Network Working Group                                         E. Stephan
Internet-Draft                                            France Telecom
Intended status: Standards Track                                L. Liang
Expires: December 28, 2008 April 3, 2009                              University of Surrey
                                                               A. Morton
                                                               AT&T Labs
                                                           June 26,
                                                      September 30, 2008

        IP Performance Metrics (IPPM) for spatial and multicast
                    draft-ietf-ippm-multimetrics-07
                    draft-ietf-ippm-multimetrics-08

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Abstract

   The IETF has standardized 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).

Requirements Language

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

Table of Contents

   1.  Introduction and Scope . . . . . . . . . . . . . . . . . . . . . . . . .  4  3
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  6
     2.1.  Path Digest Hosts  . .  3
   3.  Brief Metric Descriptions  . . . . . . . . . . . . . . . . . .  6
     2.2.  Multiparty metric  7
   4.  Motivations  . . . . . . . . . . . . . . . . . . . .  6
     2.3.  Spatial metric . . . . .  9
   5.  Spatial vector metrics definitions . . . . . . . . . . . . . . 11
   6.  Spatial Segment Metrics Definitions  . . .  7
     2.4.  One-to-group metric . . . . . . . . . . 18
   7.  One-to-group metrics definitions . . . . . . . . .  7
     2.5.  Points of interest . . . . . . 23
   8.  One-to-group Sample Statistics . . . . . . . . . . . . . .  7
     2.6.  Reference point . . 26
   9.  Measurement Methods: Scalability and Reporting . . . . . . . . 36
   10. Manageability Considerations . . . . . . . . . . .  8
     2.7.  Vector . . . . . . 39
   11. Security Considerations  . . . . . . . . . . . . . . . . . . . 44
   12. Acknowledgments  .  8
     2.8.  Matrix . . . . . . . . . . . . . . . . . . . . . . 45
   13. IANA Considerations  . . . .  9
   3.  Motivations . . . . . . . . . . . . . . . . . 45
   14. References . . . . . . . .  9
     3.1.  Motivations for spatial metrics . . . . . . . . . . . . .  9
     3.2.  Motivations for One-to-group metrics . . . . . 49
     14.1.  Normative References  . . . . . . 10
     3.3.  Discussion on Group-to-one and Group-to-group metrics . . 11
   4.  Spatial vectors metrics definitions . . . . . . . . . . 49
     14.2.  Informative References  . . . 11
     4.1.  A Definition for Spatial One-way Delay Vector . . . . . . 12
     4.2.  A Definition for Spatial One-way Packet Loss Vector . . . 13
     4.3.  A Definition for Spatial One-way Ipdv Vector . . . . . 50
   Authors' Addresses . . 14
     4.4.  Spatial Methodology . . . . . . . . . . . . . . . . . . . 16
   5.  Spatial Segments metrics definitions . . . 50
   Intellectual Property and Copyright Statements . . . . . . . . . . 17
     5.1.  A Definition 51

1.  Introduction and Scope

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

   The purpose of the path  . . . . . . . . . . . . . . . . . . . . . . . 18
     5.2.  A Definition of a sample memo is to define metrics to fulfill the new
   requirements of Packet Loss measurement involving multiple measurement points.
   Spatial metrics measure the performance of a each segment
           of along a path.
   One-to-group metrics measure the path  . . . . . . . . . . . . . . . . . . . . . . . 19
     5.3.  A Definition of performance for a sample group of ipdv users.
   These metrics are derived from one-way end-to-end metrics, all of a segment using
   which follow the previous packet selection function . . . . . . . . . . 20
     5.4.  A Definition IPPM framework [RFC2330].

   This memo is organized as follows: Section 2 introduces new terms
   that extend the original IPPM framework [RFC2330].  Section 3
   motivates each metric category and briefly introduces the new
   metrics.  Sections 4 through 7 develop each category of a sample metrics with
   definitions and statistics.  Then the memo discusses the impact of ipdv
   the measurement methods on the scaleability and proposes an
   information model for reporting the measurements.  Finally, the memo
   discusses security aspects related to measurement and registers the
   metrics in the IANA IP Performance Metrics Registry [RFC4148].

   The scope of a segment this memo is limited to metrics using a single source
   packet or stream, and observations of corresponding packets along the
   path (spatial), at one or more destinations (one-to-group), or both.
   Note that all the minimum delay selection function . . . . . . . . . . . 22
   6.  One-to-group metrics definitions . . . . . . . . . . . . . . . 23
     6.1.  A Definition for One-to-group One-way Delay  . . . . . . . 23
     6.2.  A Definition for One-to-group One-way Packet Loss  . . . . 24
     6.3.  A Definition for One-to-group One-way Ipdv . . . . . . . . 25
   7.  One-to-Group Sample Statistics . . . . . . . . . . . . . . . . 26
     7.1.  Discussion on the Impact of packet loss on statistics  . . 28
     7.2.  General Metric Parameters  . . . . . . . . . . . . . . . . 29
     7.3.  One-to-Group one-way Delay Statistics  . . . . . . . . . . 30
     7.4.  One-to-Group one-way Loss Statistics . . . . . . . . . . . 32
     7.5.  One-to-Group one-way Delay Variation Statistics  . . . . . 34
   8.  Measurement Methods: Scalability and Reporting . . . . . . . . 35
     8.1.  Computation methods  . . . . . . . . . . . . . . . . . . . 36
     8.2.  Measurement  . . . . . . . . . . . . . . . . . . . . . . . 37
     8.3.  Effect of Time and Space Aggregation Order on Stats  . . . 37
   9.  Manageability Considerations . . . . . . . . . . . . . . . . . 38
     9.1.  Reporting spatial metric . . . . . . . . . . . . . . . . . 39
     9.2.  Reporting One-to-group metric  . . . . . . . . . . . . . . 40
     9.3.  Metric identification  . . . . . . . . . . . . . . . . . . 40
     9.4.  Information model  . . . . . . . . . . . . . . . . . . . . 41
   10. Security Considerations  . . . . . . . . . . . . . . . . . . . 43
     10.1. Spatial metrics  . . . . . . . . . . . . . . . . . . . . . 43
     10.2. one-to-group metric  . . . . . . . . . . . . . . . . . . . 43
   11. Acknowledgments  . . . . . . . . . . . . . . . . . . . . . . . 44
   12. IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 44
   13. References . . . . . . . . . . . . . . . . . . . . . . . . . . 48
     13.1. Normative References . . . . . . . . . . . . . . . . . . . 48
     13.2. Informative References . . . . . . . . . . . . . . . . . . 49
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 49
   Intellectual Property and Copyright Statements . . . . . . . . . . 50

1.  Introduction

   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).

   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
   [RFC2330].

   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 [RFC4148].

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

   Following is a summary of the metrics defined.

   This memo firstly defines metrics for spatial measurement based on
   the decomposition of standard end-to-end metrics defined by IETF in
   [[RFC2679], [RFC2680], [RFC3393], [RFC3432].  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:
   o  A 'Vector', called Type-P-Spatial-One-way-Delay-Vector, will be
      introduced to divide an end-to-end Type-P-One-way-Delay [RFC2679]
      into a spatial sequence of one-way delay metrics.

   o  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
      [RFC2680] in a spatial sequence of packet loss metrics.
   o  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.
   o  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

2.  Terminology

2.1.  Naming of the path;
   o  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

   The names of
      interest the metrics, including capitalization letters, are as
   close as possible of the path;
   o  Using names of the Type-P-Spatial-One-way-Delay-Vector metric, a 'sample',
      called Type-P-Segment-ipdv-prev-Stream, will be introduced to
      compute ipdv one-way end-to-end metrics over time between two points they
   are derived from.

2.2.  Terms Defined Elsewhere

   host: section 5 of interest RFC 2330

   loss threshold: section 2.8.2 of
      the RFC 2680

   path: section 5 of RFC 2330

   path using the previous packet selection function;
   o  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 digest: section 5 of interest RFC 2330

   sample: section 11 of RFC 2330

   singleton: section 11 of RFC 2330

2.3.  Path Digest Hosts

   The list of the hosts on a path using the shortest delay selection function;

   Then the memo defines one-to-group metrics and one-to-group
   statistics.

   Three one-to-group metrics are defined to measure from the one-way
   performance between a source and a group of receivers.  Definitions
   derive from one-way metrics definitions of RFCs in [RFC2679],
   [RFC2680], [RFC3393], [RFC3432]:
   o  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;
   o  A 'Vector', called Type-P-One-to-Group-One-way-Packet-Loss-Vector,
      will be introduced destination,
   also referred to collect as the set of Type-P-One-way-Packet-
      Loss singletons between one sender and N receivers;
   o host path digest.

2.4.  Multiparty metric

   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.

   Then, based on the One-to-group vector metrics listed above,
   statistics are defined metric is said to capture single receiver performance, group
   performance and relative performance situation inside a be multiparty
   communication for each packet sent during if the test interval between topology involves more than
   one sender measurement collection point.  All multiparty metrics designate a
   set of hosts as "points of interest", where one host is the source
   and N receivers:

   o  Using other hosts are 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 measurement collection points.  For example,
   if the mean set of delays between one sender points of interest is < ha, hb, hc, ..., hn >, where ha
   is the source and a
      receiver 'n'.  Then, based on this definition, 3 metrics will be
      defined to characterize < hb, hc, ..., hn > are the mean delay over destinations, then
   measurements may be conducted between < ha, hb>, < ha, hc>, ..., <ha,
   hn >.

   For the entire group
      during purposes of this interval:
      *  a metric called Type-P-One-to-Group-Mean-Delay, will be
         introduced to present memo (reflecting the mean scope of delays;
      * a single
   source), the only multiparty metrics are one-to-group metrics.

2.5.  Spatial metric called Type-P-One-to-Group-Range-Mean-Delay will be
         introduced

   A metric is said to present the range be spatial if one of mean delays;
      * the hosts (measurement
   collection points) involved is neither the source nor a metric called Type-P-One-to-Group-Max-Mean-Delay destination
   of the measured packet(s).  Such measurement hosts will usually be
         introduced to present the maximum
   members of mean delays;
   o  Using the Type-P-one-to-group-One-way-Packet-Loss-Vector, a path digest.

2.6.  One-to-group metric
      called Type-P-One-to-Group-Receiver-n-Loss-Ratio will be
      introduced

   A metric is said 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 one-to-group if the entire group during
      this interval:
      *  a metric called Type-P-One-to-Group-Loss-Ratio will be
         introduced to capture measured packet loss ratio overall over is sent by
   one source and (potentially) received by more than one destination.
   Thus, the entire topology of the communication group or all receivers;
      *  a metric called Type-P-One-to-Group-Range-Loss-Ratio will can be
         introduced to present comparative packet loss ratio for each
         packet during viewed as a
   center-distributed or server-client topology with the test interval between one sender and N
         Receivers.
   o  Using Type-P-one-to-group-One-way-ipdv-Vector, source as the
   center/server in the topology.

2.7.  Points of interest

   Points of interest are the hosts (as per the RFC 2330 definition,
   "hosts" include routing nodes) that are measurement collection
   points, a metric called
      Type-P-One-to-Group-Range-Delay-Variation will be introduced sub-set of the set of hosts involved in the delivery of the
   packets (in addition to
      present the range source itself).

   For spatial metrics, points of delay variation between one sender and interest are a
      group (possibly arbitrary)
   sub-set of receivers.

2.  Terminology

2.1.  Path Digest Hosts

   The list all the hosts involved in the path.

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

                         Src                   Dst
                         `.          ,-.
                           `.      ,'   `...... 1
                             `.   ;       :
                               `. ;       :
                                 ;         :... 2
                                 |         |
                                 :         ;
                                  :       ;.... 3
                                  :       ;
                                   `.   ,'
                                     `-'....... N

                 Figure 1: One-to-group points of interest

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

2.2.  Multiparty metric

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

               Note: 'x' are nodes which are not points of interest

                   Figure 2: Spatial points of interest

2.8.  Reference point

   A metric reference point is said to defined as the server where the statistical
   calculations will be multiparty if carried out.  It is usually a centralized server
   in the topology involves more than
   one measurement collection point.  All multiparty metrics define architecture that is controlled by a
   set of hosts called "points of interest", network
   operator, where one host measurement data can be collected for further
   processing.  The reference point is the
   source and other distinctly different from hosts are the
   at measurement collection points.  For
   example, if points, where the set of actual measurements are
   carried out (e.g., points of interest is < ha, hb, hc, ..., hn >,
   where ha interest).

2.9.  Vector

   A vector is a set of singletons (single atomic results) comprised of
   observations corresponding to a single source packet at different
   hosts in a network.  For instance, if the one-way delay singletons
   observed at N receivers for Packet P sent by the source and < hb, hc, ..., hn > Src are the destinations, dT1,
   dT2,..., dTN, then measurements may a vector V with N elements can be conducted between < ha, hb>, < ha, hc>, ...,
   <ha, hn >.

   For organized as
   {dT1, dT2,..., dTN}.  The element dT1 is distinct from all others as
   the purposes of this memo (reflecting singleton at receiver 1 in response to a packet sent from the scope of
   source at a single
   source), specific time.  The complete vector gives information
   over the only multiparty metrics are one-to-group metrics.

2.3.  Spatial metric

   A metric is said to be spatial if one dimension of the hosts (measurement space; a set of N receivers in this example.

   The singleton elements of any vector are distinctly different from
   each other in terms of their measurement collection points) involved is neither point.  Different
   vectors for common measurement points of interest are distinguished
   by the source nor packet sending time.

2.10.  Matrix

   Several vectors form a destination
   of matrix, which contains results observed over a
   sampling interval at different places in a network at different
   times.  For example, the measured packet.

2.4.  One-to-group metric One-way delay vectors V1={dT11, dT12,...,
   dT1N}, V2={dT21, dT22,..., dT2N},..., Vm={dTm1, dTm2,..., dTmN} for
   Packet P1, P2,...,Pm, form a One-way delay Matrix {V1, V2,...,Vm}.
   The matrix organizes the vector information to present network
   performance in both space and time.

   A metric is said one-dimensional matrix (row) corresponds to be one-to-group if the measured packet is sent by
   one source a sample in simple
   point-to-point measurement.

   The relationship among singleton, sample, vector and (potentially) received by several destinations.  Thus, matrix is
   illustrated in the topology following Figure 3.

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

                                vector           matrix
                               (space)      (time and space)

      Figure 3: Relationship between singletons, samples, vectors and
                                  matrix

3.  Brief Metric Descriptions

   The metrics for spatial and one-to-group measurement are based on the communication group can be viewed as a centre-
   distributed
   source-to-destination, or server-client topology with the source as the centre/
   server end-to-end metrics defined by IETF in the topology.

2.5.  Points
   [[RFC2679], [RFC2680], [RFC3393], [RFC3432].

   This memo defines seven new spatial metrics using the [RFC2330]
   framework of interest

   Points parameters, units of interest are the hosts* (as per RFC2330 definition, that
   includes routing nodes) that are measure, and measurement collection points,
   methodologies.  Each definition includes a
   sub-set of the set of hosts involved in section that describes
   measurements constraints and issues, and provides guidance to
   increase the delivery accuracy of the packets
   (in addition to the source itself).  Note that results.

   The spatial metrics are:
   o  Type-P-Spatial-One-way-Delay-Vector divides the points end-to-end Type-P-
      One-way-Delay [RFC2679] into a spatial vector of interest
   are one-way delay
      singletons.
   o  Type-P-Spatial-One-way-Packet-Loss-Vector divides an end-to-end
      Type-P-One-way-Packet-Loss [RFC2680] into a possibly arbitrary sub-set spatial vector of all the hosts involved in the
   path.

   Points
      packet loss singletons.
   o  Type-P-Spatial-One-way-ipdv-Vector divides an end-to-end Type-P-
      One-way-ipdv into a spatial vector of interest ipdv singletons.
   o  Using elements of one-to-group metrics are the intended
   destination hosts for packets from the source (in addition to the
   source itself).

                         Src                  Recv
                         `.          ,-.
                           `.      ,'   `...... 1
                             `.   ;       :
                               `. ;       :
                                 ;         :... 2
                                 |         |
                                 :         ;
                                  :       ;.... 3
                                  :       ;
                                   `.   ,'
                                     `-'....... N

                 Figure 1: One-to-group Type-P-Spatial-One-way-Delay-Vector metric,
      a sample called Type-P-Segment-One-way-Delay-Stream collects one-
      way delay metrics between two points of interest

   A candidate point of interest for spatial metrics is a host from the
   set of hosts involved in on the delivery path over
      time.
   o  Likewise, using elements of the packets from the source.

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

               Note: 'x' are nodes which are not points of interest

                   Figure 2: Spatial Type-P-Spatial-Packet-Loss-Vector
      metric, a sample called Type-P-Segment-Packet-Loss-Stream collects
      one-way delay metrics between two points of interest

2.6.  Reference point

   A reference point is defined as on the server where path
      over time.
   o  Using the statistical
   calculations Type-P-Spatial-One-way-Delay-Vector metric, a sample
      called Type-P-Segment-ipdv-prev-Stream, will be carried out.  A centre/server in introduced to
      compute ipdv metrics (using the
   multimetrics measurement that is controlled by a network operator is
   a good example previous packet selection
      function) between two points of interest on the path over time.
   o  Again using the Type-P-Spatial-One-way-Delay-Vector metric, a reference point, where measurement data can be
   collected for further processing.  However,
      sample called Type-P-Segment-ipdv-min-Stream will define another
      set of ipdv metrics (using the actual measurements
   have to be carried out at all minimum delay packet selection
      function) between two points of interest.

2.7.  Vector

   A Vector is interest on the path over time.

   The memo also defines three one-to-group metrics to measure the one-
   way performance between a set of singletons, which are source and a set of results group of receivers.  They are:
   o  Type-P-One-to-group-Delay-Vector collects the
   observation set of Type-P-one-
      way-delay singletons between one sender and N receivers.
   o  Type-P-One-to-group-Packet-Loss-Vector collects the behaviour set of Type-P-
      One-way-Packet-Loss singletons between one sender and N receivers.
   o  Type-P-One-to-group-ipdv-Vector collects the same packet at different places set of a network at different times.  For instance, if one-way delay Type-P-One-
      way-ipdv singletons observed at between one sender and N receivers for Packet P sent by receivers.

   Finally, based on the source
   Src one-to-group vector metrics listed above,
   statistics are dT1, dT2,..., dTN, it can be say that defined to capture single receiver performance, group
   performance and the relative performance for a vector V with N
   elements can be organized as {dT1, dT2,..., dTN}.  The elements in multiparty
   communication:
   o  Using the Type-P-One-to-group-Delay-Vector, a metric called Type-
      P-One-to-group-Receiver-n-Mean-Delay or RnMD, presents the mean of
      delays between one vector sender and a single receiver 'n'.  From this
      metric, 3 additional metrics are singletons distinct with each other in terms defined to characterize the mean
      delay over the entire group of both
   measurement point and sending time.  Given receivers during the vector V as an
   example, same time
      interval:
      *  Type-P-One-to-group-Mean-Delay or GMD, presents the element dT1 is distinct from all others as mean of
         delays;
      *  Type-P-One-to-group-Range-Mean-Delay or GRMD, presents the singleton
   at
         range of mean delays;
      *  Type-P-One-to-group-Max-Mean-Delay or GMMD, presents the
         maximum of mean delays.
   o  Using the Type-P-One-to-group-Packet-Loss-Vector, a metric called
      Type-P-One-to-group-Receiver-n-Loss-Ratio or RnLR, captures the
      packet loss ratio between one sender and a single receiver 1 in response 'n'.
      Based on this definition, 2 more metrics are defined to a
      characterize packet sent from loss over the source at entire group during the same
      time
   T1.  The complete Vector gives information over interval:
      *  Type-P-One-to-group-Loss-Ratio or GLR, captures the dimension overall
         packet loss ratio for the entire group of
   space.

2.8.  Matrix

   Several vectors form a Matrix, which contains results observed in a
   sampling receivers;
      *  Type-P-One-to-group-Range-Loss-Ratio, or GRLR, presents the
         comparative packet loss ratio during the test 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 between
         one sender and N receivers.
   o  Using the information given by a Vector, Type-P-One-to-group-Packet-Loss-Vector, a
   Matrix is more powerful to present network performance in both space
   and time dimensions.  It normally corresponds to metric called
      Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio, or RnCLR, computes
      a sample in simple
   point-to-point measurement.

   The relation among Singleton, Vector and Matrix can be shown in packet loss ratio using the maximum number of packets received
      at any receiver.
   o  Using Type-P-One-to-group-ipdv-Vector, a metric called Type-P-One-
      to-group-Range-Delay-Variation, or GRDV, presents the
   following Figure 3.

                 Point range 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)

         Figure 3: Relation beween Singletons, vectors
      delay variation between one sender and matrix

3. a group of receivers.

4.  Motivations

   All existing 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
   extend them to multiparty measurements situations such as one to one trajectory
   metrics and one to multipoint metrics.

3.1.

4.1.  Motivations for spatial metrics

   Decomposition of instantaneous end-to-end measures is needed:

   Spatial metrics are needed for:
   o  Decomposing the performance of interdomain an inter-domain path is desirable to quantify
      the per-AS contribution to the end-to-end performance.  It is
      valuable to define standard spatial metrics before pursuing inter-
      domain path performance specifications.
   o  Traffic engineering and troubleshooting applications troubleshooting, which benefit from
      spatial views of one-way delay and ipdv consumption, and or
      identification of the location of the lost of packets. path segment where packets were lost.
   o  Monitoring the decomposed performance of a multicast tree composed based on
      of MPLS point-to-multipoint and inter-domain communication require spatial
      decomposition of the one-way delay, ipdv, and packet loss. communications.
   o  Composition of metrics is needed to  Dividing end-to-end metrics, so that some segment measurements can
      be re-used and help measurement systems reach
      large scale large-scale
      coverage.  Spatial measures typically give could characterize the
      individual performance of
      an intra domain intra-domain segment and provide an elementary piece of
      information needed to estimate interdomain inter-domain performance based on composition of metrics.

3.2. to another
      destination using Spatial Composition metrics
      [I-D.ietf-ippm-spatial-composition].

4.2.  Motivations for One-to-group metrics

   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
   point-to-point metric cannot completely describe the multiparty
   situation.  New one-to-group metrics assess performance of all the
   multiple 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. RFCs.  One-to-group metrics are one-way one-
   way metrics from one source to a group of destinations. destinations, or receivers.
   The metrics are helpful for judging the network overall performance of a
   multiparty communications network, and can also be used to describe for describing the variation of performance delivered to
   variation across a group of destination hosts and their
   users. destinations.

   One-to-group performance metrics are needed for several reasons:

   o  For designing and engineering multicast trees and MPLS point-to-
      multipoint LSP; for:

   o  For evaluating  Designing and controlling of the quality of the engineering multicast
      services; trees and MPLS point-to-
      multipoint LSPs.
   o  For  Evaluating and controlling the performance quality of the inter domain multicast
      services; services,
      including inter-domain multicast.
   o  For presenting  Presenting and evaluating the performance requirements for
      multiparty communications and overlay multicast.
   To understand the packet transfer performance between one source and
   any one receiver in the multiparty communication group, we need to
   collect instantaneous end-to-end metrics, or singletons.  It will
   give  This gives
   a very detailed insight view into the performance of each branch of the
   multicast tree
   in terms of end-to-end absolute performance.  This detail tree, and can provide clear and helpful information for
   engineers to identify the sub-path branch with problems in a complex
   multiparty routing tree.

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

3.3.

4.3.  Discussion on Group-to-one and Group-to-group metrics

   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
   this section gives some clues here insights on these two cases.

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

   For the

   The group-to-group connection topology, it is difficult to define communication topology has no obvious focal point:
   the reference point sources and therefore the measurement collection points can be anywhere.
   However, it is difficult possible to define organize the
   measurement points.  However, we can always avoid this confusion problem by
   treating the connections as applying
   measurements in one-to-group or group-to-one topologies for each host
   in our
   measurements without consideration on a uniform way (without taking account of how the real
   communication will might be carried out. out).  For example, if one group of hosts
   < ha, hb, hc, ..., hn > are acting might act as sources to send data to another
   group of hosts < Ha, Hb, Hc, ..., Hm >, we and they can always decompose them be organized
   into n sets of points of interest for one-to-group communications as communications:

   < ha, Ha, Hb, Hc, ..., Hm >, < hb, Ha, Hb, Hc, ..., Hm >, <hc, Ha,
   Hb, Hc, ..., Hm >, ..., < hn, Ha, Hb, Hc, ..., Hm >.

4.

5.  Spatial vectors vector metrics definitions

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

   Spatial vectors vector metrics are based on the decomposition of standard
   end-to-end metrics defined by the IPPM WG in [RFC2679], [RFC2680],
   [RFC3393] and [RFC3432].

   Definitions

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

4.1.

5.1.  A Definition for Spatial One-way Delay Vector

   This section is coupled with the definition of Type-P-One-way-Delay
   of the section 3 of [RFC2679].  When a parameter of this from the definition
   in [RFC2679] is first used re-used in this section, it the first instance will be
   tagged with a trailing asterisk.

   Sections 3.5 to 3.8 of [RFC2679] give requirements and applicability
   statements for end-to-end one-way-delay measurements.  They are
   applicable to each point of interest Hi interest, Hi, involved in the measure.
   Spatial one-way-delay measurement SHOULD be respectful of MUST respect them, especially those
   related to methodology, clock, uncertainties and reporting.

4.1.1.

5.1.1.  Metric Name

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

4.1.2.

5.1.2.  Metric Parameters

   o  Src*, the IP address of the sender.
   o  Dst*, the IP address of the receiver.
   o  i, An an integer in the ordered list <1,2,...,n> of hosts in the
      path.
   o  Hi, A host* of a host in the path digest.
   o  T*, a time, the sending (or initial observation) time for a
      measured packet.
   o  dT*, a delay, the one-way delay for a measured packet.
   o  <dT1,...,  dTi, a delay, the one-way delay for a measured packet from the
      source to host Hi.
   o  <dT1,... dTi,... dTn> a list of delay. n delay singletons.
   o  P*,  Type-P*, the specification of the packet type.
   o  <H1, H2,..., Hn>, hosts a path host digest.

4.1.3.

5.1.3.  Metric Units

   The value of Type-P-Spatial-One-way-Delay-Vector is a sequence of
   times.

4.1.4.
   times (a real number in the dimension of seconds with sufficient
   resolution to convey the results).

5.1.4.  Definition

   Given a Type-P packet sent by the sender Src at wire-time (first bit) T to
   the receiver Dst in on the path <H1, H2,..., Hn>.  Given the  There is a sequence
   of values <T+dT1,T+dT2,...,T+dTn,T+dT> such that dT is the
   Type-P-One-way-Delay Type-P-
   One-way-Delay from Src to Dst 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. does not pass Hi
   within a specified loss threshold* time.

   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>.

4.1.5.

5.1.5.  Discussion

   Following are

   Some specific issues which that may occur: occur are as follows:
   o  the delay looks singletons "appear" to decrease: dTi > DTi+1.  This may
      occur despite
      it does not make sense per definition: being physically impossible with the definition
      used.
      *  This is frequently due to some a measurement clock synchronization
         issue.  This point is discussed in the section 3.7.1.  "Errors
         or uncertainties related to Clocks" of [RFC2679].
         Consequently,
         times the values of a measure delays measured at different multiple hosts do
         may not guaranty match the
         ordering order of the those hosts on the path of a measure. path.
      *  During some change of routes the  The actual order of 2 hosts may change on the main path; path may change due to
         reconvergence (e.g., recovery from a link failure).
      *  The location of the measurement collection 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'

4.2. time'.

5.2.  A Definition for Spatial One-way Packet Loss Vector

   This section is coupled with the definition of Type-P-One-way-Packet-
   Loss.  Then when  When a parameter from the section 2 of [RFC2680] is first used in
   this section, it the first instance will be tagged with a trailing
   asterisk.

   Sections 2.5 to 2.8 of [RFC2680] give requirements and applicability
   statements for end-to-end one-way packet loss measurements.  They are
   applicable to each point of interest Hi interest, Hi, involved in the measure.
   Spatial packet loss measurement SHOULD be respectful of MUST respect them, especially those
   related to methodology, clock, uncertainties and reporting.

   Following we

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

4.2.1.

5.2.1.  Metric Name

   Type-P-Spatial-One-way-Packet-Loss-Vector

4.2.2.

   Type-P-Spatial-Packet-Loss-Vector

5.2.2.  Metric Parameters

   o  Src*, the IP address of the sender.
   o  Dst*, the IP address of the receiver.
   o  i, an integer which ordered in the ordered list <1,2,...,n> of hosts in the
      path.

   o  Hi, points of interests of interest from the path digest.
   o  T*, a time, the sending time for a measured packet.
   o  <dT1,..., dTn, dT>,  dTi, a delay, the one-way delay for a measured packet from the
      source to host Hi.
   o  <dT1,..., dTn>, list of delay. n delay singletons.
   o  P*,  Type-P*, the specification of the packet type.
   o  <H1, H2,..., Hn>, hosts a host path digest.
   o  <L1, L2, ...,Ln>, a list of Boolean values.

4.2.3.

5.2.3.  Metric Units

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

4.2.4.

5.2.4.  Definition

   Given a Type-P packet sent by the sender Src at time T to the receiver Dst in
   on the path <H1, H2, ..., Hn>.  Given  For the sequence of times <T+dT1,T+dT2,...,T+dTn> <T+dT1,T+
   dT2,..., T+dTi, ...,T+dTn> the packet passes in <H1, H2 H2, ..., Hi,
   ..., Hn>,
   we define Type-P-One-way-Packet-Lost-Vector the Type-P-Packet-Loss-Vector metric as the sequence
   of values <L1, <T, 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.

4.2.5.

5.2.5.  Discussion

   Following are

   Some specific issues which that may occur: occur are as follows:
   o  The result includes might include the sequence 1,0.  This may occur under
      specific situations:
      *  During some change of routes a values 1,0.  Although
      this appears physically impossible (a packet is lost, then re-
      appears later on the path):
      *  The actual hosts on the path may be seen by change due to reconvergence
         (e.g., recovery from a host but
         not by it successor link failure).
      *  The order of hosts on the main path; path may change due to reconvergence.
      *  A packet may not be observed in a host due to some buffer or
         CPU overflow in at the point of interest;

4.3. measurement collection point.

5.3.  A Definition for Spatial One-way Ipdv Vector

   This section uses parameters from the definition of Type-P-One-way-
   ipdv.

   When a parameter from section 2 of [RFC3393] (the definition of Type-
   P-One-way-ipdv) is first used in this section, it the first instance will be
   tagged with a trailing asterisk.

   In the

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

4.3.1.

5.3.1.  Metric Name

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

4.3.2.

5.3.2.  Metric Parameters

   o  Src*, the IP address of the sender.
   o  Dst*, the IP address of the receiver.
   o  i, An an integer in the ordered list <1,2,...,n> of hosts in the
      path.
   o  Hi, A host* a host of the path digest.
   o  T1*, a time, the sending time for a first measured packet.
   o  T2*, a time, the sending time for a second measured packet.
   o  dT*, a delay, the one-way delay for a measured packet.
   o  P*,  dTi, a delay, the one-way delay for a measured packet from the
      source to host Hi.
   o  Type-P*, the specification of the packets type.
   o  P1, the first packet sent at time T1.
   o  P2, the second packet sent at time T2.
   o  <H1, H2,..., Hn>, hosts a host path digest.
   o  <T1,dT1.1, dT1.2,..., dT1.n,dT1>, the Type-P-Spatial-One-way-
      Delay-Vector for packet sent at time T1.
   o  <T2,dT2.1, dT2.2,..., dT2.n,dT2>, the Type-P-Spatial-One-way-
      Delay-Vector for packet sent at time T2.
   o  L*, a packet length in bits.  The packets of a Type P packet
      stream from which the Type-P-Spatial-One-way-Delay-Vector metric
      is taken MUST all be of the same length.

4.3.3.

5.3.3.  Metric Units

   The value of Type-P-Spatial-One-way-ipdv-Vector is a sequence of
   times.

4.3.4.
   times (a real number in the dimension of seconds with sufficient
   resolution to convey the results).

5.3.4.  Definition

   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>.

   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.

   Type-P-Spatial-One-way-ipdv-Vector metric is defined as the sequence
   of values <T2-T1, <T1, T2, 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 pass Hi at wire-
   time wire-time
   (last bit) dT1.i, respectively dT2.i, dT1.i and dT2.i respectively, or undefined if at least one
   of them never passes Hi.  T2-T1 Hi (and the respective one-way delay is
   undefined).  The T1,T2* pair indicates the inter-packet emission
   interval and dT2-dT1 is ddT* the Type-P-One-way-ipdv at T1,T2*.

4.4. Type-P-One-way-ipdv.

5.4.  Spatial Methodology

   Methodology,

   The methodology, reporting specifications, and uncertainties points
   specified in section 3 of [RFC2679] applies apply to each point of interest Hi
   (or measurement collection point), Hi, measuring a an element of a
   spatial delay vector.

   Methodology,

   Likewise, the methodology, reporting specifications, and
   uncertainties points specified in section 2 of [RFC2680] applies apply to each point
   of interest Hi interest, Hi, measuring a an element of a spatial packet loss
   vector.

   Sections 3.5 to 3.7 of [RFC3393] give requirements and applicability
   statements for end-to-end One-way ipdv measurements.  They are
   applicable to each point of interest Hi interest, Hi, involved in the measure.
   Spatial One-way ipdv measurement SHOULD be respectful of MUST respect the methodology, clock,
   uncertainties and reporting aspects given in this section. there.

   Generally, for a given Type-P packet of length L, in L at a given specific Hi,
   the methodology for spatial vector metrics may proceed as follows:
   o  At each Hi, points of interest interest/measurement collection points
      prepare to capture the packet sent
      a at time T, take record a timestamp
      Ti', and determine the internal delay correction dTi' (See section
      3.7.1.  "Errors or uncertainties related to Clocks" of [RFC2679]), [RFC2679]);
   o  Each Hi extracts the path ordering information from the packet
      (e.g. time-to-live);
   o  Each Hi compute computes the corrected 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;
   o  Each Hi extracts the timestamp T from the packet;
   o  Each Hi computes the one-way-delay from Src to Hi: dTi = Ti - T;
   o  The reference point gathers the result of each Hi and order arranges
      them according to the path ordering information received to build
      the type-P spatial one-way vector (e.g.  Type-P-Spatial-One-way-Delay-
      Vector  Type-P-Spatial-One-way-
      Delay-Vector metric <T, dT1, dT2,..., dTn, dT> ) dT>) over the path
      <Src, H1, H2,..., Hn, Dst> at time T.

4.4.1.  Loss threshold

5.4.1.  Packet Loss threshold is Detection

   In an pure end-to-end measurement, packet losses are detected by the centrality
   receiver only.  A packet is lost when Type-P-One-way-Delay is
   undefined or very large (See section 2.4 ans 2.5 of any methodology because it
   determines [RFC2680] and
   section 3.5 of [RFC2680]).  A packet is deemed lost by the presence receiver
   after a duration which starts at the packet in time the packet is sent.  This
   timeout value is chosen by a measurement process of the
   point of interest and consequently determines any ground truth metric
   result. process; It determines the presence of an effective delay, and bias
   the measure of ipdv, of
   threshold between recording a long packet loss and of the statistics.

   This is consistent for end-to-end but impacts transfer time as a finite
   value or an undefined value.

   In a spatial measure:
   depending measurement, packet losses may be detected at several
   measurement collection points.  Depending on the consistency of the
   packet loss threshold detections among the points of interest, a packet may be
   considered loss a as lost at one host but present
   in point despite having a finite delay at
   another one, or may be observed by the last host (last hop) measurement collection
   point of the path but considered lost by Dst. The analysis

   There is a risk of misinterpreting such results is not
   deterministic: results: Has the path change?  Does
   changed?  Did the packet arrive at the destination or was it lost during on
   the very last mile? link?

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

   The loss threshold should be set up with the same
   value in each host of the path observation/measurement collection points and in the destination. destination
   SHOULD use consistent methods to detect packets losses.  The loss
   threshold methods
   and parameters must be systematically reported to permit careful
   introspection
   comparison and to avoid the introduction of introducing any contradiction confounding factors in the statistic computation process.

4.4.2.
   analysis.

5.4.2.  Host Path Digest

   The methodology given above relies on knowing the order of the hosts/
   measurement collection points of
   interest over on the path to [RFC2679] one's.

   A [RFC2330].

   Path instability might cause a test packets may cross several times packet to be observed more than
   once by the same host host, resulting in the repetition of one or several more
   hosts in the Path Digest.

   As an example.  This occurs typically

   For example, repeated observations may occur 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 was from Ha to Hb and that
   the new path is from Hb to Ha.

   Consequently, duplication of hosts in the Path Digest path digest of a vectors vector
   MUST be identified before statistics computation of statistics to avoid
   producing corrupted
   results' production.

5. information.

6.  Spatial Segments metrics definitions Segment Metrics Definitions

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

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

   Then it defines 2 different samples of ipdv.  The first metric, Type-
   P-Segment-One-way-ipdv-prev-Stream, ipdv: Type-P-Segment-ipdv-
   prev-Stream uses the current and previous packet packets as the selection function.  The second metric, Type-P-Segment-One-way-ipdv-
   min-Stream,
   function, and Type-P-Segment-ipdv-min-Stream, uses the minimum delay
   as one of the selection.

5.1. selected packets in every pair.

6.1.  A Definition of a sample Sample of One-way Delay of a segment Segment of the path Path

   This metric defines a sample of One-way delays over time between a
   pair of hosts of on a path.

   As its semantic  Since it is very close semantically to the
   metric Type-P-Packet-loss-Stream Type-P-One-way-Delay-Poisson-Stream defined in section 4 of
   [RFC2679], sections 4.5 to 4.8 of [RFC2679] are part integral parts of the current definition.

5.1.1.
   definition text below.

6.1.1.  Metric Name

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

5.1.2.

6.1.2.  Metric Parameters

   o  Src*,  Src, the IP address of the sender.
   o  Dst*,  Dst, the IP address of the receiver.
   o  P*,  Type-P, the specification of the packet type.
   o  i, an integer in the ordered list <1,2,...,n> of hosts in the
      path.
   o  k, an integer which orders the packets sent.
   o  a and b, 2 two integers where b > a.
   o  Hi, a host* host of the path digest.
   o  <H1,..., Ha, ..., Hb, ...., Hn>, hosts a host path digest.
   o  <T1, T2, ..., Tm>, a list of times.

5.1.3.

6.1.3.  Metric Units

   The value of a Type-P-Segment-One-way-Delay-Stream is a pair of of:
      A list of times <T1, T2, ..., Tm>;
      A sequence of delays.

5.1.4.

6.1.4.  Definition

   Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb, ...,
   Hn>, given and 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> :
      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>;
      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>;
      ...
      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.

   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 sent at time Tk passes Ha and Hb or undefined if this
   packet never passes Ha or (inclusive) never passes Hb.

5.1.5.

6.1.5.  Discussion

   Following are

   Some specific issues which that may occur: occur are as follows:
   o  the delay looks singletons "appear" to decrease: dTi > DTi+1:
      *  This is typically due to clock synchronization issue. this
         point DTi+1, and is
      discussed in the section 3.7.1.  "Errors or
         uncertainties related to Clocks" of of [RFC2679]; 5.1.5.
      *  This may occurs too could also occur when the clock resolution of one probe
         measurement collection point is
         bigger larger than the minimum delay
         of a path.  As an example this
         happen when measuring  For example, the minimum delay of a path which is 500 km long
         with one probe synchronized using NTP having path
         through optical fiber facilities is 2.5ms, but the measurement
         collection point has a clock resolution of 8ms.
   The metric can not SHALL be performed on invalid for times < T1 , T2, ..., Tm-1, Tm> in if
   the following cases: conditions occur:
   o  Ha or Hb disappears from the path due to some change of routes; routing change.
   o  The order of Ha and Hb changes in the path;

5.2. path.

6.2.  A Definition of a sample Sample of Packet Loss of a segment Segment of the path Path

   This metric defines a sample of packet lost loss over time between a pair
   of hosts of a path.  As its semantic  Since it is very close semantically to the
   metric Type-P-Packet-loss-Stream defined in section 3 of [RFC2680],
   sections 3.5 to 3.8 of [RFC2680] are part integral parts of the current definition.

5.2.1. definition
   text below.

6.2.1.  Metric Name

   Type-P-segment-Packet-loss-Stream

5.2.2.

   Type-P-segment-Packet-Loss-Stream

6.2.2.  Metric Parameters

   o  Src*,  Src, the IP address of the sender.

   o  Dst*,  Dst, the IP address of the receiver.
   o  P*,  Type-P, the specification of the packet type.
   o  k, an integer which orders the packets sent.
   o  n, an integer which orders the hosts on the path.
   o  a and b, 2 two integers where b > a.
   o  <H1, H2, ..., Ha, ..., Hb, ...,Hn>, hosts a host path digest.
   o  Hi, exchange points of the path digest.
   o  <T1, T2, ..., Tm>, a list of times.
   o  <L1, L2, ..., Ln> Ln>, a list of boolean Boolean values.

5.2.3.

6.2.3.  Metric Units

   The value of a Type-P-segment-Packet-loss-Stream Type-P-segment-Packet-Loss-Stream is a pair of of:
      A The list of times <T1, T2, ..., Tm>;
      a
      A sequence of booleans.

5.2.4. Boolean values.

6.2.4.  Definition

   Given 2 two hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,
   ..., Hn>, given and the matrix of Type-P-Spatial-Packet-loss-Vector Type-P-Spatial-Packet-Loss-Vector for the
   packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :
      <L1.1,
      <T1, L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L>,
      <L2.1,
      <T2, L2.1, L2.2,..., L2.a, ..., L2.b, ..., L2.n, L>,
      ...,
      <Lm.1,
      <Tm, Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L>.

   We define the value of the sample Type-P-segment-Packet-Lost-Stream
   from Ha to Hb as the sequence of booleans Booleans <L1.ab, L2.ab,..., Lk.ab,
   ..., Lm.ab> such that for each Tk:
   o  A value of Lk of 0 means that Ha and Hb observed the packet sent
      at time Tk (Lk.a (both Lk.a and Lk.b have a value of 0); 0).
   o  A value of Lk of 1 means that Ha observed the packet sent at time
      Tk (Lk.a has a value of 0) and that Hb did not observed observe the packet
      sent at time Tk (Lk.b have has a value of 1); 1).
   o  The value of Lk is undefined when Neither neither Ha or nor Hb observe observed the
      packet;

5.2.5.
      packet (both Lk.a and Lk.b have a value of 1).

6.2.5.  Discussion

   Unlike Type-P-Packet-loss-Stream, Type-P-Segment-Packet-loss-Stream Type-P-Segment-Packet-Loss-Stream
   relies on the stability of the host path digest.  The metric can not SHALL be performed on
   invalid for times < T1 , T2, ..., Tm-1, Tm> in if the following cases:
   conditions occur:
   o  Ha or Hb disappears from the path due to some change of routes; routing change.
   o  the  The order of Ha and Hb changes in the path; path.
   o  Lk.a or Lk.b is undefined; undefined.

   o  Lk.a has the value 1 (not observed) and Lk.b has the value 0
      (observed);
   o  L has the value 0 (the packet was received by Dst) and Lk.ab has
      the value 1 (the packet was lost between Ha and Hb).

5.3.

6.3.  A Definition of a sample Sample of ipdv of a segment Segment using the previous
      packet selection function Previous
      Packet Selection Function

   This metric defines a sample of ipdv [RFC3393] over time between a
   pair of hosts using the previous packet as the selection function.

5.3.1.

6.3.1.  Metric Name

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

5.3.2.

   Type-P-Segment-ipdv-prev-Stream

6.3.2.  Metric Parameters

   o  Src*,  Src, the IP address of the sender.
   o  Dst*,  Dst, the IP address of the receiver.
   o  P*,  Type-P, the specification of the packet type.
   o  k, an integer which orders the packets sent.
   o  n, an integer which orders the hosts on the path.
   o  a and b, 2 two integers where b > a.
   o  <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the hosts path digest.
   o  <T1, T2, ..., Tm-1, Tm>, a list of times.
   o  <Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk>, a
      Type-P-Spatial-One-way-Delay-Vector.

5.3.3.

6.3.3.  Metric Units

   The value of a Type-P-Segment-One-way-ipdv-prev-Stream Type-P-Segment-ipdv-prev-Stream is a pair of:
      The list of <T1, T2, ..., Tm-1, Tm>;
      A list of pairs of interval of times and delays;

5.3.4.

6.3.4.  Definition

   Given 2 two hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,
   ..., Hn>, given and 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> :
      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,
      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,
      ...
      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.

   We define the Type-P-Segment-One-way-ipdv-prev-Stream Type-P-Segment-ipdv-prev-Stream as the sequence of pair of
   packet intervals time pairs and delay variations <(dT2_1.a

   <(T1, T2 , dT2.ab - dT1.ab) ,..., (dTk_k-1.a,
   (Tk-1, Tk, dTk.ab - dTk-1.ab), ..., (dTm_m-1.a,

   (Tm-1, Tm, dTm.ab - dTm-1.ab)> such that for each Tk:
   o  dTk_k-1.a

   For any pair, Tk, Tk-1 in k=1 through m, the difference dTk.ab - dTk-
   1.ab is either undefined if if:
   o  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; OR
   o  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, delay dTk.b 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.

5.3.5. dTk-1.b is undefined.

6.3.5.  Discussion

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

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

5.4.

6.4.  A Definition of a sample Sample of ipdv of a segment Segment  using the minimum
      delay selection function Minimum
      Delay Selection Function

   This metric defines a sample of ipdv [RFC3393] over time between a
   pair of hosts of on a path using the shortest minimum delay as one of the selection
   function.

5.4.1.
   selected packets in every pair.

6.4.1.  Metric Name

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

5.4.2.

6.4.2.  Metric Parameters

   o  Src*,  Src, the IP address of the sender.
   o  Dst*,  Dst, the IP address of the receiver.
   o  P*,  Type-P, the specification of the packet type.
   o  k, an integer which orders the packets sent.
   o  i, an integer which identifies a packet sent.
   o  n, an integer which orders the hosts on the path.
   o  a and b, 2 two integers where b > a.
   o  <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the hosts host path digest.
   o  <T1, T2, ..., Tm-1, Tm>, a list of times.

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

5.4.3.

6.4.3.  Metric Units

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

5.4.4. times.

6.4.4.  Definition

   Given 2 two hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,
   ..., Hn>, given and 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> :
      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,
      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,
      ...
      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.

   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: where:
   o  min(dTi.ab) is the minimum value of the tuples (dTk.b - dTk.a);
   o  for each time Tk, dTk.ab is undefined if dTk.a or (inclusive)
      dTk.b is undefined, or the real number (dTk.b - dTk.a).

5.4.5. dTk.a) is
      undefined.

6.4.5.  Discussion

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

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

6.
   Hb, because a wide range of spacings are reflected in any PDV
   distribution.

7.  One-to-group metrics definitions

   This metric section defines metrics to measure the performance metrics between a source and a group
   of receivers.

6.1.

7.1.  A Definition for One-to-group One-way Delay

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

6.1.1.

7.1.1.  Metric Name

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

6.1.2.

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

7.1.2.  Metric Parameters

   o  Src, the IP address of a host acting as the source.
   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as
      receivers.
   o  T, a time.
   o  dT1,...,dTn a list of time. times.
   o  P,  Type-P, the specification of the packet type.
   o  Gr, the receiving group identifier.  The parameter Gr is the
      multicast group address if the measured packets are transmitted
      over IP multicast.  This parameter is to differentiate the
      measured traffic from other unicast and multicast traffic.  It is
      optional in the
      OPTIONAL for this metric to avoid losing any generality, i.e. to
      make the metric also applicable to unicast measurement where there
      is only one receiver.

6.1.3.

7.1.3.  Metric Units

   The value of a Type-P-One-to-group-One-way-Delay-Vector Type-P-One-to-group-Delay-Vector is a set of
   Type-P-One-way-Delay Type-P-
   One-way-Delay singletons [RFC2679].

6.1.4. [RFC2679], which is a sequence of times (a
   real number in the dimension of seconds with sufficient resolution to
   convey the results).

7.1.4.  Definition

   Given a Type P Type-P packet sent by the source Src at Time time T, given and the N
   hosts { Recv1,...,RecvN } which receive the packet at the time {
   T+dT1,...,T+dTn }, or the packet does not pass a Type-P-One-to-group-One-way-Delay-Vector receiver within a
   specified loss threshold time, then the Type-P-One-to-group-Delay-
   Vector is defined as the set of the Type-P-One-way-Delay singleton singletons
   between Src and each receiver with value of { dT1, dT2,...,dTn }.

6.2. },
   where any of the singletons may be undefined if the packet did not
   pass the corresponding receiver within a specified loss threshold
   time.

7.2.  A Definition for One-to-group One-way Packet Loss

6.2.1.

7.2.1.  Metric Name

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

6.2.2.

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

7.2.2.  Metric Parameters

   o  Src, the IP address of a host acting as the source.
   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as
      receivers.
   o  T, a time.
   o  T1,...,Tn a list of time.
   o  P,  Type-P, the specification of the packet type.
   o  Gr, the receiving group identifier.

6.2.3. identifier, OPTIONAL.

7.2.3.  Metric Units

   The value of a Type-P-One-to-group-One-way-Packet-Loss-Vector Type-P-One-to-group-Packet-Loss-Vector is a set of
   Type-P-One-way-Packet-Loss singletons [RFC2680].

6.2.4.

   o  T, time the source packet was sent
   o  L1,...,LN a list of boolean values

7.2.4.  Definition

   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 Type-P-One-to-group-Packet-Loss-Vector is
   defined as a set of the Type-P-One-way-Packet-Loss singleton singletons between
   Src and each of the receivers {<T1,0|1>,<T2,0|1>,..., <Tn,0|1>}.

6.3.

   {T, <L1=0|1>,<L2=0|1>,..., <LN=0|1>},

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

7.3.  A Definition for One-to-group One-way Ipdv

6.3.1. ipdv

7.3.1.  Metric Name

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

6.3.2.

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

7.3.2.  Metric Parameters

   o  Src, the IP address of a host acting as the source.
   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as
      receivers.
   o  T1, a time.
   o  T2, a time.

   o  ddT1, ...,ddTn, a list of time. times.
   o  P,  Type-P, the specification of the packet type.
   o  F, a selection function non-ambiguously defining unambiguously the two packets
      from the stream selected for the metric.
   o  Gr, the receiving group identifier.  The parameter Gr is the
      multicast group address if the measured packets are transmitted
      over IP multicast.  This parameter is to differentiate the
      measured traffic from other unicast and multicast traffic.  It is
      optional
      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.

6.3.3.

7.3.3.  Metric Units

   The value of a Type-P-One-to-group-One-way-ipdv-Vector Type-P-One-to-group-ipdv-Vector is a set of
   Type-P-One-way-ipdv Type-P-
   One-way-ipdv singletons [RFC3393].

6.3.4.

7.3.4.  Definition

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

   Therefore, for

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

7.  One-to-Group second packet), and that {dT'1-
   dT1,...,dT'n-dTn} ={ddT1,...,ddTn}.

   For any pair of selected packets, the difference dT'n-dTn is
   undefined if:
   o  the delay dTn to Receiver n is undefined, OR
   o  the delay dT'n to Receiver n is undefined.

8.  One-to-group Sample Statistics

   The defined one-to-group metrics defined above can all be are directly achieved
   from the by
   collecting relevant unicast one-way metrics.  They collect all unicast
   measurement results of one-way metrics together in one profile measurements results and
   sort them
   by receivers and packets in a receiving group. gathering them per group of receivers.  They
   provide sufficient information regarding the produce network
   performance in
   terms of each receiver and guide information which guides engineers to identify toward potential
   problem
   problems which may have happened on each any branch of a multicast routing
   tree.
   However,

   The results of these metrics cannot be are not directly used usable to conveniently present the
   performance in terms of a group and neither because each result is made of a huge number
   of singletons which are difficult to identify read and analyze.  As an
   example, delay are not comparable because the distance between
   receiver and sender differs.  Furthermore they don't capture relative
   performance situation. situation a multiparty communication.

   From the performance point of view, the multiparty communication
   services not only require the support of absolute performance support
   information but also
   the relative performance. information on "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.

   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 Figure 4.  For a Matrix M each row is a set of One-way
   singletons spreading over the time dimension and each column is
   another set of One-way singletons spreading over the space dimension.

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

                         Figure 4: Matrix M (n*m)

   In Matrix M, each element is a one-way delay singleton.  Each column
   is a delay vector 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.

   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.

   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.

   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.

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

   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.

7.1.

8.1.  Discussion on the Impact of packet loss on statistics

   The packet loss does have effects on one-way metrics and their
   statistics.  For example, the lost packet can result in an infinite one-
   way
   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 complexity of building a Matrix, matrix, which
   is needed for calculation of the statistics proposed in this memo.

   The situation is that measurement results obtained by different end
   users might have different packet loss pattern.  For example, for
   User1, packet A was observed 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.

   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.

7.2.

8.2.  General Metric Parameters

   o  Src, the IP address of a host;
   o  G, the receiving group identifier;
   o  N, the number of Receivers (Recv1, Recv2, ...  RecvN);
   o  T, a time (start of test interval);
   o  Tf, a time (end of test interval);
   o  K, the number of packets sent from the source during the test
      interval;
   o  J[n], the number of packets received at a particular Receiver, n,
      where 1<=n<=N;
   o  lambda, a rate in reciprocal seconds (for Poisson Streams);
   o  incT, the nominal duration of inter-packet interval, first bit to
      first bit (for Periodic Streams);
   o  T0, a time that MUST be selected at random from the interval [T,
      T+I] to start generating packets and taking measurements (for
      Periodic Streams);
   o  TstampSrc, the wire time of the packet as measured at MP(Src) (the
      Source Measurement Point);
   o  TstampRecv, the wire time of the packet as measured at MP(Recv),
      assigned to packets that arrive within a "reasonable" time;
   o  Tmax, a maximum waiting time for packets at the destination, set
      sufficiently long to disambiguate packets with long delays from
      packets that are discarded (lost), thus the distribution of delay
      is not truncated;
   o  dT, shorthand notation for a one-way delay singleton value;
   o  L, shorthand notation for a one-way loss singleton value, either
      zero or one, where L=1 indicates loss and L=0 indicates arrival at
      the destination within TstampSrc + Tmax, may be indexed over n
      Receivers;
   o  DV, shorthand notation for a one-way delay variation singleton
      value;

7.3.  One-to-Group one-way
      value.

8.3.  One-to-group Delay Statistics

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

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

       1      R1dT1   R1dT2     R1dT3 ... R1dTk    R1DM    R1MD  \
                                                          |
       2      R2dT1   R2dT2     R2dT3 ... R2dTk    R2DM    R2MD   |
                                                          |
       3      R3dT1   R3dT2     R3dT3 ... R3dTk    R2DM    R2MD    > Group delay
       .                                                  |
       .                                                  |
       .                                                  |
       n      RndT1   RndT2     RndT3 ... RndTk    RnDM    RnMD  /

                                                 Receiver-n
                                                   delay

                     Figure 5: One-to-Group One-to-group Mean Delay

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

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

7.3.1.  Type-P-One-to-Group-Receiver-n-Mean-Delay

8.3.1.  Type-P-One-to-group-Receiver-n-Mean-Delay

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

   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
   [RFC2679].  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.

                               J[n]
                               ---
                          1    \
               RnDM
               RnMD =    --- *  >  TstampRecv[i] - TstampSrc[i]
                         J[n]  /
                               ---
                               i = 1

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

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

7.3.2.  Type-P-One-to-Group-Mean-Delay

8.3.2.  Type-P-One-to-group-Mean-Delay

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

                                         N
                                        ---
                                   1    \
                            GMD =  - *   >   RnDM
                                   N    /
                                        ---
                                        n = 1

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

   Note that the Group Mean Delay can also be calculated by summing the
   Finite one-way Delay singletons in the Matrix, and dividing by the
   number of Finite One-way Delay singletons.

7.3.3.  Type-P-One-to-Group-Range-Mean-Delay

8.3.3.   Type-P-One-to-group-Range-Mean-Delay

   This section defines a metric for the range of mean delays over all N
   receivers in the Group, group (R1DM, R2DM,...RnDM).

   Type-P-One-to-Group-Range-Mean-Delay

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

7.3.4.  Type-P-One-to-Group-Max-Mean-Delay

8.3.4.  Type-P-One-to-group-Max-Mean-Delay

   This section defines a metric for the maximum of mean delays over all
   N receivers in the Group, group (R1DM, R2DM,...RnDM).

   Type-P-One-to-Group-Max-Mean-Delay

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

7.4.  One-to-Group one-way

8.4.  One-to-group Packet Loss Statistics

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

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

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

                                           Receiver-n
                                           Loss Ratio

                     Figure 8: One-to-Group One-to-group Loss Ratio

   Statistics are computed on the sample of Type-P-One-way-Packet-Loss
   [RFC2680] of the matrix above.

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

7.4.1.  Type-P-One-to-Group-Receiver-n-Loss-Ratio

8.4.1.  Type-P-One-to-group-Receiver-n-Loss-Ratio

   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 [RFC2680].  The Type-P-
   One-way-Packet-Loss-Average and the Type-P-One-to-Group-Receiver-n- Type-P-One-to-group-Receiver-n-
   Loss-Ratio, also named RnLR, are equivalent metrics.  In terms of the
   parameters used here, these metrics definitions can be expressed as
                                           K
                                          ---
                                     1    \
                             RnLR =  - *   >   RnLk
                                     K    /
                                          ---
                                         k = 1

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

7.4.2.  Type-P-One-to-Group-Receiver-n-Comp-Loss-Ratio Type-P-One-to-group-Receiver-n-Loss-Ratio

8.4.2.  Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio

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

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

                                           K
                                          ---
                                          \
                                           >   Ln(k)
                                          /
                                          ---
                                          k=1
                     RnCLR =  -----------------------------
                                       /    K         \
                                       |   ---        |
                                       |   \          |
                               K - Min |    >   Ln(k) |
                                       |   /          |
                                       |   ---        |
                                       \   k=1        / N

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

7.4.3.  Type-P-One-to-Group-Loss-Ratio

   Type-P-One-to-Group-Loss-Ratio, Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio

8.4.3.  Type-P-One-to-group-Loss-Ratio

   Type-P-One-to-group-Loss-Ratio, the overall Group loss ratio, also
   named GLR, is defined as
                                         K,N
                                         ---
                                   1     \
                            GLR = --- *   >   L(k,n)
                                  K*N    /
                                         ---
                                        k,n = 1

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

7.4.4.  Type-P-One-to-Group-Range-Loss-Ratio Type-P-One-to-group-Loss-Ratio

8.4.4.  Type-P-One-to-group-Range-Loss-Ratio

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

   Type-P-One-to-Group-Range-Loss-Ratio

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

   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.

7.5.  One-to-Group one-way

8.5.  One-to-group Delay Variation Statistics

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

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

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

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

   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.

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

7.5.1.  Type-P-One-to-Group-Delay-Variation-Range

8.5.1.  Type-P-One-to-group-Range-Delay-Variation

   This section defines a metric for the range of delays variation over
   all N receivers in the Group.

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

   Type-P-One-to-Group-Delay-Variation-Range

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

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

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

8.

9.  Measurement Methods: Scalability and Reporting

   Virtually all the guidance on measurement processes supplied by the
   earlier IPPM RFCs (such as [RFC2679] and [RFC2680]) for one-to-one
   scenarios is applicable here in the spatial and multiparty
   measurement scenario.  The main difference is that the spatial and
   multiparty configurations require multiple points of interest where a
   stream of singletons will be collected.  The amount of information
   requiring storage grows with both the number of metrics and the
   points of interest, so the scale of the measurement architecture
   multiplies the number of singleton results that must be collected and
   processed.

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

   In recognition of the likely need to minimize 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).

8.1.

9.1.  Computation methods

   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.

8.2.

9.2.  Measurement

   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.

8.3.

9.3.  Effect of Time and Space Aggregation Order on Stats

   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.

   multimetrics co-located and that results are
   gathered in a point of reference for further usages.

   Multimetrics samples are represented in a matrix as illustrated below

      Point of
      interest
        1      R1S1   R1S1     R1S1 ... R1Sk    \
                                                 |
        2      R2S1   R2S2     R2S3 ... R2Sk     |
                                                 |
        3      R3S1   R3S2     R3S3 ... R3Sk      >  sample over space
        .                                        |
        .                                        |
        .                                        |
        n      RnS1   RnS2     RnS3 ... RnSk    /

               S1M    S2M      S3M  ... SnM     Stats over space

               \-------------  ------------/
                             \/
                 Stat over space and time

        Figure 13: Impact of space aggregation on multimetrics Stat

   2 methods are available to compute statistics on the resulting a matrix:
   o  Method 1: The statistic metric is computed over time and then over
      space;
   o  Method 2: The statistic metric is computed over space and then
      over time.

   They

   These 2 methods differ only by the order of the time and of the space aggregation.  View as a matrix this  The
   order is neutral as does not impact the result, but computation resources required.  It does
   not change the impact on a measurement deployment is
   critical.

   In both cases value of the result.  However, it impacts severely the
   minimal volume of data to report is proportional report:

   o  Method 1: Each point of interest computes periodically statistics
      over time to lower the volume of data to report.  They are
      reported to the reference point for computing the stat over space.
      This volume no longer depends on the number of probes.  But there samples.  It is a major difference between these 2
   methods:

      method2: In space and time aggregation mode
      only proportional to the computation period;
   o  Method 2: The volume of data to
      collect report is proportional to the
      number of test packets received; samples.  Each received packet RiSi triggers out a block of data that sample, RiSi, must be reported to a common place the
      reference point for computing the stat statistic over space;
      method1: In time and space aggregation mode the and statistic
      over time.  The volume increases with the number of data to
      collect samples.  It
      is proportional to the period of aggregation, so it does
      not depend on the number of packet received; test packets;

   Method 2 property has severe drawbacks in terms of security and dimensioning:
      The increasing of
   o  Increasing the rate of the test packets may result in a
      sort Denial of DoS
      Service toward the computation points; points of reference;
   o  The dimensioning of a measurement system is quite impossible to
      validate.
      validate because any increase of the rate of the test packets will
      increase the bandwidth requested to collect the raw results.

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

   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..

8.3.1.

9.3.1.  Impact on spatial statistics

   2 methods are available to compute spatial statistics:
   o  method  Method 1: spatial segment metrics and statistics are preferably
      computed over time by each points of interest;
   o  method  Method 2: Vectors metrics are intrinsically instantaneous space
      metrics which must be reported using method2 whenever
      instantaneous metrics information is needed.

8.3.2.

9.3.2.  Impact on one-to-group statistics

   2 methods are available to compute group statistics:
   o  method1:  Method1: Figure 5 andFigure and Figure 8 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;
   o  method2:  Method2: Figure 13 presents the second one, metric is computed
      over space and then over time.

9.

10.  Manageability Considerations

   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.

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

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

9.1.

10.1.  Reporting spatial metric

   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.

9.1.1.

10.1.1.  Path

   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
   [RFC2679]).  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.

9.1.2.

10.1.2.  Host order

   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.

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

9.1.3.

10.1.3.  Timestamping bias

   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.

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

9.1.4.

10.1.4.  Reporting spatial One-way Delay

   The reporting includes information to report for one-way-delay as the
   Section 3.6 of [RFC2679].  The same apply for packet loss and ipdv.

9.2.

10.2.  Reporting One-to-group metric

   All reporting rules described in RFC2679-80 [RFC2679] and [RFC2680] apply to the
   corresponding One-to-group metrics.  Following are specific
   parameters that should be reported.

9.2.1.

10.2.1.  Path

   As suggested by the RFC2679-80, [RFC2679] and [RFC2680] , 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 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 travelled through this
   incomplete path?

9.2.2.

10.2.2.  Group size

   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.

9.2.3.

10.2.3.  Timestamping bias

   It is the same as described in section 9.1.3.

9.2.4. 10.1.3.

10.2.4.  Reporting One-to-group One-way Delay

   It is the same as described in section 9.1.4.

9.2.5. 10.1.4.

10.2.5.  Measurement method

   As explained in section 8, 9, the measurement method will have impact on
   the analysis of the measurement result.  Therefore, it should be
   reported.

9.3.

10.3.  Metric identification

   IANA assigns each metric defined by the IPPM WG with a unique
   identifier as per [RFC4148] in the IANA-IPPM-METRICS-REGISTRY-MIB.

9.4.

10.4.  Information model

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

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

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

   o  Packet_type, The Type-P of test packets (Type-P);
   o  Packet_length, a packet length in bits (L);
   o  Src_host, the IP address of the sender;
   o  Dst_host, the IP address of the receiver;
   o  Hosts_serie: <H1, H2,..., Hn>, a list of points of interest;
   o  Loss_threshold: The threshold of infinite delay;
   o  Systematic_error: constant delay between wire time and
      timestamping;
   o  Calibration_error: maximal uncertainty;
   o  Src_time, the sending time for a measured packet;
   o  Dst_time, the receiving time for a measured packet;
   o  Result_status : an indicator of usability of a result 'Resource
      exhaustion' 'infinite', 'lost';
   o  Delays_serie: <dT1,..., dTn> a list of delays;
   o  Losses_serie: <B1, B2, ..., Bi, ..., Bn>, a list of Boolean values
      (spatial) or a set of Boolean values (one-to-group);
   o  Result_status_serie: a list of results status;
   o  dT: a delay;
   o  Singleton_number: a number of singletons;
   o  Observation_duration: An observation duration;
   o  metric_identifier.

   Following is the information of each vector that should be available
   to compute samples:

   o  Packet_type;
   o  Packet_length;
   o  Src_host, the sender of the packet;
   o  Dst_host, the receiver of the packet, apply only for spatial
      vectors;
   o  Hosts_serie: not ordered for one-to-group;
   o  Src_time, the sending time for the measured packet;
   o  dT, the end-to-end one-way delay for the measured packet, apply
      only for spatial vectors;
   o  Delays_serie: apply only for delays and ipdv vector, not ordered
      for one-to-group;
   o  Losses_serie: apply only for packets loss vector, not ordered for
      one-to-group;
   o  Result_status_serie;
   o  Observation_duration: the difference between the time of the last
      singleton and the time of the first singleton.
   o  Following is the context information (measure, points of
      interests) that should be available to compute samples :
      *  Loss threshold;
      *  Systematic error: constant delay between wire time and
         timestamping;
      *  Calibration error: maximal uncertainty;

   A spatial or a one-to-group sample is a collection of singletons
   giving the performance from the sender to a single point of interest.
   Following is the information that should be available for each sample
   to compute statistics:

   o  Packet_type;
   o  Packet_length;
   o  Src_host, the sender of the packet;
   o  Dst_host, the receiver of the packet;
   o  Start_time, the sending time of the first packet;
   o  Delays_serie: apply only for delays and ipdv samples;
   o  Losses_serie: apply only for packets loss samples;
   o  Result_status_serie;
   o  Observation_duration: the difference between the time of the last
      singleton of the last sample and the time of the first singleton
      of the first sample.
   o  Following is the context information (measure, points of
      interests) that should be available to compute statistics :
      *  Loss threshold;
      *  Systematic error: constant delay between wire time and
         timestamping;
      *  Calibration error: maximal uncertainty;

   Following is the information of each statistic that should be
   reported:

   o  Result;
   o  Start_time;
   o  Duration;
   o  Result_status;
   o  Singleton_number, the number of singletons the statistic is
      computed on;

10.

11.  Security Considerations

   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 [RFC2679] , in packet loss metrics definitions of
   [RFC2680] and in IPDV metrics definitions of[RFC3393] and [RFC3432]
   apply to metrics defined in this memo.

10.1.

11.1.  Spatial metrics

   Malicious generation of packets with spoofing addresses may corrupt
   the results without any possibility to detect the spoofing.

   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.

10.2.  one-to-group metric

11.2.  One-to-group metrics

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

   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.

   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.

11.

12.  Acknowledgments

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

12.

13.  IANA Considerations

   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 [RFC4148] :

   IANA is asked to register the following metrics in the IANA-IPPM-
   METRICS-REGISTRY-MIB :

   ietfSpatialOneWayDelayVector OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Spatial-One-way-Delay-Vector"
      REFERENCE
         "Reference "RFCyyyy, section 4.1." 5.1."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSpatialPacketLossVector OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Spatial-Packet-Loss-Vector"
      REFERENCE
         "Reference "RFCyyyy, section 4.2." 5.2."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSpatialOneWayIpdvVector OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Spatial-One-way-ipdv-Vector"
      REFERENCE
         "Reference "RFCyyyy, section 4.3." 5.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSegmentOneWayDelayStream OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Segment-One-way-Delay-Stream"
      REFERENCE
         "Reference "RFCyyyy, section 5.1." 6.1."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSegmentPacketLossStream OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Segment-Packet-Loss-Stream"
      REFERENCE
         "Reference "RFCyyyy, section 5.2." 6.2."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSegmentOneWayIpdvPrevStream

   ietfSegmentIpdvPrevStream OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Segment-One-way-ipdv-prev-Stream"
         "Type-P-Segment-ipdv-prev-Stream"
      REFERENCE
         "Reference "RFCyyyy, section 5.3." 6.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSegmentOneWayIpdvMinStream

   ietfSegmentIpdvMinStream OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-Segment-One-way-ipdv-min-Stream"
         "Type-P-Segment-ipdv-min-Stream"
      REFERENCE
         "Reference "RFCyyyy, section 5.4." 6.4."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   -- One-to-group metrics

   ietfOneToGroupOneWayDelayVector

   ietfOneToGroupDelayVector OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-group-One-way-Delay-Vector"
         "Type-P-One-to-group-Delay-Vector"
      REFERENCE
         "Reference "RFCyyyy, section 6.1." 7.1."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupOneWayPktLossVector

   ietfOneToGroupPacketLossVector OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-One-way-Packet-Loss-Vector"
         "Type-P-One-to-group-Packet-Loss-Vector"
      REFERENCE
         "Reference "RFCyyyy, section 6.2." 7.2."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupOneWayIpdvVector

   ietfOneToGroupIpdvVector OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-One-way-ipdv-Vector"
         "Type-P-One-to-group-ipdv-Vector"
      REFERENCE
         "Reference "RFCyyyy, section 6.3." 7.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   -- One to group statistics

   --

   ietfOnetoGroupReceiverNMeanDelay OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Receiver-n-Mean-Delay"
         "Type-P-One-to-group-Receiver-n-Mean-Delay"
      REFERENCE
         "Reference "RFCyyyy, section 7.3.1." 8.3.1."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupMeanDelay OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Mean-Delay"
         "Type-P-One-to-group-Mean-Delay"
      REFERENCE
         "Reference "RFCyyyy, section 7.3.2." 8.3.2."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn
   ietfOneToGroupRangeMeanDelay OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Range-Mean-Delay"
         "Type-P-One-to-group-Range-Mean-Delay"
      REFERENCE
         "Reference "RFCyyyy, section 7.3.3." 8.3.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupMaxMeanDelay OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Max-Mean-Delay"
         "Type-P-One-to-group-Max-Mean-Delay"
      REFERENCE
         "Reference "RFCyyyy, section 7.3.4." 8.3.4."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupReceiverNLossRatio OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Receiver-n-Loss-Ratio"
         "Type-P-One-to-group-Receiver-n-Loss-Ratio"
      REFERENCE
         "Reference "RFCyyyy, section 7.4.1." 8.4.1."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn
   --

   ietfOneToGroupReceiverNCompLossRatio OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Receiver-n-Comp-Loss-Ratio"
         "Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio"
      REFERENCE
         "Reference "RFCyyyy, section 7.4.2." 8.4.2."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupLossRatio OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Loss-Ratio"
         "Type-P-One-to-group-Loss-Ratio"
      REFERENCE
         "Reference "RFCyyyy, section 7.4.3." 8.4.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn
   --

   ietfOneToGroupRangeLossRatio OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Range-Loss-Ratio"
         "Type-P-One-to-group-Range-Loss-Ratio"
      REFERENCE
         "Reference "RFCyyyy, section 7.4.4." 8.4.4."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfOneToGroupRangeDelayVariation OBJECT-IDENTITY
      STATUS current
      DESCRIPTION
         "Type-P-One-to-Group-Range-Delay-Variation"
         "Type-P-One-to-group-Range-Delay-Variation"
      REFERENCE
         "Reference "RFCyyyy, section 7.5.1." 8.5.1."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note
      := { ianaIppmMetrics nn } -- IANA assigns nn

   --

13.

14.  References

13.1.

14.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2679]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Delay Metric for IPPM", RFC 2679, September 1999.

   [RFC2680]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Packet Loss Metric for IPPM", RFC 2680, September 1999.

   [RFC3393]  Demichelis, C. and P. Chimento, "IP Packet Delay Variation
              Metric for IP Performance Metrics (IPPM)", RFC 3393,
              November 2002.

   [RFC4148]  Stephan, E., "IP Performance Metrics (IPPM) Metrics
              Registry", BCP 108, RFC 4148, August 2005.

13.2.

14.2.  Informative References

   [I-D.ietf-ippm-spatial-composition]
              Morton, A. and E. Stephan, "Spatial Composition of
              Metrics", draft-ietf-ippm-spatial-composition-07 (work in
              progress), July 2008.

   [RFC2330]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
              "Framework for IP Performance Metrics", RFC 2330,
              May 1998.

   [RFC3432]  Raisanen, V., Grotefeld, G., and A. Morton, "Network
              performance measurement with periodic streams", RFC 3432,
              November 2002.

Authors' Addresses

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

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

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

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

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

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

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