mean of delays;</t>

              <t>a metric called Type-P-One-to-Group-Range-Mean-Delay will be
              introduced to present the range of mean delays;</t>

              <t>a metric called Type-P-One-to-Group-Max-Mean-Delay will be
              introduced to present the maximum of mean delays;</t>
            </list></t>

          <t>Using the Type-P-one-to-group-One-way-Packet-Loss-Vector, a
          metric called Type-P-One-to-Group-Receiver-n-Loss-Ratio will be
          introduced to capture packet loss ratio between one sender and a
          receiver 'n'. Then based on this definition, 2 metrics will be
          defined to characterize packet loss over the entire group during
          this interval:<list>
              <t>a metric called Type-P-One-to-Group-Loss-Ratio will be
              introduced to capture packet loss ratio overall over the entire
              group or all receivers;</t>

              <t>a metric called Type-P-One-to-Group-Range-Loss-Ratio will be
              introduced to present comparative packet loss ratio for each
              packet during the test interval between one sender and N
              Receivers.</t>
            </list></t>

          <t>Using Type-P-one-to-group-One-way-ipdv-Vector, a metric called
          Type-P-One-to-Group-Range-Delay-Variation will be introduced to
          present the range of delay variation between one sender and a group
          of receivers.</t>
        </list></t>
    </section>

    <section title="Terminology">
      <section title="Path Digest Hosts">
        <t>The list of the hosts on a path from the source to the
        destination.</t>
      </section>

      <section title="Multiparty metric">
        <t>A metric is said to be multiparty if the topology involves more
        than one measurement collection point. All multiparty metrics define a
        set of hosts called "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 < ha, hb, hc, ..., hn >, where
        ha is the source and < hb, hc, ..., hn > are the destinations,
        then measurements may be conducted between < ha, hb>, < ha,
        hc>, ..., <ha, hn >.</t>

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

      <section title="Spatial metric">
        <t>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.</t>
      </section>

      <section title="One-to-group metric">
        <t>A metric is said to be one-to-group if the measured packet is sent
        by one source and (potentially) received by several destinations.
        Thus, the topology of the communication group can be viewed as a
        centre-distributed or server-client topology with the source as the
        centre/server in the topology.</t>
      </section>

      <section title="Points of interest">
        <t>Points of interest are the hosts* (as per RFC2330 definition, that
        includes routing nodes) that are measurement collection points, a
        sub-set of the set of hosts involved in the delivery of the packets
        (in addition to the source itself). Note that the points of interest
        are a possibly arbitrary sub-set of all the hosts involved in the
        path.</t>

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

        <t><figure anchor="FigPointO2g"
            title="One-to-group points of interest">
            <artwork align="center"><![CDATA[Src                  Recv
`.          ,-.      
  `.      ,'   `...... 1
    `.   ;       :
      `. ;       :
        ;         :... 2
        |         |
        :         ;
         :       ;.... 3
         :       ;
          `.   ,'
            `-'....... N

]]></artwork>
          </figure></t>

        <t></t>

        <t></t>

        <t>A candidate point of interest for spatial metrics is a host from
        the set of hosts involved in the delivery of the packets from the
        source.</t>

        <figure anchor="FigPointSpatial" title="Spatial points of interest">
          <artwork align="center"><![CDATA[

                Src ------.           Hosts
                           \
                            `---X   ... 1
                                \
                                 x
                                /
                     .---------X   .... 2
                   /
                  x 
                   \
                   `---X           .... 3
                          \
                           \
                            \
                             X     .... N
                              \
                               \
                                \
                                 `---- Dst
                                  

       Note: 'x' are nodes which are not points of interest
]]></artwork>
        </figure>
      </section>

      <section title="Reference point">
        <t>A reference point is defined as the server where the statistical
        calculations will be carried out. A centre/server in the multimetrics
        measurement that is controlled by a network operator is a good example
        of a reference point, where measurement data can be collected for
        further processing. However, the actual measurements have to be
        carried out at all points of interest.</t>
      </section>

      <section title="Vector ">
        <t>A Vector is a set of singletons, which are a set of results of the
        observation of the behaviour of the same packet at different places of
        a network at different times. For instance, if one-way delay
        singletons observed at N receivers for Packet P sent by the source Src
        are dT1, dT2,…, dTN, it can be say that a vector V with N
        elements can be organized as {dT1, dT2,…, dTN}. The elements in
        one vector are singletons distinct with each other in terms of both
        measurement point and sending time. Given the vector V as an example,
        the element dT1 is distinct from all others as the singleton at
        receiver 1 in response to a packet sent from the source at time T1.
        The complete Vector gives information over the dimension of space.</t>
      </section>

      <section title="Matrix">
        <t>Several vectors form a Matrix, which contains results observed in a
        sampling interval at different places in a network at different times.
        For instance, given One-way delay vectors V1={dT11, dT12,..., dT1N},
        V2={dT21, dT22,…, dT2N},…, Vm={dTm1, dTm2,…,
        dTmN} for Packet P1, P2,…,Pm, we can have a One-way delay
        Matrix {V1, V2,…,Vm}. Additional to the information given by a
        Vector, a Matrix is more powerful to present network performance in
        both space and time dimensions. It normally corresponds to a sample in
        simple point-to-point measurement.</t>

        <t>The relation among Singleton, Vector and Matrix can be shown in the
        following <xref target="Figmatrix"></xref>.</t>

        <t><figure anchor="Figmatrix"
            title="Relation beween Singletons, vectors and matrix">
            <artwork align="center"><![CDATA[              Point of          Singleton
              interest            /          Samples
               ,----.    ^      /
              /   R1.....|  / R1dT1   R1dT2   R1dT3 ... R3dTk \
             /         \ | |                                   |
            ;  R2........| |  R2dT1   R2dT2   R2dT3 ... R3dTk  |
       Src  |           || |                                   |
            |      R3....| |  R3dT1   R3dT2   R3dT3 ... R3dTk  |
            |           || |                                   |
            :           ;| |                                   |
             \         / | |                                   |
              \  Rn......|  \ RndT1   RndT2   RndT3 ... RndTk /
               `-----'   +-------------------------------------> time
                              
                             Vector           Matrix
                            (space)           (time)
]]></artwork>
          </figure></t>
      </section>
    </section>

    <section title="Motivations">
      <t>All IPPM metrics are defined for end-to-end (source to destination)
      measurement of point-to-point paths. It is a logical extension to define
      metrics for multiparty measurements such as one to one trajectory
      metrics and one to multipoint metrics.</t>

      <section title="Motivations for spatial metrics">
        <t>Decomposition of instantaneous end-to-end measures is needed: <list
            style="symbols">
            <t>Decomposing the performance of interdomain path is desirable to
            quantify the per-AS contribution to the performance. It is
            valuable to define standard spatial metrics before pursuing
            inter-domain path performance specifications.</t>

            <t>Traffic engineering and troubleshooting applications benefit
            from spatial views of one-way delay and ipdv consumption, and
            identification of the location of the lost of packets.</t>

            <t>Monitoring the performance of a multicast tree composed of MPLS
            point-to-multipoint and inter-domain communication require spatial
            decomposition of the one-way delay, ipdv, and packet loss.</t>

            <t>Composition of metrics is needed to help measurement systems
            reach large scale coverage. Spatial measures typically give the
            individual performance of an intra domain segment and provide an
            elementary piece of information needed to estimate interdomain
            performance based on composition of metrics.</t>
          </list></t>
      </section>

      <section title="Motivations for One-to-group metrics">
        <t>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 one-way metric cannot completely describe the multiparty
        situation. New one-to-group metrics assess performance of all the
        paths for further statistical analysis. The new metrics proposed in
        this stage are named one-to-group performance metrics, and they are
        based on the unicast metrics defined in IPPM WG. One-to-group metrics
        are one-way metrics from one source to a group of destinations. The
        metrics are helpful for judging the network performance of multiparty
        communications and can also be used to describe the variation of
        performance delivered to a group of destination hosts and their
        users.</t>

        <t>One-to-group performance metrics are needed for several
        reasons:</t>

        <t><list style="symbols">
            <t>For designing and engineering multicast trees and MPLS
            point-to-multipoint LSP;</t>

            <t>For evaluating and controlling of the quality of the multicast
            services;</t>

            <t>For controlling the performance of the inter domain multicast
            services;</t>

            <t>For presenting and evaluating the performance requirements for
            multiparty communications and overlay multicast.</t>
          </list>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. It
        will give a very detailed insight into each branch of the multicast
        tree in terms of end-to-end absolute performance. This detail can
        provide clear and helpful information for engineers to identify the
        sub-path with problems in a complex multiparty routing tree.</t>

        <t>The one-to-group metrics described in this memo introduce the
        multiparty topology to the IPPM working group; the goal is to measure
        the performance delivered to a group of users who are receiving
        packets from the same source. The concept extends the "path" in the
        one-way measurement to "path tree" to cover both one-to-one and
        one-to-many communications. If applied to one-to-one communications,
        the one-to-group metrics provide exactly the same results as the
        corresponding one-to-one metrics.</t>
      </section>

      <t></t>

      <section title="Discussion on Group-to-one and Group-to-group metrics">
        <t>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 currently beyond the scope of this memo, because they
        would involve multiple packets launched from different sources.
        However, we can give some clues here on these two cases.</t>

        <t>The measurements for group-to-one topology can be easily derived
        from the one-to-group measurement. The measurement point is the
        reference point that is acting as a receiver while all of
        clients/receivers defined for one-to-group measurement act as sources
        in this case.</t>

        <t>For the group-to-group connection topology, it is difficult to
        define the reference point and therefore it is difficult to define the
        measurement points. However, we can always avoid this confusion by
        treating the connections as one-to-group or group-to-one in our
        measurements without consideration on how the real communication will
        be carried out. For example, if one group of hosts < ha, hb, hc,
        ..., hn > are acting as sources to send data to another group of
        hosts < Ha, Hb, Hc, ..., Hm >, we can always decompose them into
        n one-to-group communications as < ha, Ha, Hb, Hc, ..., Hm >,
        < hb, Ha, Hb, Hc, ..., Hm >, <hc, Ha, Hb, Hc, ..., Hm >,
        ..., < hn, Ha, Hb, Hc, ..., Hm >.</t>
      </section>
    </section>

    <section title="Spatial vectors metrics definitions">
      <t>This section defines vectors for the decomposition of end-to-end
      singleton metrics over a path.</t>

      <t>Spatial vectors metrics are based on the decomposition of standard
      end-to-end metrics defined by the IPPM WG in <xref
      target="RFC2679"></xref>, <xref target="RFC2680"></xref>, <xref
      target="RFC3393"></xref> and <xref target="RFC3432"></xref>.</t>

      <t>Definitions are coupled with the corresponding end-to-end metrics.
      Methodology specificities are common to all the vectors defined and are
      consequently discussed in a common section.</t>

      <section title="A Definition for Spatial One-way Delay Vector">
        <t>This section is coupled with the definition of Type-P-One-way-Delay
        of the section 3 of <xref target="RFC2679"></xref>. When a parameter
        of this definition is first used in this section, it will be tagged
        with a trailing asterisk.</t>

        <t>Sections 3.5 to 3.8 of <xref target="RFC2679"></xref> 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 measurement SHOULD be
        respectful of them, especially those related to methodology, clock,
        uncertainties and reporting.</t>

        <section title="Metric Name">
          <t>Type-P-Spatial-One-way-Delay-Vector</t>
        </section>

        <section title="Metric Parameters">
          <t><list style="symbols">
              <t>Src*, the IP address of the sender.</t>

              <t>Dst*, the IP address of the receiver.</t>

              <t>i, An integer in the ordered list <1,2,...,n> of hosts
              in the path.</t>

              <t>Hi, A host* of the path digest.</t>

              <t>T*, a time, the sending (or initial observation) time for a
              measured packet.</t>

              <t>dT*, a delay, the one-way delay for a measured packet.</t>

              <t><dT1,..., dTn> a list of delay.</t>

              <t>P*, the specification of the packet type.</t>

              <t><H1, H2,..., Hn>, hosts path digest.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t>The value of Type-P-Spatial-One-way-Delay-Vector is a sequence of
          times.</t>
        </section>

        <section title="Definition">
          <t>Given a Type-P packet sent by the sender Src at wire-time (first
          bit) T to the receiver Dst in the path <H1, H2,..., Hn>. Given
          the sequence of values <T+dT1,T+dT2,...,T+dTn,T+dT> such that
          dT is the Type-P-One-way-Delay from Src to Dst and such that 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 never passes Hi.</t>

          <t>Type-P-Spatial-One-way-Delay-Vector metric is defined for the
          path <Src, H1, H2,..., Hn, Dst> as the sequence of values
          <T,dT1,dT2,...,dTn,dT>.</t>
        </section>

        <section title="Discussion">
          <t>Following are specific issues which may occur: <list
              style="symbols">
              <t>the delay looks to decrease: dTi > DTi+1. This may occur
              despite it does not make sense per definition:<list
                  style="symbols">
                  <t>This is frequently due to some clock synchronization
                  issue. This point is discussed in the section 3.7.1. "Errors
                  or uncertainties related to Clocks" of <xref
                  target="RFC2679"></xref>. Consequently, times of a measure
                  at different hosts do not guaranty the ordering of the hosts
                  on the path of a measure.</t>

                  <t>During some change of routes the order of 2 hosts may
                  change on the main path;</t>

                  <t>The location of the point of interest 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'</t>
                </list></t>
            </list></t>
        </section>
      </section>

      <section title="A Definition for Spatial One-way Packet Loss Vector">
        <t>This section is coupled with the definition of
        Type-P-One-way-Packet-Loss. Then when a parameter from the section 2
        of <xref target="RFC2680"></xref> is first used in this section, it
        will be tagged with a trailing asterisk.</t>

        <t>Sections 2.5 to 2.8 of <xref target="RFC2680"></xref> 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
        SHOULD be respectful of them, especially those related to methodology,
        clock, uncertainties and reporting.</t>

        <t>Following we define the spatial metric, then we adapt some of the
        points above and introduce points specific to spatial measurement.</t>

        <section title="Metric Name">
          <t>Type-P-Spatial-One-way-Packet-Loss-Vector</t>
        </section>

        <section title="Metric Parameters">
          <t><list style="symbols">
              <t>Src*, the IP address of the sender.</t>

              <t>Dst*, the IP address of the receiver.</t>

              <t>i, an integer which ordered the hosts in the path.</t>

              <t>Hi, points of interests of the path digest.</t>

              <t>T*, a time, the sending time for a measured packet.</t>

              <t><dT1,..., dTn, dT>, a list of delay.</t>

              <t>P*, the specification of the packet type.</t>

              <t><H1, H2,..., Hn>, hosts path digest.</t>

              <t><L1, L2, ...,Ln>, a list of Boolean values.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t>The value of Type-P-Spatial-One-way-Packet-Loss-Vector is a
          sequence of Boolean values.</t>
        </section>

        <section title="Definition">
          <t>Given a Type-P packet sent by the sender Src at time T to the
          receiver Dst in the path <H1, H2, ..., Hn>. Given the sequence
          of times <T+dT1,T+dT2,...,T+dTn> the packet passes in <H1,
          H2 ..., Hn>, we define Type-P-One-way-Packet-Lost-Vector metric
          as the sequence of values <L1, L2, ..., Ln> 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.</t>
        </section>

        <section title="Discussion">
          <t>Following are specific issues which may occur: <list
              style="symbols">
              <t>The result includes the sequence 1,0. This may occur under
              specific situations:<list style="symbols">
                  <t>During some change of routes a packet may be seen by a
                  host but not by it successor on the main path;</t>

                  <t>A packet may not be observed in a host due to some buffer
                  or CPU overflow in the point of interest;</t>
                </list></t>
            </list></t>
        </section>
      </section>

      <section title="A Definition for Spatial One-way Ipdv Vector">
        <t>This section uses parameters from the definition of
        Type-P-One-way-ipdv. When a parameter from section 2 of <xref
        target="RFC3393"></xref> is first used in this section, it will be
        tagged with a trailing asterisk.</t>

        <t>In the following we adapt some of them and introduce points
        specific to spatial measurement.</t>

        <section title="Metric Name">
          <t>Type-P-Spatial-One-way-ipdv-Vector</t>
        </section>

        <section title="Metric Parameters">
          <t></t>

          <t><list style="symbols">
              <t>Src*, the IP address of the sender.</t>

              <t>Dst*, the IP address of the receiver.</t>

              <t>i, An integer in the ordered list <1,2,...,n> of hosts
              in the path.</t>

              <t>Hi, A host* of the path digest.</t>

              <t>T1*, a time, the sending time for a first measured
              packet.</t>

              <t>T2*, a time, the sending time for a second measured
              packet.</t>

              <t>dT*, a delay, the one-way delay for a measured packet.</t>

              <t>P*, the specification of the packets type.</t>

              <t>P1, the first packet sent at time T1.</t>

              <t>P2, the second packet sent at time T2.</t>

              <t><H1, H2,..., Hn>, hosts path digest.</t>

              <t><T1,dT1.1, dT1.2,..., dT1.n,dT1>, the
              Type-P-Spatial-One-way-Delay-Vector for packet sent at time
              T1.</t>

              <t><T2,dT2.1, dT2.2,..., dT2.n,dT2>, the
              Type-P-Spatial-One-way-Delay-Vector for packet sent at time
              T2.</t>

              <t>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.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t>The value of Type-P-Spatial-One-way-ipdv-Vector is a sequence of
          times.</t>
        </section>

        <section title="Definition">
          <t>Given P1 the Type-P packet sent by the sender Src at wire-time
          (first bit) T1 to the receiver Dst and <T1, dT1.1, dT1.2,...,
          dT1.n, dT1> its Type-P-Spatial-One-way-Delay-Vector over the path
          <H1, H2,..., Hn>.</t>

          <t>Given P2 the Type-P packet sent by the sender Src at wire-time
          (first bit) T2 to the receiver Dst and <T2, dT2.1, dT2.2,...,
          dT2.n, dT2> its Type-P-Spatial-One-way-Delay-Vector over the same
          path.</t>

          <t>Type-P-Spatial-One-way-ipdv-Vector metric is defined as the
          sequence of values <T2-T1, dT2.1-dT1.1, dT2.2-dT1.2 ,...,
          dT2.n-dT1.n, dT2-dT1> such that for each Hi of the path <H1,
          H2,..., Hn>, dT2.i-dT1.i is either a real number if the packets
          P1 and P2 passe Hi at wire-time (last bit) dT1.i, respectively
          dT2.i, or undefined if at least one of them never passes Hi. T2-T1
          is the inter-packet emission interval and dT2-dT1 is ddT* the
          Type-P-One-way-ipdv at T1,T2*.</t>
        </section>
      </section>

      <section anchor="spatial_meth" title="Spatial Methodology ">
        <t>Methodology, reporting and uncertainties points specified in
        section 3 of <xref target="RFC2679"></xref> applies to each point of
        interest Hi measuring a element of a spatial delay vector.</t>

        <t>Methodology, reporting and uncertainties points specified in
        section 2 of <xref target="RFC2680"></xref> applies to each point of
        interest Hi measuring a element of a spatial packet loss vector.</t>

        <t>Sections 3.5 to 3.7 of <xref target="RFC3393"></xref> 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 SHOULD be
        respectful of methodology, clock, uncertainties and reporting aspects
        given in this section.</t>

        <t>Generally, for a given Type-P of length L, in a given Hi, the
        methodology for spatial vector metrics may proceed as follows:<list
            style="symbols">
            <t>At each Hi, points of interest prepare to capture the packet
            sent a time T, take a timestamp Ti', determine the internal delay
            correction dTi' (See section 3.7.1. "Errors or uncertainties
            related to Clocks" of <xref target="RFC2679"></xref>),</t>

            <t>Each Hi extracts the path ordering information from the packet
            (e.g. time-to-live);</t>

            <t>Each Hi compute the wiretime from Src to Hi: Ti = Ti' - dTi'.
            This arrival time is undefined (infinite) if the packet is not
            detected after the 'loss threshold' duration;</t>

            <t>Each Hi extracts the timestamp T from the packet;</t>

            <t>Each Hi computes the one-way-delay from Src to Hi: dTi = Ti -
            T;</t>

            <t>The reference point gathers the result of each Hi and order
            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 <T, dT1, dT2,...,
            dTn, dT> ) over the path <Src, H1, H2,..., Hn, Dst> at
            time T.</t>
          </list></t>

        <section title="Loss threshold ">
          <t>Loss threshold is the centrality of any methodology because it
          determines the presence the packet in the measurement process of the
          point of interest and consequently determines any ground truth
          metric result. It determines the presence of an effective delay, and
          bias the measure of ipdv, of packet loss and of the statistics.</t>

          <t>This is consistent for end-to-end but impacts spatial measure:
          depending on the consistency of the loss threshold among the points
          of interest, a packet may be considered loss a one host but present
          in another one, or may be observed by the last host (last hop) of
          the path but considered lost by Dst. The analysis of such results is
          not deterministic: Has the path change? Does the packet arrive at
          destination or was it lost during the last mile? The same applies,
          of course, for one-way-delay measures: a delay measured may be
          infinite at one host but a real value in another one, or may be
          measured as a real value by the last host of the path but observed
          as infinite by Dst. The loss threshold should be set up with the
          same value in each host of the path and in the destination. The loss
          threshold must be systematically reported to permit careful
          introspection and to avoid the introduction of any contradiction in
          the statistic computation process.</t>
        </section>

        <section title="Host Path Digest ">
          <t>The methodology given above relies on the order of the points of
          interest over the path to <xref target="RFC2679"></xref> one's.</t>

          <t>A test packets may cross several times the same host resulting in
          the repetition of one or several hosts in the Path Digest.</t>

          <t>As an example. This occurs typically during rerouting phases
          which introduce temporary micro loops. During such an event the host
          path digest for a packet crossing Ha and Hb may include the pattern
          <Hb, Ha, Hb, Ha, Hb> meaning that Ha ended the computation of
          the new path before Hb and that the initial path wath from Ha to Hb
          and that the new path is from Hb to Ha.</t>

          <t>Consequently, duplication of hosts in the Path Digest of a
          vectors MUST be identified before statistics computation to avoid
          corrupted results' production.</t>
        </section>
      </section>

      <t></t>
    </section>

    <section title="Spatial Segments metrics definitions">
      <t>This section defines samples to measure the performance of a segment
      of a path over time. Definitions rely on matrix of the spatial vector
      metrics defined above.</t>

      <t>Firstly it 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.</t>

      <t>Then it defines 2 different samples of ipdv. The first metric,
      Type-P-Segment-One-way-ipdv-prev-Stream, uses the previous packet as the
      selection function. The second metric,
      Type-P-Segment-One-way-ipdv-min-Stream, uses the minimum delay as the
      selection.</t>

      <section anchor="seg_delay"
               title="A Definition of a sample of One-way Delay of a segment of the path">
        <t>This metric defines a sample of One-way delays over time between a
        pair of hosts of a path.</t>

        <t>As its semantic is very close to the metric
        Type-P-Packet-loss-Stream defined in section 4 of <xref
        target="RFC2679"></xref>, sections 4.5 to 4.8 of <xref
        target="RFC2679"></xref> are part of the current definition.</t>

        <section title="Metric Name">
          <t>Type-P-Segment-One-way-Delay-Stream</t>
        </section>

        <section title="Metric Parameters">
          <t><list style="symbols">
              <t>Src*, the IP address of the sender.</t>

              <t>Dst*, the IP address of the receiver.</t>

              <t>P*, the specification of the packet type.</t>

              <t>i, an integer in the ordered list <1,2,...,n> of hosts
              in the path.</t>

              <t>k, an integer which orders the packets sent.</t>

              <t>a and b, 2 integers where b > a.</t>

              <t>Hi, a host* of the path digest.</t>

              <t><H1,..., Ha, ..., Hb, ...., Hn>, hosts path digest.</t>

              <t><T1, T2, ..., Tm>, a list of times.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t>The value of a Type-P-Segment-One-way-Delay-Stream is a pair
          of<list>
              <t>list of times <T1, T2, ..., Tm>;</t>

              <t>sequence of delays.</t>
            </list></t>
        </section>

        <section title="Definition">
          <t>Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ...,
          Hb, ..., Hn>, given the matrix of
          Type-P-Spatial-One-way-Delay-Vector for the packets sent from Src to
          Dst at times <T1, T2, ..., Tm-1, Tm> :<list>
              <t><T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n,
              dT1>;</t>

              <t><T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n,
              dT2>;</t>

              <t>...</t>

              <t><Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n,
              dTm>.</t>
            </list></t>

          <t>We define the sample Type-P-segment-One-way-Delay-Stream as the
          sequence <dT1.ab, dT2.ab, ..., dTk.ab, ..., dTm.ab> such that
          for each time Tk, 'dTk.ab' is either the real number 'dTk.b - dTk.a'
          if the packet send a time Tk passes Ha and Hb or undefined if this
          packet never passes Ha or (inclusive) never passes Hb.</t>
        </section>

        <section title="Discussion">
          <t>Following are specific issues which may occur: <list
              style="symbols">
              <t>the delay looks to decrease: dTi > DTi+1:<list>
                  <t>This is typically due to clock synchronization issue.
                  this point is discussed in the section 3.7.1. "Errors or
                  uncertainties related to Clocks" of of <xref
                  target="RFC2679"></xref>;</t>

                  <t>This may occurs too when the clock resolution of one
                  probe is bigger than the minimum delay of a path. As an
                  example this happen when measuring the delay of a path which
                  is 500 km long with one probe synchronized using NTP having
                  a clock resolution of 8ms.</t>
                </list></t>
            </list>The metric can not be performed on < T1 , T2, ..., Tm-1,
          Tm> in the following cases: <list style="symbols">
              <t>Ha or Hb disappears from the path due to some change of
              routes;</t>

              <t>The order of Ha and Hb changes in the path;</t>
            </list></t>
        </section>
      </section>

      <section anchor="seg_dl"
               title="A Definition of a sample of Packet Loss of a segment of the path">
        <t>This metric defines a sample of packet lost over time between a
        pair of hosts of a path. As its semantic is very close to the metric
        Type-P-Packet-loss-Stream defined in section 3 of <xref
        target="RFC2680"></xref>, sections 3.5 to 3.8 of <xref
        target="RFC2680"></xref> are part of the current definition.</t>

        <section title="Metric Name">
          <t>Type-P-segment-Packet-loss-Stream</t>
        </section>

        <section title="Metric Parameters">
          <t><list style="symbols">
              <t>Src*, the IP address of the sender.</t>

              <t>Dst*, the IP address of the receiver.</t>

              <t>P*, the specification of the packet type.</t>

              <t>k, an integer which orders the packets sent.</t>

              <t>n, an integer which orders the hosts on the path.</t>

              <t>a and b, 2 integers where b > a.</t>

              <t><H1, H2, ..., Ha, ..., Hb, ...,Hn>, hosts path
              digest.</t>

              <t>Hi, exchange points of the path digest.</t>

              <t><T1, T2, ..., Tm>, a list of times.</t>

              <t><L1, L2, ..., Ln> a list of boolean values.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t></t>

          <t>The value of a Type-P-segment-Packet-loss-Stream is a pair
          of<list>
              <t>The list of times <T1, T2, ..., Tm>;</t>

              <t>a sequence of booleans.</t>
            </list></t>
        </section>

        <section title="Definition">
          <t>Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ...,
          Hb, ..., Hn>, given the matrix of
          Type-P-Spatial-Packet-loss-Vector for the packets sent from Src to
          Dst at times <T1, T2, ..., Tm-1, Tm> : <list>
              <t><L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L>,</t>

              <t><L2.1, L2.2,..., L2.a, ..., L2.b, ..., L2.n, L>,</t>

              <t>...,</t>

              <t><Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L>.</t>
            </list></t>

          <t>We define the value of the sample
          Type-P-segment-Packet-Lost-Stream from Ha to Hb as the sequence of
          booleans <L1.ab, L2.ab,..., Lk.ab, ..., Lm.ab> such that for
          each Tk:<list style="symbols">
              <t>A value of Lk of 0 means that Ha and Hb observed the packet
              sent at time Tk (Lk.a and Lk.b have a value of 0);</t>

              <t>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 observed the
              packet sent at time Tk (Lk.b have a value of 1);</t>

              <t>The value of Lk is undefined when Neither Ha or Hb observe
              the packet;</t>
            </list></t>
        </section>

        <section title="Discussion">
          <t>Unlike Type-P-Packet-loss-Stream,
          Type-P-Segment-Packet-loss-Stream relies on the stability of the
          host path digest. The metric can not be performed on < T1 , T2,
          ..., Tm-1, Tm> in the following cases: <list style="symbols">
              <t>Ha or Hb disappears from the path due to some change of
              routes;</t>

              <t>the order of Ha and Hb changes in the path;</t>

              <t>Lk.a or Lk.b is undefined;</t>

              <t>Lk.a has the value 1 (not observed) and Lk.b has the value 0
              (observed);</t>

              <t>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).</t>
            </list></t>
        </section>
      </section>

      <section anchor="seg_ipdv"
               title="A Definition of a sample of ipdv of a segment using the previous packet selection function">
        <t>This metric defines a sample of ipdv <xref target="RFC3393"></xref>
        over time between a pair of hosts using the previous packet as the
        selection function.</t>

        <section title="Metric Name">
          <t>Type-P-Segment-One-way-ipdv-prev-Stream</t>
        </section>

        <section title="Metric Parameters"></section>

        <t><list style="symbols">
            <t>Src*, the IP address of the sender.</t>

            <t>Dst*, the IP address of the receiver.</t>

            <t>P*, the specification of the packet type.</t>

            <t>k, an integer which orders the packets sent.</t>

            <t>n, an integer which orders the hosts on the path.</t>

            <t>a and b, 2 integers where b > a.</t>

            <t><H1, H2, ..., Ha, ..., Hb, ...,Hn>, the hosts path
            digest.</t>

            <t><T1, T2, ..., Tm-1, Tm>, a list of times.</t>

            <t><Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n,
            dTk>, a Type-P-Spatial-One-way-Delay-Vector.</t>
          </list></t>

        <section title="Metric Units"></section>

        <t>The value of a Type-P-Segment-One-way-ipdv-prev-Stream is a pair
        of:<list>
            <t>The list of <T1, T2, ..., Tm-1, Tm>;</t>

            <t>A list of pairs of interval of times and delays;</t>
          </list></t>

        <section title="Definition">
          <t>Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ...,
          Hb, ..., Hn>, given the matrix of
          Type-P-Spatial-One-way-Delay-Vector for the packets sent from Src to
          Dst at times <T1, T2, ..., Tm-1, Tm> :<list>
              <t><T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n,
              dT1>,</t>

              <t><T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n,
              dT2>,</t>

              <t>...</t>

              <t><Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n,
              dTm>.</t>
            </list></t>

          <t>We define the Type-P-Segment-One-way-ipdv-prev-Stream as the
          sequence of pair of packet intervals and delay variations
          <(dT2_1.a , dT2.ab - dT1.ab) ,..., (dTk_k-1.a, dTk.ab -
          dTk-1.ab), ..., (dTm_m-1.a, dTm.ab - dTm-1.ab)> such that for
          each Tk:<list style="symbols">
              <t>dTk_k-1.a is either undefined if the delay dTk.a or the delay
              dTk-1.a is undefined, or the interval of time, 'dTk.a -
              dTk-1.a', between the 2 packets at Ha;</t>

              <t>dTk_k-1.ab, is either undefined if one of the delays dTk.b,
              dTk.a, dTk-1.b or dTk-1.a is undefined, or , (dTk.b - dTk.a) -
              (dTk-1.b - dTk-1.a), the delay variation from Ha to Hb between
              the 2 packets sent at time Tk and Tk-1.</t>
            </list></t>
        </section>

        <section title="Discussion">
          <t>This metric belongs to the family of inter packet delay variation
          metrics (IPDV in upper case) which results can be extremely
          sensitive to the inter-packet interval.</t>

          <t>The inter-packet interval of a end-to-end IPDV metric is under
          the control of the ingress point of interest which corresponds
          exactly to the Source of the packet. Unlikely, the inter-packet
          interval of a segment IPDV metric is not under the control the
          ingress point of interest of the measure, Ha. However, the interval
          will vary if there is delay variation between the Source and Ha.
          Therefore, the actual inter-packet interval must be known at Ha in
          order to fully comprehend the delay variation between Ha and Hb.</t>
        </section>
      </section>

      <section anchor="seg_pdv"
               title="A Definition of a sample of ipdv of a segment  using the minimum delay selection function">
        <t>This metric defines a sample of ipdv <xref target="RFC3393"></xref>
        over time between a pair of hosts of a path using the shortest delay
        as the selection function.</t>

        <section title="Metric Name">
          <t>Type-P-Segment-One-way-ipdv-min-Stream</t>
        </section>

        <section title="Metric Parameters"></section>

        <t><list style="symbols">
            <t>Src*, the IP address of the sender.</t>

            <t>Dst*, the IP address of the receiver.</t>

            <t>P*, the specification of the packet type.</t>

            <t>k, an integer which orders the packets sent.</t>

            <t>i, an integer which identifies a packet sent.</t>

            <t>n, an integer which orders the hosts on the path.</t>

            <t>a and b, 2 integers where b > a.</t>

            <t><H1, H2, ..., Ha, ..., Hb, ...,Hn>, the hosts path
            digest.</t>

            <t><T1, T2, ..., Tm-1, Tm>, a list of times.</t>

            <t><Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n,
            dTk>, a Type-P-Spatial-One-way-Delay-Vector.</t>
          </list></t>

        <section title="Metric Units"></section>

        <t>The value of a Type-P-Segment-One-way-ipdv-min-Stream is a pair
        of:<list>
            <t>The list of <T1, T2, ..., Tm-1, Tm>;</t>

            <t>A list of times;</t>
          </list></t>

        <section title="Definition">
          <t>Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ...,
          Hb, ..., Hn>, given the matrix of
          Type-P-Spatial-One-way-Delay-Vector for the packets sent from Src to
          Dst at times <T1, T2, ..., Tm-1, Tm> :<list>
              <t><T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n,
              dT1>,</t>

              <t><T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n,
              dT2>,</t>

              <t>...</t>

              <t><Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n,
              dTm>.</t>
            </list></t>

          <t>We define the Type-P-Segment-One-way-ipdv-min-Stream as the
          sequence of times <dT1.ab - min(dTi.ab) ,..., dTk.ab -
          min(dTi.ab), ..., dTm.ab - min(dTi.ab)> such that:<list>
              <t>min(dTi.ab) is the minimum value of the tuples (dTk.b -
              dTk.a);</t>

              <t>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).</t>
            </list></t>
        </section>

        <section title="Discussion">
          <t>This metric belongs to the family of packet delay variation
          metrics (PDV). PDV distributions are less sensitive to inter-packet
          interval variations than IPDV results.</t>

          <t>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.</t>
        </section>
      </section>
    </section>

    <section title="One-to-group metrics definitions">
      <t>This metric defines metrics to measure the performance between a
      source and a group of receivers.</t>

      <section title="A Definition for One-to-group One-way Delay ">
        <t>This metric defines a metric to measure one-way delay between a
        source and a group of receivers.</t>

        <section title="Metric Name">
          <t>Type-P-One-to-group-One-way-Delay-Vector</t>
        </section>

        <section title="Metric Parameters"></section>

        <t><list style="symbols">
            <t>Src, the IP address of a host acting as the source.</t>

            <t>Recv1,..., RecvN, the IP addresses of the N hosts acting as
            receivers.</t>

            <t>T, a time.</t>

            <t>dT1,...,dTn a list of time.</t>

            <t>P, the specification of the packet type.</t>

            <t>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.</t>
          </list></t>

        <section title="Metric Units">
          <t>The value of a Type-P-One-to-group-One-way-Delay-Vector is a set
          of Type-P-One-way-Delay singletons <xref
          target="RFC2679"></xref>.</t>
        </section>

        <section title="Definition">
          <t>Given a Type P packet sent by the source Src at Time T, given the
          N hosts { Recv1,...,RecvN } which receive the packet at the time {
          T+dT1,...,T+dTn }, a Type-P-One-to-group-One-way-Delay-Vector is
          defined as the set of the Type-P-One-way-Delay singleton between Src
          and each receiver with value of { dT1, dT2,...,dTn }.</t>
        </section>
      </section>

      <section title="A Definition for One-to-group One-way Packet Loss">
        <section title="Metric Name">
          <t>Type-P-One-to-group-One-way-Packet-Loss-Vector</t>
        </section>

        <section title="Metric Parameters">
          <t><list style="symbols">
              <t>Src, the IP address of a host acting as the source.</t>

              <t>Recv1,..., RecvN, the IP addresses of the N hosts acting as
              receivers.</t>

              <t>T, a time.</t>

              <t>T1,...,Tn a list of time.</t>

              <t>P, the specification of the packet type.</t>

              <t>Gr, the receiving group identifier.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t>The value of a Type-P-One-to-group-One-way-Packet-Loss-Vector is
          a set of Type-P-One-way-Packet-Loss singletons <xref
          target="RFC2680"></xref>.</t>
        </section>

        <section title="Definition">
          <t>Given a Type P packet sent by the source Src at T and the N
          hosts, Recv1,...,RecvN, which should receive the packet at
          T1,...,Tn, a Type-P-One-to-group-One-way-Packet-Loss-Vector is
          defined as a set of the Type-P-One-way-Packet-Loss singleton between
          Src and each of the receivers {<T1,0|1>,<T2,0|1>,...,
          <Tn,0|1>}.</t>
        </section>
      </section>

      <section title="A Definition for One-to-group One-way Ipdv">
        <section title="Metric Name">
          <t>Type-P-One-to-group-One-way-ipdv-Vector</t>
        </section>

        <section title="Metric Parameters">
          <t><list style="symbols">
              <t>Src, the IP address of a host acting as the source.</t>

              <t>Recv1,..., RecvN, the IP addresses of the N hosts acting as
              receivers.</t>

              <t>T1, a time.</t>

              <t>T2, a time.</t>

              <t>ddT1, ...,ddTn, a list of time.</t>

              <t>P, the specification of the packet type.</t>

              <t>F, a selection function defining unambiguously the two
              packets from the stream selected for the metric.</t>

              <t>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.</t>
            </list></t>
        </section>

        <section title="Metric Units">
          <t>The value of a Type-P-One-to-group-One-way-ipdv-Vector is a set
          of Type-P-One-way-ipdv singletons <xref
          target="RFC3393"></xref>.</t>
        </section>

        <section title="Definition">
          <t>Given a Type P packet stream,
          Type-P-One-to-group-One-way-ipdv-Vector is defined for two packets
          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-One-way-Delay-Vector from Src to {
          Recv1,..., RecvN } at time T1 and the value of the
          Type-P-One-to-group-One-way-Delay-Vector from Src to {
          Recv1,...,RecvN } at time T2. T1 is the wire-time at which Src sent
          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-One-way-Delay-Vector metric.</t>

          <t>Therefore, for a set of real number
          {ddT1,...,ddTn},Type-P-One-to-group-One-way-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}.</t>
        </section>
      </section>
    </section>

    <section anchor="o2gsample" title="One-to-Group Sample Statistics">
      <t></t>

      <t>The defined one-to-group metrics above can all be directly achieved
      from the relevant unicast one-way metrics. They collect all unicast
      measurement results of one-way metrics together in one profile and sort
      them by receivers and packets in a receiving group. They provide
      sufficient information regarding the network performance in terms of
      each receiver and guide engineers to identify potential problem happened
      on each branch of a multicast routing tree. However, these metrics
      cannot be directly used to conveniently present the performance in terms
      of a group and neither to identify the relative performance
      situation.</t>

      <t>From the performance point of view, the multiparty communication
      services not only require the absolute performance support but also the
      relative performance. The 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 the online gaming. A very light difference in
      delay might result in failure in the game. We have to use multicast
      specific statistic metrics to define exactly how small the relative
      delay the online gaming requires. 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.</t>

      <t>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 [RFC2679]. 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 <xref
      target="FigMatrixConcept"></xref>. 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.</t>

      <t></t>

      <t><figure anchor="FigMatrixConcept" title="Matrix M (n*m)">
          <artwork align="center"><![CDATA[
   Receivers
    Space
      ^
    1 |    / R1dT1   R1dT2     R1dT3 ... R3dTk \
      |   |                                     |
    2 |   |  R2dT1   R2dT2     R2dT3 ... R3dTk  |
      |   |                                     |
    3 |   |  R3dT1   R3dT2     R3dT3 ... R3dTk  |  
    . |   |                                     |
    . |   |                                     |
    . |   |                                     |
    n |    \ RndT1   RndT2     RndT3 ... RndTk /
      +--------------------------------------------> time
     T0]]></artwork>
        </figure></t>

      <t>In Matrix M, each element is a one-way delay singleton. Each column
      is a delay vector contains the One-way delays of the same packet
      observed at M 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.</t>

      <t>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 provides which dimension they are interested in.
      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 to know 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 other.</t>

      <t>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
      lower transmission rate can have the time interval longer and ones with
      higher transmission rate can have the time interval shorter. However,
      this is out of the scope of this memo.</t>

      <t>Moreover, after knowing the statistics over the time dimension, one
      might want to know how this statistics 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 good the service has been delivered to a group of
      users during a sampling interval in terms of delay. It needs twice
      calculation to have this statistic over both time and space dimensions.
      We name this kind of statistics 2-level statistics to distinct with
      those 1-level statistics calculated over either space or time dimension.
      It can be easily prove that no matter over which dimension a 2-level
      statistic is calculated first, the results are the same. I.e. 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 two results will be exactly
      the same. Therefore, when define a 2-level statistic, there is no need
      to specify in which procedure the calculation should follow.</t>

      <t>Comment: The above statement depends on whether the order of
      operations has any affect on the outcome.</t>

      <t>Many statistics can be defined for the proposed one-to-group metrics
      over either the space dimension or 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.</t>

      <section title="Discussion on the Impact of packet loss on statistics">
        <t>The packet loss does have effects on one-way metrics and their
        statistics. For example, the lost packet can result 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 so 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 complex of building a Matrix, which is needed for
        calculation of the statistics proposed in this memo.</t>

        <t>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 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 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
        can not calculate the statistics. In an extreme situation, no single
        packet arrives all users in the measurement and the Matrix will be
        empty. 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… R1DM } 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.</t>

        <t>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,
        User1 calculates the Type-P-Finite-One-way-Delay-Mean R1DM as shown in
        Figure. 8 without any packet loss and User2 calculates the R2DM with
        N-2 packet loss. The R1DM and R2DM should not be treated with equal
        weight because R2DM was calculated only based on 2 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.</t>

        <t></t>
      </section>

      <section title="General Metric Parameters">
        <t><list style="symbols">
            <t>Src, the IP address of a host;</t>

            <t>G, the receiving group identifier;</t>

            <t>N, the number of Receivers (Recv1, Recv2, ... RecvN);</t>

            <t>T, a time (start of test interval);</t>

            <t>Tf, a time (end of test interval);</t>

            <t>K, the number of packets sent from the source during the test
            interval;</t>

            <t>J[n], the number of packets received at a particular Receiver,
            n, where 1<=n<=N;</t>

            <t>lambda, a rate in reciprocal seconds (for Poisson Streams);</t>

            <t>incT, the nominal duration of inter-packet interval, first bit
            to first bit (for Periodic Streams);</t>

            <t>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);</t>

            <t>TstampSrc, the wire time of the packet as measured at MP(Src)
            (the Source Measurement Point);</t>

            <t>TstampRecv, the wire time of the packet as measured at
            MP(Recv), assigned to packets that arrive within a "reasonable"
            time;</t>

            <t>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;</t>

            <t>dT, shorthand notation for a one-way delay singleton value;</t>

            <t>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;</t>

            <t>DV, shorthand notation for a one-way delay variation singleton
            value;</t>
          </list></t>
      </section>

      <section title="One-to-Group one-way Delay Statistics">
        <t>This section defines the overall one-way delay statistics for a
        receiver and for an entire group as illustrated by the matrix
        below.</t>

        <t><figure anchor="FigGMD" title="One-to-Group Mean Delay">
            <artwork align="center"><![CDATA[  Recv    /----------- Sample -------------\   Stats      Group Stat

   1      R1dT1   R1dT2     R1dT3 ... R1dTk    R1DM  \
                                                      |
   2      R2dT1   R2dT2     R2dT3 ... R2dTk    R2DM   |
                                                      |   
   3      R3dT1   R3dT2     R3dT3 ... R3dTk    R2DM    > Group delay
   .                                                  |
   .                                                  |
   .                                                  |
   n      RndT1   RndT2     RndT3 ... RndTk    RnDM  /    
                                         
                                             Receiver-n
                                               delay  ]]></artwork>
          </figure></t>

        <t>Statistics are computed on the finite One-way delays of the matrix
        above.</t>

        <t>All One-to-group delay statistics are expressed in seconds with
        sufficient resolution to convey 3 significant digits.</t>

        <section title="Type-P-One-to-Group-Receiver-n-Mean-Delay">
          <t>This section defines Type-P-One-to-Group-Receiver-n-Mean-Delay
          the Delay Mean at each Receiver N, also named RnDM.</t>

          <t>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 <xref target="RFC2679"></xref>. 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.</t>

          <figure anchor="RnDM"
                  title="Type-P-One-to-Group-Receiver-Mean-Delay ">
            <preamble></preamble>

            <artwork align="center"><![CDATA[                  J[n]                                     
                  ---                                      
             1    \                                      
  RnDM =    --- *  >  TstampRecv[i] - TstampSrc[i]         
            J[n]  /                                      
                  ---                                      
                  i = 1                                                         ]]></artwork>

            <postamble></postamble>
          </figure>

          <t>where all packets i= 1 through J[n] have finite singleton
          delays.</t>
        </section>

        <section title="Type-P-One-to-Group-Mean-Delay">
          <t>This section defines Type-P-One-to-Group-Mean-Delay, the Mean
          One-way delay calculated over the entire Group, also named GMD.</t>

          <figure anchor="GMD" title="Type-P-One-to-Group-Mean-Delay">
            <preamble></preamble>

            <artwork align="center"><![CDATA[               N
              ---
         1    \
  GMD =  - *   >   RnDM
         N    /
              ---
              n = 1
            ]]></artwork>

            <postamble></postamble>
          </figure>

          <t>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.</t>
        </section>

        <section title="Type-P-One-to-Group-Range-Mean-Delay ">
          <t>This section defines a metric for the range of mean delays over
          all N receivers in the Group, (R1DM, R2DM,...RnDM).</t>

          <t>Type-P-One-to-Group-Range-Mean-Delay = GRMD = max(RnDM) -
          min(RnDM)</t>
        </section>

        <section title="Type-P-One-to-Group-Max-Mean-Delay">
          <t>This section defines a metric for the maximum of mean delays over
          all N receivers in the Group, (R1DM, R2DM,...RnDM).</t>

          <t>Type-P-One-to-Group-Max-Mean-Delay = GMMD = max(RnDM)</t>
        </section>
      </section>

      <section title="One-to-Group one-way Loss Statistics">
        <t>This section defines the overall one-way loss statistics for a
        receiver and for an entire group as illustrated by the matrix
        below.</t>

        <t><figure anchor="FigGLR" title="One-to-Group Loss Ratio">
            <preamble></preamble>

            <artwork align="center"><![CDATA[ Recv    /----------- Sample ----------\   Stats     Group Stat

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

                                        Receiver-n
                                        Loss Ratio]]></artwork>

            <postamble></postamble>
          </figure></t>

        <t>Statistics are computed on the sample of Type-P-One-way-Packet-Loss
        <xref target="RFC2680"></xref> of the matrix above.</t>

        <t>All loss ratios are expressed in units of packets lost to total
        packets sent.</t>

        <section title="Type-P-One-to-Group-Receiver-n-Loss-Ratio">
          <t>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 <xref
          target="RFC2680"></xref>. 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<figure anchor="RnLR"
              title="Type-P-One-to-Group-Receiver-n-Loss-Ratio">
              <preamble></preamble>

              <artwork align="center"><![CDATA[                   K
                  ---
             1    \
     RnLR =  - *   >   RnLk
             K    /
                  ---
                 k = 1        ]]></artwork>

              <postamble></postamble>
            </figure></t>
        </section>

        <section title="Type-P-One-to-Group-Receiver-n-Comp-Loss-Ratio">
          <t>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.</t>

          <t>The Comparative Loss Ratio, also named, RnCLR, is defined
          as<figure anchor="RnCLR"
              title="Type-P-One-to-Group-Receiver-n-Comp-Loss-Ratio">
              <preamble></preamble>

              <artwork align="center"><![CDATA[                          K
                         ---
                         \
                          >   Ln(k)
                         /
                         ---
                         k=1
    RnCLR =  -----------------------------
                      /    K         \
                      |   ---        |
                      |   \          |
              K - Min |    >   Ln(k) | 
                      |   /          |
                      |   ---        |
                      \   k=1        / N  ]]></artwork>

              <postamble></postamble>
            </figure></t>
        </section>

        <section title="Type-P-One-to-Group-Loss-Ratio">
          <t>Type-P-One-to-Group-Loss-Ratio, the overall Group loss ratio,
          also named GLR, is defined as</t>

          <t><figure anchor="GLR" title="Type-P-One-to-Group-Loss-Ratio">
              <preamble></preamble>

              <artwork align="center"><![CDATA[                 K,N
                 ---
           1     \
    GLR = --- *   >   L(k,n)
          K*N    /
                 ---
                k,n = 1
]]></artwork>

              <postamble></postamble>
            </figure></t>
        </section>

        <section title="Type-P-One-to-Group-Range-Loss-Ratio">
          <t>The One-to-Group Loss Ratio Range is defined as:</t>

          <t>Type-P-One-to-Group-Range-Loss-Ratio = max(RnLR) - min(RnLR)</t>

          <t>It is most effective to indicate the range by giving both the max
          and minimum loss ratios for the Group, rather than only reporting
          the difference between them.</t>
        </section>
      </section>

      <t></t>

      <section title="One-to-Group one-way Delay Variation Statistics">
        <t>This section defines one-way delay variation (DV) statistics for an
        entire group as illustrated by the matrix below.</t>

        <t><figure anchor="FigRnDDT"
            title="One-to-Group Delay Variation Matrix (DVMa)">
            <artwork align="center"><![CDATA[ Recv    /------------- Sample --------------\   Stats       

  1      R1ddT1   R1ddT2     R1ddT3 ... R1ddTk   R1DV  \   
                                                        |
  2      R2ddT1   R2ddT2     R2ddT3 ... R2ddTk   R2DV   |  
                                                        | 
  3      R3ddT1   R3ddT2     R3ddT3 ... R3ddTk   R3DV    > Group Stat
  .                                                     |  
  .                                                     |  
  .                                                     |  
  n      RnddT1   RnddT2     RnddT3 ... RnddTk   RnDV  /              
                          ]]></artwork>
          </figure></t>

        <t>Statistics are computed on the sample of
        Type-P-One-way-Delay-Variation singletons of the group delay variation
        matrix above where RnddTk is the Type-P-One-way-Delay-Variation
        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.</t>

        <t>All One-to-group delay variation statistics are expressed in
        seconds with sufficient resolution to convey 3 significant digits.</t>

        <section title="Type-P-One-to-Group-Delay-Variation-Range">
          <t>This section defines a metric for the range of delays variation
          over all N receivers in the Group.</t>

          <t>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.</t>

          <t>Type-P-One-to-Group-Delay-Variation-Range = GDVR =</t>

          <t>= max(RnDV) – min(RnDV) for all n receivers</t>

          <t>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.</t>
        </section>
      </section>
    </section>

    <section title="Measurement Methods: Scalability and Reporting">
      <t>Virtually all the guidance on measurement processes supplied by the
      earlier IPPM RFCs (such as <xref target="RFC2679"></xref> and <xref
      target="RFC2680"></xref>) 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.</t>

      <t>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.</t>

      <t>In recognition of the likely need to minimize 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 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).</t>

      <section title="Computation methods">
        <t></t>

        <t>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 one is a
        centralized statistic calculation method and the latter one 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 huge number of the points of interest.
        It can lead to a scalability issue at the reference point by over load
        the network resources. The distributed calculation method can save
        much more bandwidth and release the pressure of the scalability issue
        at the reference point side. However, it can result in the lack of
        information because not all measured singletons are obtained for
        building up the group matrix. The performance over time can be hidden
        from the analysis. For example, the loss pattern can be missed by
        simply accepting the loss ratio as well as the delay pattern. This
        tradeoff between the bandwidth consuming and the information acquiring
        has to be taken into account when design the measurement campaign to
        optimize the measurement results delivery. The possible solution could
        be to transit the statistic parameters to the reference point first to
        obtain the general information of the group performance. If the detail
        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.</t>
      </section>

      <section title="Measurement">
        <t>To prevent any bias in the result, the configuration of a
        one-to-many measure must take in consideration that implicitly more
        packets will to be routed than send and selects a test packets rate
        that will not impact the network performance.</t>
      </section>

      <section title="Effect of Time and Space Aggregation Order on Stats">
        <t>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 managed remotely and not co-located.</t>

        <t>multimetrics samples represented a matrix as illustrated below</t>

        <t><figure anchor="FigSpaceTimeOrder"
            title="Impact of space aggregation on multimetrics Stat">
            <artwork align="center"><![CDATA[ Point of                                       
 interest
   1      R1S1   R1S1     R1S1 ... R1Sk    \
                                            |
   2      R2S1   R2S2     R2S3 ... R2Sk     |
                                            |
   3      R3S1   R3S2     R3S3 ... R3Sk      >  sample over space 
   .                                        |
   .                                        |
   .                                        |
   n      RnS1   RnS2     RnS3 ... RnSk    /

          S1M    S2M      S3M  ... SnM     Stats over space

          \-------------  ------------/  
                        \/
            Stat over space and time
]]></artwork>
          </figure></t>

        <t>2 methods are available to compute statistics on the resulting
        matrix: <list style="symbols">
            <t>metric is computed over time and then over space;</t>

            <t>metric is computed over space and then over time.</t>
          </list></t>

        <t>They differ only by the order of the time and of the space
        aggregation. View as a matrix this order is neutral as does not impact
        the result, but the impact on a measurement deployment is
        critical.</t>

        <t>In both cases the volume of data to report is proportional to the
        number of probes. But there is a major difference between these 2
        methods: <list>
            <t>method2: In space and time aggregation mode the volume of data
            to collect is proportional to the number of test packets received;
            Each received packet RiSi triggers out a block of data that must
            be reported to a common place for computing the stat over
            space;</t>

            <t>method1: In time and space aggregation mode the volume of data
            to collect is proportional to the period of aggregation, so it
            does not depend on the number of packet received;</t>
          </list></t>

        <t>Method 2 property has severe drawbacks in terms of security and
        dimensioning: <list>
            <t>The increasing of the rate of the test packets may result in a
            sort of DoS toward the computation points;</t>

            <t>The dimensioning of a measurement system is quite impossible to
            validate.</t>
          </list></t>

        <t>The time aggregation interval provides the reporting side with a
        control of various collecting aspects such as bandwidth and
        computation and storage capacities. So this draft defines metrics
        based on method 1.</t>

        <t>Note: In some specific cases one may need sample of singletons over
        space. To address this need it is suggested firstly to limit the
        number of test and the number of test packets per seconds. Then
        reducing the size of the sample over time to one packet give sample of
        singleton over space..</t>

        <section title="Impact on spatial statistics">
          <t>2 methods are available to compute spatial statistics: <list
              style="symbols">
              <t>method 1: spatial segment metrics and statistics are
              preferably computed over time by each points of interest;</t>

              <t>method 2: Vectors metrics are intrinsically instantaneous
              space metrics which must be reported using method2 whenever
              instantaneous metrics information is needed.</t>
            </list></t>
        </section>

        <section title="Impact on one-to-group statistics">
          <t>2 methods are available to compute group statistics: <list
              style="symbols">
              <t>method1: <xref target="FigGMD"></xref> and<xref
              target="FigGLR"> </xref> illustrate the method chosen: the
              one-to-one statistic is computed per interval of time before the
              computation of the mean over the group of receivers;</t>

              <t>method2: <xref target="FigSpaceTimeOrder"></xref> presents
              the second one, metric is computed over space and then over
              time.</t>
            </list></t>
        </section>
      </section>
    </section>

    <section title="Manageability Considerations">
      <t>Usually IPPM WG documents defines each metric reporting within its
      definition. This document defines the reporting of all the metrics
      introduced in a single section to provide consistent information, to
      avoid repetitions and to conform to IESG recommendation of gathering
      manageability considerations in a dedicated section.</t>

      <t>Information models of spatial metrics and of one-to-group metrics are
      similar excepted that points of interests of spatial vectors must be
      ordered.</t>

      <t>The complexity of the reporting relies on the number of points of
      interests.</t>

      <section title="Reporting spatial metric">
        <t>The reporting of spatial metrics shares a lot of aspects with
        RFC2679-80. 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
        shall be reported.</t>

        <section title="Path">
          <t>End-to-end metrics can't determine the path of the measure
          despite IPPM RFCs recommend it to be reported (See Section 3.8.4 of
          <xref target="RFC2679"></xref>). Spatial metrics vectors provide
          this path. The report of a spatial vector must include the points of
          interests involved: the sub set of the hosts of the path
          participating to the instantaneous measure.</t>
        </section>

        <section title="Host order">
          <t>A spatial vector must order the points of interest according to
          their order in the path. It is highly suggested to use the TTL in
          IPv4, the Hop Limit in IPv6 or the corresponding information in
          MPLS.</t>

          <t>The report of a spatial vector must include the ordered list of
          the hosts involved in the instantaneous measure.</t>
        </section>

        <section title="Timestamping bias">
          <t>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 3 milliseconds
          then the minimal uncertainty reported be 3 ms if the internal delay
          is unknown at the time of the timestamping.</t>

          <t>The report of a spatial vector must include the uncertainty of
          the timestamping compared to wire time.</t>
        </section>

        <section title="Reporting spatial One-way Delay">
          <t>The reporting includes information to report for one-way-delay as
          the Section 3.6 of <xref target="RFC2679"></xref>. The same apply
          for packet loss and ipdv.</t>
        </section>
      </section>

      <section title="Reporting One-to-group metric">
        <t>All reporting rules described in RFC2679-80 apply to the
        corresponding One-to-group metrics. Following are specific parameters
        that should be reported.</t>

        <section title="Path">
          <t>As suggested by the RFC2679-80, the path traversed by the packet
          SHOULD be reported, if possible. For One-to-group metrics, there is
          a path tree SHOULD be reported rather than A path. This is even more
          impractical. If, by anyway, partial information is available to
          report, it might not be as valuable as it is in the one-to-one case
          because the incomplete path might be difficult to identify its
          position in the path tree. For example, how many points of interest
          are reached by the packet traveled through this incomplete path?</t>
        </section>

        <section title="Group size">
          <t>The group size should be reported as one of the critical
          management parameters. Unlike the spatial metrics, there is no need
          of order of points of interests.</t>
        </section>

        <section title="Timestamping bias">
          <t>It is the same as described in section 9.1.3.</t>
        </section>

        <section title="Reporting One-to-group One-way Delay">
          <t>It is the same as described in section 9.1.4.</t>
        </section>

        <section title="Measurement method">
          <t>As explained in section 8, the measurement method will have
          impact on the analysis of the measurement result. Therefore, it
          should be reported.</t>
        </section>
      </section>

      <section title="Metric identification">
        <t>IANA assigns each metric defined by the IPPM WG with a unique
        identifier as per <xref target="RFC4148"></xref> in the
        IANA-IPPM-METRICS-REGISTRY-MIB.</t>
      </section>

      <section title="Information model">
        <t>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.</t>

        <t>The information model is build with pieces of information
        introduced and explained in one-way delay definitions <xref
        target="RFC2679"></xref>, in packet loss definitions <xref
        target="RFC2680"> </xref> and in IPDV definitions of <xref
        target="RFC3393"></xref> and <xref target="RFC3432"></xref>. It
        includes not only information given by "Reporting the metric" sections
        but by sections "Methodology" and "Errors and Uncertainties"
        sections.</t>

        <t>Following are the elements of information taken from end-to-end
        definitions referred in this memo and from spatial and multicast
        metrics it defines:</t>

        <t><list style="symbols">
            <t>Packet_type, The Type-P of test packets (Type-P);</t>

            <t>Packet_length, a packet length in bits (L);</t>

            <t>Src_host, the IP address of the sender;</t>

            <t>Dst_host, the IP address of the receiver;</t>

            <t>Hosts_serie: <H1, H2,..., Hn>, a list of points of
            interest;</t>

            <t>Loss_threshold: The threshold of infinite delay;</t>

            <t>Systematic_error: constant delay between wire time and
            timestamping;</t>

            <t>Calibration_error: maximal uncertainty;</t>

            <t>Src_time, the sending time for a measured packet;</t>

            <t>Dst_time, the receiving time for a measured packet;</t>

            <t>Result_status : an indicator of usability of a result 'Resource
            exhaustion' 'infinite', 'lost';</t>

            <t>Delays_serie: <dT1,..., dTn> a list of delays;</t>

            <t>Losses_serie: <B1, B2, ..., Bi, ..., Bn>, a list of
            Boolean values (spatial) or a set of Boolean values
            (one-to-group);</t>

            <t>Result_status_serie: a list of results status;</t>

            <t>dT: a delay;</t>

            <t>Singleton_number: a number of singletons;</t>

            <t>Observation_duration: An observation duration;</t>

            <t>metric_identifier.</t>
          </list></t>

        <t>Following is the information of each vector that should be
        available to compute samples:</t>

        <t><list style="symbols">
            <t>Packet_type;</t>

            <t>Packet_length;</t>

            <t>Src_host, the sender of the packet;</t>

            <t>Dst_host, the receiver of the packet, apply only for spatial
            vectors;</t>

            <t>Hosts_serie: not ordered for one-to-group;</t>

            <t>Src_time, the sending time for the measured packet;</t>

            <t>dT, the end-to-end one-way delay for the measured packet, apply
            only for spatial vectors;</t>

            <t>Delays_serie: apply only for delays and ipdv vector, not
            ordered for one-to-group;</t>

            <t>Losses_serie: apply only for packets loss vector, not ordered
            for one-to-group;</t>

            <t>Result_status_serie;</t>

            <t>Observation_duration: the difference between the time of the
            last singleton and the time of the first singleton.</t>

            <t>Following is the context information (measure, points of
            interests) that should be available to compute samples :<list
                style="symbols">
                <t>Loss threshold;</t>

                <t>Systematic error: constant delay between wire time and
                timestamping;</t>

                <t>Calibration error: maximal uncertainty;</t>
              </list></t>
          </list></t>

        <t>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.
        Following is the information that should be available for each sample
        to compute statistics:</t>

        <t><list style="symbols">
            <t>Packet_type;</t>

            <t>Packet_length;</t>

            <t>Src_host, the sender of the packet;</t>

            <t>Dst_host, the receiver of the packet;</t>

            <t>Start_time, the sending time of the first packet;</t>

            <t>Delays_serie: apply only for delays and ipdv samples;</t>

            <t>Losses_serie: apply only for packets loss samples;</t>

            <t>Result_status_serie;</t>

            <t>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.</t>

            <t>Following is the context information (measure, points of
            interests) that should be available to compute statistics :<list
                style="symbols">
                <t>Loss threshold;</t>

                <t>Systematic error: constant delay between wire time and
                timestamping;</t>

                <t>Calibration error: maximal uncertainty;</t>
              </list></t>
          </list></t>

        <t>Following is the information of each statistic that should be
        reported:</t>

        <t><list style="symbols">
            <t>Result;</t>

            <t>Start_time;</t>

            <t>Duration;</t>

            <t>Result_status;</t>

            <t>Singleton_number, the number of singletons the statistic is
            computed on;</t>
          </list></t>
      </section>
    </section>

    <section title="Security Considerations">
      <t>Spatial and one-to-group metrics are defined on the top of end-to-end
      metrics. Security considerations discussed in One-way delay metrics
      definitions of <xref target="RFC2679"></xref> , in packet loss metrics
      definitions of <xref target="RFC2680"></xref> and in IPDV metrics
      definitions of<xref target="RFC3393"></xref> and <xref
      target="RFC3432"></xref> apply to metrics defined in this memo.</t>

      <section title="Spatial metrics">
        <t>Malicious generation of packets with spoofing addresses may corrupt
        the results without any possibility to detect the spoofing.</t>

        <t>Malicious generation of packets which match systematically the hash
        function used to detect the packets may lead to a DoS attack toward
        the point of reference.</t>
      </section>

      <section title="one-to-group metric">
        <t>Reporting of measurement results from a huge number of probes may
        overload reference point ressources (network, network interfaces,
        computation capacities ...).</t>

        <t>The configuration of a measurement must take in consideration that
        implicitly more packets will to be routed than send and selects a test
        packets rate accordingly. Collecting statistics from a huge number of
        probes may overload any combination of the network where the
        measurement controller is attached to, measurement controller network
        interfaces and measurement controller computation capacities.</t>

        <t>One-to-group metrics measurement 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 deny of service
        attacks.</t>
      </section>

      <t></t>
    </section>

    <section title="Acknowledgments">
      <t>Lei would like to acknowledge Prof. Zhili Sun from CCSR, University
      of Surrey, for his instruction and helpful comments on this work.</t>
    </section>

    <section anchor="IANA" title="IANA Considerations">
      <t>Metrics defined in this memo Metrics defined in this memo are
      designed to be registered in the IANA IPPM METRICS REGISTRY as described
      in initial version of the registry <xref target="RFC4148"></xref> :</t>

      <t>IANA is asked to register the following metrics in the
      IANA-IPPM-METRICS-REGISTRY-MIB :</t>

      <t>ietfSpatialOneWayDelayVector OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Spatial-One-way-Delay-Vector"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 4.1."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfSpatialPacketLossVector OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Spatial-Packet-Loss-Vector"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 4.2."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t></t>

      <t>ietfSpatialOneWayIpdvVector OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Spatial-One-way-ipdv-Vector"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 4.3."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfSegmentOneWayDelayStream OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Segment-One-way-Delay-Stream"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 5.1."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfSegmentPacketLossStream OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Segment-Packet-Loss-Stream"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 5.2."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfSegmentOneWayIpdvPrevStream OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Segment-One-way-ipdv-prev-Stream"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 5.3."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfSegmentOneWayIpdvMinStream OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-Segment-One-way-ipdv-min-Stream"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 5.4."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>-- One-to-group metrics</t>

      <t>ietfOneToGroupOneWayDelayVector OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-group-One-way-Delay-Vector"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 6.1."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfOneToGroupOneWayPktLossVector OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-One-way-Packet-Loss-Vector"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 6.2."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfOneToGroupOneWayIpdvVector OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-One-way-ipdv-Vector"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 6.3."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>-- One to group statistics</t>

      <t>--</t>

      <t></t>

      <t>ietfOnetoGroupReceiverNMeanDelay OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Receiver-n-Mean-Delay"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.3.1."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfOneToGroupMeanDelay OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Mean-Delay"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.3.2."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t></t>

      <t>ietfOneToGroupRangeMeanDelay OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Range-Mean-Delay"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.3.3."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t></t>

      <t>ietfOneToGroupMaxMeanDelay OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Max-Mean-Delay"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.3.4."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfOneToGroupReceiverNLossRatio OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Receiver-n-Loss-Ratio"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.4.1."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list>--</t>

      <t>ietfOneToGroupReceiverNCompLossRatio OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Receiver-n-Comp-Loss-Ratio"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.4.2."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfOneToGroupLossRatio OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Loss-Ratio"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.4.3."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list>--</t>

      <t>ietfOneToGroupRangeLossRatio OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Range-Loss-Ratio"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.4.4."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>ietfOneToGroupRangeDelayVariation OBJECT-IDENTITY<list>
          <t>STATUS current</t>

          <t>DESCRIPTION<list>
              <t>"Type-P-One-to-Group-Range-Delay-Variation"</t>
            </list></t>

          <t>REFERENCE<list>
              <t>"Reference "RFCyyyy, section 7.5.1."</t>

              <t>-- RFC Ed.: replace yyyy with actual RFC number & remove
              this note</t>
            </list> := { ianaIppmMetrics nn } -- IANA assigns nn</t>
        </list></t>

      <t>--</t>
    </section>
  </middle>

  <back>
    <references title="Normative References">
      <?rfc include="reference.RFC.2119"?>

      <?rfc include="reference.RFC.2679" ?>

      <?rfc include="reference.RFC.2680" ?>

      <?rfc include="reference.RFC.3393" ?>

      <?rfc include="reference.RFC.4148" ?>
    </references>

    <references title="Informative References">
      <?rfc include="reference.RFC.2330" ?>

      <?rfc include="reference.RFC.3432" ?>
    </references>
  </back>
</rfc>

PAFTECH AB 2003-20262026-04-24 16:27:29