Network Working Group                                         E. Stephan
Internet-Draft                                            France Telecom
Intended status: Informational                                  L. Liang
Expires: May 21, August 17, 2008                            University of Surrey
                                                               A. Morton
                                                               AT&T Labs
                                                       November 18, 2007
                                                       February 14, 2008

        IP Performance Metrics (IPPM) for spatial and multicast
                    draft-ietf-ippm-multimetrics-05
                    draft-ietf-ippm-multimetrics-06

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Copyright Notice

   Copyright (C) The IETF Trust (2007). (2008).

Abstract

   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).

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  6
     2.1.  Path Digest Hosts  . . . . . . . . . . . . . . . . . . . .  6
     2.2.  Multiparty metric  . . . . . . . . . . . . . . . . . . . .  6
     2.3.  Spatial metric . . . . . . . . . . . . . . . . . . . . . .  6
     2.4.  One-to-group metric  . . . . . . . . . . . . . . . . . . .  6
     2.5.  Points of interest . . . . . . . . . . . . . . . . . . . .  6  7
     2.6.  Reference point  . . . . . . . . . . . . . . . . . . . . .  8
     2.7.  Vector . . . . . . . . . . . . . . . . . . . . . . . . . .  8
     2.8.  Matrix . . . . . . . . . . . . . . . . . . . . . . . . . .  9
   3.  Motivations  . . . . . . . . . . . . . . . . . . . . . . . . .  9
     3.1.  Motivations for spatial metrics  . . . . . . . . . . . . .  9
     3.2.  Motivations for One-to-group metrics . . . . . . . . . . . 10
     3.3.  Discussion on Group-to-one and Group-to-group metrics  . . 11
   4.  Spatial vectors metrics definitions  . . . . . . . . . . . . . 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 . . . . . . . 15
     4.4.  Spatial Methodology  . . . . . . . . . . . . . . . . . . . 17 16
   5.  Spatial Segments metrics definitions . . . . . . . . . . . . . 19 18
     5.1.  A Definition of a sample of One-way Delay of a segment
           of the path  . . . . . . . . . . . . . . . . . . . . . . . 19 18
     5.2.  A Definition of a sample of Packet Loss of a segment
           of the path  . . . . . . . . . . . . . . . . . . . . . . . 20
     5.3.  A Definition of a sample of One-way Ipdv ipdv of a segment
           of using
           the path  . . previous packet selection function . . . . . . . . . . 22
     5.4.  A Definition of a sample of ipdv of a segment  using
           the minimum delay selection function . . . . . . . . . . . 23 24
   6.  One-to-group metrics definitions . . . . . . . . . . . . . . . 23 25
     6.1.  A Definition for one-to-group One-to-group One-way Delay  . . . . . . . 23 26
     6.2.  A Definition for one-to-group One-to-group One-way Packet Loss  . . . . 24 26
     6.3.  A Definition for one-to-group One-to-group One-way Ipdv . . . . . . . . 25 27
   7.  One-to-Group Sample Statistics . . . . . . . . . . . . . . . . 26 28
     7.1.  Discussion on the Impact of packet loss on statistics  . . 29 31
     7.2.  General Metric Parameters  . . . . . . . . . . . . . . . . 30 32
     7.3.  One-to-Group one-way Delay Statistics  . . . . . . . . . . 31 33
     7.4.  One-to-Group one-way Loss Statistics . . . . . . . . . . . 33 36
     7.5.  One-to-Group one-way Delay Variation Statistics  . . . . . 35 38
   8.  Measurement Methods: Scaleability Scalability and Reporting . . . . . . . 35 . 38
     8.1.  Computation methods  . . . . . . . . . . . . . . . . . . . 36 39
     8.2.  Measurement  . . . . . . . . . . . . . . . . . . . . . . . 37 40
     8.3.  Effect of Time and Space Aggregation Order on Stats  . . . 37 40
   9.  Manageability Considerations . . . . . . . . . . . . . . . . . 39 42
     9.1.  Reporting spatial metric . . . . . . . . . . . . . . . . . 39 42
     9.2.  Reporting One-to-group metric  . . . . . . . . . . . . . . 40 43
     9.3.  Metric identification  . . . . . . . . . . . . . . . . . . 41 44
     9.4.  Reporting data model . . . . . . . . . . . . . . . . . . . 41 44
   10. Open issues  . . . . . . . . . . . . . . . . . . . . . . . . . 44 47
   11. Security Considerations  . . . . . . . . . . . . . . . . . . . 45 47
     11.1. Spatial metrics  . . . . . . . . . . . . . . . . . . . . . 45 48
     11.2. one-to-group metric  . . . . . . . . . . . . . . . . . . . 45 48
   12. Acknowledgments  . . . . . . . . . . . . . . . . . . . . . . . 45 48
   13. IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 46 48
   14. References . . . . . . . . . . . . . . . . . . . . . . . . . . 51 54
     14.1. Normative References . . . . . . . . . . . . . . . . . . . 51 54
     14.2. Informative References . . . . . . . . . . . . . . . . . . 51 55
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 52 55
   Intellectual Property and Copyright Statements . . . . . . . . . . 54 57

1.  Introduction

   The IP Performance Metrics (IPPM) WG has defined a framework for
   metric definitions and end-to-end, or source to destination
   measurements:

   o  A general framework for defining performance metrics, described in
      the Framework for IP Performance Metrics [RFC2330];

   The Working Group has specified a set of end-to-end metrics using the
   framework, and a registry for the metrics:

   o  The IPPM Metrics for Measuring Connectivity [RFC2678];

   o  The One-way Delay Metric for IPPM [RFC2679];

   o  The One-way Packet Loss Metric for IPPM [RFC2680];

   o  The Round-trip Delay Metric for IPPM [RFC2681];

   o  A Framework for Defining Empirical Bulk Transfer Capacity Metrics
      [RFC3148];

   o  One-way Loss Pattern Sample Metrics [RFC3357];

   o  IP Packet Delay Variation Metric for IPPM [RFC3393];

   o  Network performance measurement for periodic streams [RFC3432];

   o  Packet Reordering Metrics [RFC4737];

   o  An IP Performance Metrics Registry [RFC4148];

   IPPM has also developed a protocol for one-way source to destination
   measurements

   o  A One-way Active Measurement Protocol Requirements [RFC3763];

   o  A One-way Active Measurement Protocol (OWAMP) [RFC4656];

   This memo defines two new categories of metrics that extend the
   coverage to multiple measurement points.  It first defines spatial
   metrics for measuring the performance of segments of a source to
   destination path:

   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 a nested set of one-way delay metrics over time between the source,
      intermediate two points of interest, and
      interest of the destination; 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 a nested set of packet loss metrics over time between the source,
      intermediate two points of interest, and
      interest of the destination; path;

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

   o  Using the source, intermediate Type-P-Spatial-One-way-Delay-Vector metric, a 'sample',
      called Type-P-Segment-ipdv-min-Stream, will be introduced to
      compute ipdv metrics over time between two points of
      interest, and interest of
      the path using the destination; shortest delay selection function;

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

   Next, this memo defines one-to-group metrics.

   o  Using one test packet sent from one sender to a group of
      receivers, a metric called Type-P-one-to-group-One-way-Delay-
      Vector will be introduced to collect the set of Type-P-one-way-
      delay [RFC2679] singletons between this sender and the group of
      receivers.

   o  Using one test packet sent from one sender to a group of
      receivers, a metric called Type-P-one-to-group-One-way-Packet-
      Loss-Vector, will be introduced to collect the set of Type-P-One-
      way-Packet-Loss [RFC2680] singletons between this sender and the
      group of receivers
   o  Using one test packet sent from one sender to a group of
      receivers, a metric 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 this sender and the group of receivers

   o  A discussion section presents the set of statistics that may be
      computed using these metrics to present the network performance in
      the view of a group of users.  The statistics may be the basis for
      requirements (e.g. fairness) on multiparty communications. .

   Metric Reporting is defined in the "Manageability Considerations"
   section.

2.  Terminology

2.1.  Path Digest Hosts

   The list of the hosts on a path from the source to the destination.

2.2.  Multiparty metric

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

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

2.3.  Spatial metric

   A metric is said to be spatial if one of the hosts (measurement
   collection points) involved is neither the source nor the a destination
   of the measured packet.

2.4.  One-to-group metric

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

2.5.  Points of interest

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

   Points of interest of One-to-group 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 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 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 points of interest

2.6.  Reference point

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

2.7.  Vector

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

2.8.  Matrix

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

   The relation among Singleton, Vector and Matrix can be shown in the
   following Figure 3.

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

                                Vector           Matrix
                               (space)           (time)

         Figure 3: Relation beween Singletons, vectors and matrix

3.  Motivations

   All IPPM metrics are defined for end-to-end (source to destination)
   measurement of point-to-point paths.  It is a logical extension to
   define metrics for multiparty measurements such as one to one
   trajectory metrics and one to multipoint metrics.

3.1.  Motivations for spatial metrics

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

   o  Decomposing the performance of interdomain path is desirable to
      quantify the per-AS contribution to the performance.  It is
      valuable to define standard spatial metrics before pursuing inter-
      domain path performance specifications.

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

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

   o  Composition of metrics [I-D.ietf-ippm-spatial-composition] is
      needed to help measurement systems reach large scale coverage.
      Spatial measure measures typically give the individual performance of an
      intra domain segment and provide an elementary piece of
      information needed to estimate interdomain performance based on
      composition of metrics.

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

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

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

   o  For evaluating and controlling of the quality of the multicast
      services;

   o  For controlling the performance of the inter domain multicast
      services;

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

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

3.3.  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 group-to-one and Group-to-group group-to-group topologies.  These
   topologies are currently beyond the scope of this memo, because they
   would involve multiple packets launched from different sources.
   However, we can give some clues here on these two cases.

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

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

4.  Spatial vectors metrics definitions

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

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

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

4.1.  A Definition for Spatial One-way Delay Vector

   This section is coupled with the definition of Type-P-One-way-Delay. Type-P-One-way-Delay
   of the section 3 of [RFC2679].  When a parameter from section 3 of [RFC2679] is this definitionis
   first used in this section, it 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 involved in the measure.
   Spatial one-way-delay measurement SHOULD be respectful of them,
   especially those related to methodology, clock, uncertainties and
   reporting.

   Following we adapt some of them and introduce points specific to
   spatial measurement.

4.1.1.  Metric Name

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

4.1.2.  Metric Parameters

   o  Src*, the IP address of the sender.

   o  Dst*, the IP address of the receiver.

   o  i, An integer if in the ordered list <1,2,...,n> which ordered the of hosts in the
      path.

   o  Hi, A host* of the path digest.

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

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

   o  <dT1,..., dTn> a list of delay.

   o  P*, the specification of the packet type.

   o  <H1, H2,..., Hn>, hosts path digest.

4.1.3.  Metric Units

   A

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

4.1.4.  Definition

   Given a Type-P packet sent by the sender Src at wire-time (first bit)
   T to the receiver Dst in the path <H1, H2,..., Hn>.  Given the
   sequence of values <T+dT1,T+dT2,...,T+dTn,T+dT> such that dT is the
   Type-P-One-way-Delay from Src to Dst and such that for each Hi of the
   path, T+dTi is either a real number corresponding to the wire-time
   the packet passes (last bit received) Hi, or undefined if the packet
   never passes Hi.

   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.  Discussion

   Following are specific issues which may occur:

   o  the delay looks to decrease: dTi > DTi+1.  This seem typically du may occur despite
      it does not make sense per definition:

      *  This is frequently due to some clock synchronisation synchronization issue.
         This point is discussed in the section 3.7.1.  "Errors or
         uncertainties related to Clocks" of
      of [RFC2679].  One consequence of these uncertainties is that  Consequently,
         times of a measure at different hosts shall do not be used to order guaranty the
         ordering of the hosts on the path of a measure;

   o measure.

      *  During some change of routes the order of 2 hosts may change on
         the main path;

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

4.2.  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 a parameter from the section 2 of [RFC2680] is first
   used in this section, it 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 one-way packet loss measurements.  They are
   applicable to each point of interest Hi involved in the measure.
   Spatial packet loss measurement SHOULD be respectful of them,
   especially those related to methodology, clock, uncertainties and
   reporting.

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

4.2.1.  Metric Name

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

4.2.2.  Metric Parameters

    +

   o  Src*, the IP address of the sender.

    +

   o  Dst*, the IP address of the receiver.

    +

   o  i, An an integer which ordered the hosts in the path.

    +

   o  Hi, exchange points of interests of the path digest.

    +

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

    + dT1,...,

   o  <dT1,..., dTn, dT, dT>, a list of delay.

    +

   o  P*, the specification of the packet type.

    + <SH1,

   o  <H1, H2,..., Hn>, hosts path digest.

    + B1, B2, ..., Bi, ..., Bn,

   o  <L1, L2, ...,Ln>, a list of Boolean values.

4.2.3.  Metric Units

   A

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

4.2.4.  Definition

   Given a Type-P packet sent by the sender Src at time T to the
   receiver Dst in the path <H1, H2, ..., Hn>.  Given the sequence of
   times <T+dT1,T+dT2,...,T+dTn,T+dT> <T+dT1,T+dT2,...,T+dTn> the packet passes in <H1, H2 ..., Hn,
   Dst>, Hn>,
   we define Type-P-One-way-Packet-Lost-Vector metric is defined as the sequence of
   values <B1, B2, <L1, L2, ..., Bn> Ln> such that for each Hi of the path, a value
   of Bi of 0 for Li means that dTi is a finite value, and a value of 1 means
   that dTi is undefined.

4.2.5.  Discussion

   Following are specific issues which may occur:

   o  the  The result includes the sequence 1,0.  This case means that the may occur under
      specific situations:

      *  During some change of routes a packet was may be seen by a host but
         not by it successor on the main path;

   The location of the point of interest in the device influences the
   result:

   o  Even if the

      *  A packet is received by a host, it may be not be observed
      by in a host due to some buffer or
         CPU overflow in the point of interest located after a buffer; interest;

4.3.  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] is first used in
   this section, it will be tagged with a trailing asterisk.

   Following

   In the following we adapt some of them and introduce points specific which
   are
   to spatial measurement.

4.3.1.  Metric Name

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

4.3.2.  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, exchange points A host* of the path digest.

        +

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

        + measured packet.

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

        + P, measured packet.

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

   o  P*, the specification of the packet packets type.

        +

   o  P1, the first packet sent at time T1.

        +

   o  P2, the second packet sent at time T2.

        +

   o  <H1, H2,..., Hn>, host hosts path digest.

        +

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

        + T1.

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

        + 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.  Metric Units

   A

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

4.3.4.  Definition

   Given P1 the Type-P packet having the size L and sent by the sender Src at wire-time (first
   bit) T1 to the receiver Dst in 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 having the size L and sent by the sender Src at wire-time (first
   bit) T2 to the receiver Dst in and <T2, dT2.1, dT2.2,..., dT2.n, dT2>
   its Type-P-Spatial-One-way-Delay-Vector over the same path.

   Given the Type-P-Spatial-One-way-Delay-Vector <T1,dT1.1, dT1.2,...,
   dT1,n,dT1> of the packet P1.

   Given the Type-P-Spatial-One-way-Delay-Vector <T2,dT2.1, dT2.2,...,
   dT2,n,dT2> of the packet P2.

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

4.4.  Spatial Methodology

   Methodology, reporting and uncertainties points specified in section
   3 of [RFC2679][RFC2679] [RFC2679] applies to each point of interest Hi measuring a
   element of a spatial delay vector.

   Methodology, reporting and uncertainties points specified in section
   2 of [RFC2680][RFC2680] [RFC2680] applies to each point of interest Hi measuring a
   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 involved in the measure.
   Spatial One-way ipdv measurement SHOULD be respectful of methodology,
   clock, uncertainties and reporting aspects given in this section.

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

   o  At each Hi, points of interest prepare to capture the packet sent
      a time T, take a timestamp Ti', determine the internal delay
      correction dTi' (See section 3.7.1.  "Errors or uncertainties
      related to Clocks" of [RFC2679]),

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

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

   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 and time-to-live of each Hi and order them
      according to the path ordering information received to build the Type-P-Spatial-
      One-way-Delay-Vector metric <T,dT1,dT2,...,dTn,dT>
      type-P spatial one-way vector (e.g.  Type-P-Spatial-One-way-Delay-
      Vector metric <T, dT1, dT2,..., dTn, dT> ) over the path
      <Src,H1, <Src, H1,
      H2,..., Hn, Dst>. Dst> at time T.

4.4.1.  Loss threshold

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

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

4.4.2.  Host Path Digest

   The methodology given above adds relies on the order of the points of
   interest over the path to [RFC2679] one's.

   A perfect Host Path Digest (hum! of cource from test packets may cross several times the measurement point same host resulting in the
   repetition of view only, that is, corresponding to one or several hosts in the real path Path Digest.

   As an example.  This occurs typically during rerouting phases which
   introduce temporary micro loops.  During such an event the test host path
   digest for a packet
   experimented) crossing Ha and Hb may include several times several hosts:

   o  <Ha,..., Ha> coresponds the pattern <Hb,
   Ha, Hb, Ha, Hb> meaning that Ha ended the computation of the new path
   before Hb and that the initial path wath from Ha to a loop in Hb and that the path;

   o  <Ha,..,Hb,..., Ha,...,Hb> coresponds
   new path is from Hb to a loop Ha.

   Consequently, duplication of hosts in the path which
      may occurs during rerouting phases;

   These cases Path Digest of a vectors
   MUST be identified before statistics computation to avoid corrupted
   results' production.  This applies especially to the
   measure of segments which are build from results of a measure of a
   vector metric.

5.  Spatial Segments metrics definitions

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

   Firstly it defines a sample of one-way delay, Type-P-Segment-One-way-
   Delay-Stream, and a sequence sample of ipdv between packet loss, Type-P-segment-Packet-
   loss-Stream.

   Then it defines 2 hosts different samples of ipdv.  The first metric, Type-
   P-Segment-One-way-ipdv-prev-Stream, uses the path,
   a segment.  Singletons are taken from segments of vectors defined
   above. previous packet as the
   selection function.  The second metric, Type-P-Segment-One-way-ipdv-
   min-Stream, uses the minimum delay as the selection.

5.1.  A Definition of a sample of One-way Delay of a segment of the path

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

   As its semantic is very close to the metric Type-P-Packet-loss-Stream
   defined in section 4 of [RFC2679], sections 4.5 to 4.8 of [RFC2679]
   are part of the current definition.

5.1.1.  Metric Name

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

5.1.2.  Metric Parameters

        +

   o  Src*, the IP address of the sender.

        +

   o  Dst*, the IP address of the receiver.

        +

   o  P*, the specification of the packet type;

        + type.

   o  i, An an integer which orders exchange points in the path.

        + ordered list <1,2,...,n> of hosts in the
      path.

   o  k, An an integer which orders the packets sent.

        +

   o  a and b, 2 integers where b > a.

   o  Hi, a host host* of the path digest;

        + <H1, H2,..., Hn>, host path digest.

        +

   o  <H1,..., Ha, a host of the path digest different from Dst and Hb;

        + ..., Hb, a host of the path digest different from Src and Ha.
          Hb order in the ...., Hn>, hosts path must greater that Ha;

        + digest.

   o  <T1, T2, ..., Tk>, a list of time ordered by k;

        + dT1,..., dTn Tm>, a list of delay; times.

5.1.3.  Metric Units

   A

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

      list of times <T1, T2, ..., Tm>;

      sequence of delay delays.

5.1.4.  Definition

   Given 2 hosts hosts, Ha and Hb Hb, of the path <Src, H1, <H1, H2,..., Hn, Dst>, Ha, ..., Hb, ...,
   Hn>, given
   a flow the matrix of Type-P-Spatial-One-way-Delay-Vector for the
   packets of Type-P sent from Src to Dst at the times T1,
   T2...  Tn.  At each of these times, we obtain a Type-P-Spatial-One-
   way-Delay-Vector <T1,dT1.a, <T1, T2, ..., Tm-1, Tm> :

      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>;

      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT1.b,...,, dT1.n,dT1>. dT2.b,..., dT2.n, dT2>;

      ...

      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.

   We define the value of the sample Type-P-segment-One-way-Delay-Stream as the
   sequence made up of the delays dTk.b - dTk.a. dTk.a is the delay
   between Src and Ha. dTk.b <dT1.ab, dT2.ab, ..., dTk.ab, ..., dTm.ab> such that for
   each time Tk, 'dTk.ab' is either the delay between Src and Hb. real number 'dTk.b - dTk.a' is the one-way delay experienced by if
   the packet sent by Src at
   the send a time Tk when going from passes Ha to and Hb or undefined if this
   packet never passes Ha or (inclusive) never passes Hb.

5.1.5.  Discussion

   Following are specific issues which may occur:

   o  When a is Src <Tk,dTk.b - dTk.a> is the measure of the first hop.

   o  When b is Dst <Tk,dTk.b - dTk.a> is the measure of the last hop.

   o  the delay looks to decrease: dTi > DTi+1:

      *  This is typically du due to clock synchronisation synchronization issue. this
         point is discussed in the section 3.7.1.  "Errors or
         uncertainties related to Clocks" of of [RFC2679];

      *  This may occurs too when the clock resolution of one probe is
         bigger than the minimum delay of a path.  As an example this
         happen when measuring the delay of a path which is 500 km long
         with one probe synchronized using NTP having a clock resolution
         of 8ms.

   o

   The location of the point of interest in the device influences the
      result.  If the packet is metric can not observed be performed on < T1 , T2, ..., Tm-1, Tm> in the input interface the
      delay includes buffering time and consequently an uncertainty
   following cases:

   o  Ha or Hb disappears from the path due to the difference between 'wire time' and 'host time'; some change of routes;

   o  dTk.b may be observed  The order of Ha and not dTk.a. Hb changes in the path;

5.2.  A Definition of a sample of Packet Loss of a segment of the path

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

5.2.1.  Metric Name

   Type-P-segment-Packet-loss-Stream

5.2.2.  Metric Parameters

         +

   o  Src*, the IP address of the sender.

         +

   o  Dst*, the IP address of the receiver.

         +

   o  P*, the specification of the packet type.

         +

   o  k, An an integer which orders the packets sent.

         +

   o  n, An an integer which orders the hosts on the path.

         + <H1, H2,..., Hn>, hosts path digest.

         + Ha,

   o  a host of the path digest different from Dst and Hb;

         + b, 2 integers where b > a.

   o  <H1, H2, ..., Ha, ..., Hb, a host of the path digest different from Src and Ha.
          Hb order in the ...,Hn>, hosts path must greater that Ha;

         + digest.

   o  Hi, exchange points of the path digest.

         + <B1, B2,

   o  <T1, T2, ..., Bn> Tm>, a list of bits.

         + times.

   o  <L1, L2, ..., Ln> a list of integers. boolean values.

5.2.3.  Metric Units

   A

   The value of a Type-P-segment-Packet-loss-Stream is a pair of

      The list of times <T1, T2, ..., Tm>;

      a sequence of integers <L1, L2,..., Lk> booleans.

5.2.4.  Definition

   Given 2 hosts hosts, Ha and Hb Hb, of the path <Src, H1, <H1, H2,..., Hn, Dst>, Ha, ..., Hb, ...,
   Hn>, given
   a flow the matrix of Type-P-Spatial-Packet-loss-Vector for the
   packets of Type-P sent from Src to Dst at the times T1,
   T2...  Tn.  At each of these times, we obtain a Type-P-Spatial-
   Packet-Lost-Vector <B1.1, B1.2,..., B1.n>. <T1, T2, ..., Tm-1, Tm> :

      <L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L>,

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

      ...,

      <Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L>.

   We define the value of the sample Type-P-segment-Packet-Lost-Stream between
   from Ha and to Hb as the sequence made up of the integer <L1, L2,..., Lk> booleans <L1.ab, L2.ab,..., Lk.ab,
   ..., Lm.ab> such that for each Tk:

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

   o  a  A value of Lk of 1 means that Bk.a Ha observed the packet sent at time
      Tk (Lk.a has a value of 0 (observed) 0) and that Bk.b Hb did not observed the packet
      sent at time Tk (Lk.b have a value of 1 (not observed); 1);
   o  a  The value of Lk is undefined when Neither Ha or Hb observe the
      packet;

5.2.5.  Discussion

   Unlike Type-P-Packet-loss-Stream, Type-P-Segment-Packet-loss-Stream
   relies on the stability of 2 means that Bk.a the host path digest.  The metric can not
   be performed on < T1 , T2, ..., Tm-1, Tm> in the following cases:

   o  Ha or Hb disappears from the path due to some change of routes;

   o  the order of Ha and Hb changes in the path;

   o  Lk.a or Lk.b is undefined;

   o  Lk.a has a the value of 1 (not observed) and that Bk.b have a Lk.b has the value of 0
      (observed);

   o  a value of Lk of 3 means that Bk.a  L has a value of 1 (not observed)
      and that Bk.b have a value of 1 (not observed).

5.2.5.  Discussion

   The semantic of a Type-P-segment-Packet-loss-Stream is similar to the
   one of Type-P-Packet-loss-Stream:

   o  a value of 0 means that the (the packet was observed by Ha (similar to
      'send by Src') and not observed by Hb ( similar to 'not received by Dst');

   o  a Dst) and Lk.ab has
      the value of 1 means that it (the packet was observed by lost between Ha (similar to 'send by
      Src') and observed by Hb ( similar to 'received by Dst').

   This definition Hb).

5.3.  A Definition of Type-P-segment-Packet-loss-Stream is similar to
   the Type-P-Packet-loss-Stream defined in [RFC2680] excepted that in a
   Type-P-segment-Packet-loss-Stream the rules sample of the point ipdv of interests
   Ha and Hb are symetrical: The asumption that a set of packets are
   going from Ha to Hb does not apply to Type-P-segment-Packet-loss-
   Stream because as segment using the host path digest is dynamic each previous
      packet has its
   own host path digest.

   Making the asumption that the host path digest of selection function

   This metric defines a Type-P-spatial-
   Packet-loss-vector does not change and that the set sample of (Hk, Hk+1)
   tuples is mostly stable ipdv [RFC3393] over time lead to unusable results and to the
   introduction between a
   pair of mistakes in hosts using the metrics aggregation processes.  The
   right approach consists in carefully scrutening previous packet as the path ordering
   information to build sample with elements selection function.

5.3.1.  Metric Name

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

5.3.2.  Metric Parameters

   o  Src*, the IP address of vectors sharing the same
   properties in term sender.

   o  Dst*, the IP address of the receiver.

   o  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 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.  Metric Units

   The value of a Type-P-Segment-One-way-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.  Definition

   Given 2 hosts, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb, ...,
   Hn>, given the matrix of Type-P-Spatial-One-way-Delay-Vector for the
   packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :

      <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 as the sequence
   of pair of packet intervals and delay variations <(dT2_1.a , dT2.ab -
   dT1.ab) ,..., (dTk_k-1.a, dTk.ab - dTk-1.ab), ..., (dTm_m-1.a, dTm.ab
   - dTm-1.ab)> such that for each Tk:

   o  dTk_k-1.a is either undefined if the delay dTk.a or the delay
      dTk-1.a is undefined, or the interval of time, 'dTk.a - dTk-1.a',
      between the 2 packets at Ha;

   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, 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.  Discussion

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

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

5.4.  A Definition of a sample of ipdv of a segment  using the minimum
      delay selection function

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

5.4.1.  Metric Name

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

5.4.2.  Metric Parameters

   o  Src*, the IP address of the sender.

   o  Dst*, the IP address of the receiver.

   o  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 'Ha to Hb'.  So b, 2 integers where b > a.

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

   o  <T1, T2, ..., Tm-1, Tm>, a measure list of
   Type-P-spatial-Packet-loss-vector differs from times.

   o  <Tk, dTk.1, dTk.2, ..., dTk.a, ..., dTk.b,..., dTk.n, dTk>, a Type-P-Packet-loss
   one in that it produces different samples of packet loss over time.
      Type-P-Spatial-One-way-Delay-Vector.

5.4.3.  Metric Units

   The semantic value of a Type-P-segment-Packet-loss-Stream defines 2 new
   results:

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

      The list of Lk <T1, T2, ..., Tm-1, Tm>;
      A list of times;

5.4.4.  Definition

   Given 2 (1,0) corresponds to a mistake in the ordering
      of hosts, Ha and Hb over Hb, of the path coming either from <H1, H2,..., Ha, ..., Hb, ...,
   Hn>, given the configuration
      (asumption on matrix of Type-P-Spatial-One-way-Delay-Vector for the path) or
   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 processing 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:

      min(dTi.ab) is the vectors: bad
      scrutening minimum value of the path ordering information, tuples (dTk.b - dTk.a);

      for each time Tk, dTk.ab is undefined if dTk.a or some other mistake
      in the measure (inclusive)
      dTk.b is undefined, or the reporting.  It is not in real number (dTk.b - dTk.a).

5.4.5.  Discussion

   This metric belongs to the scope family of this
      document to go in further details which packet delay variation metrics
   (PDV).  PDV distributions are mostly implementation
      dependent.  This value MUST not be used less sensitive to compute packet lost
      statistics.

   o  A value of Lk of 3 (1,1) corresponds inter-packet interval
   variations than IPDV results.

   In principle, the PDV distribution reflects the variation over many
   different inter-packet intervals, from the smallest inter-packet
   interval, up to a lost the length of the evaluation interval, Tm - T1.
   Therefore, when delay variation occurs and disturbs the packet in
      upper segment of
   spacing observed at Ha, the path.

5.3.  A Definition of a sample of One-way Ipdv of PDV results will likely compare favorably
   to a segment of PDV measurement where the source is Ha and the path destination is
   Hb.

6.  One-to-group metrics definitions

   This metric defines a sample of ipdv metrics to measure the performance between a pair of hosts of
   source and a
   path.

   Editor note: work in progress

5.3.1.  Metric Name

   Type-P-Segment-Ipdv-Stream

5.3.2.  Metric Parameters

5.3.3.  Metric Units

5.3.4.  Definition

5.3.5.  Discussion

6.  One-to-group metrics definitions group of receivers.

6.1.  A Definition for one-to-group One-to-group One-way Delay

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

6.1.1.  Metric Name

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

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

6.1.2.  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.

   o  P, the specification of the packet type.

   o  Gr, the multicast receiving group address (optional). identifier.  The parameter Gr is the
      multicast group address if the measured packets are transmitted by
      over IP multicast.  This parameter is to identify differentiate the
      measured traffic from other unicast and multicast traffic.  It is
      set to be
      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 receivers. receiver.

6.1.3.  Metric Units

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

6.1.4.  Definition

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

6.2.  A Definition for one-to-group One-to-group One-way Packet Loss

6.2.1.  Metric Name

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

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

6.2.2.  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, the specification of the packet type.

   o  Gr, the multicast receiving group address (optional). identifier.

6.2.3.  Metric Units

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

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

6.3.  A Definition for one-to-group One-to-group One-way Ipdv

6.3.1.  Metric Name

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

6.3.2.  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.

   + ddT1,...,ddTn,

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

   +

   o  P, the specification of the packet type.

   +

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

   +

   o  Gr, the multicast receiving group address (optional) identifier.

6.3.3.  Metric Units

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

6.3.4.  Definition

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

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

7.  One-to-Group Sample Statistics

   The defined one-to-group metrics above can all be directly achieved
   from the relevant unicast one-way metrics.  They managed to collect all unicast
   measurement results of one-way metrics together in one profile and
   sort them by receivers and packets in a multicast receiving group.  They can
   provide sufficient information regarding the network performance in
   terms of each receiver and guide engineers to identify potential
   problem happened on each branch of a multicast routing tree.

   However, these metrics can not cannot be directly used to conveniently
   present the performance in terms of a group and neither to identify
   the relative performance situation.

   From the performance point of view, the multiparty communication
   services not only require the absolute performance support but also
   the relative performance.  The relative performance means the
   difference between absolute performance of all users.  Directly using
   the one-way metrics cannot present the relative performance
   situation.  However, if we use the variations of all users one-way
   parameters, we can have new metrics to measure the difference of the
   absolute performance and hence provide the threshold value of
   relative performance that a multiparty service might demand.  A very
   good example of the high relative performance requirement is the
   online gaming.  A very light difference in delay might result in
   failure in the game.  We have to use multicast specific statistic
   metrics to define exactly how small the relative delay the online
   gaming requires.  There are many other services, e.g. online biding,
   online stock market, etc., that require multicast metrics in order to
   evaluate the network against their requirements.  Therefore, we can
   see the importance of new, multicast specific, statistic metrics to
   feed this need.

   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 9. 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 9: 4: Matrix M (n*m)

   In Matrix M, each element is a One-way 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 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.  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 an infinite one-
   way delay.  It is easy to handle the problem by simply ignoring the
   infinite value in the metrics and in the calculation of the
   corresponding statistics.  However, the packet loss has so strong
   impact on the statistics calculation for the one-to-group metrics
   that it can not be solved by the same method used for one-way
   metrics.  This is due to the complex of building a Matrix, which is
   needed for calculation of the statistics proposed in this memo.

   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.  It 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.  General Metric Parameters

   o  Src, the IP address of a host host;

   o  G, the Group IP address receiving group identifier;

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

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

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

   o  K, the number of packets sent from the source during the test
      interval
      interval;
   o  J[n], the number of packets received at a particular Receiver, n,
      where 1<=n<=N 1<=n<=N;

   o  lambda, a rate in reciprocal seconds (for Poisson Streams) Streams);

   o  incT, the nominal duration of inter-packet interval, first bit to
      first bit (for Periodic Streams) 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) Streams);

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

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

   o  dT, shorthand notation for a one-way delay singleton value 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
      Receivers;

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

7.3.  One-to-Group one-way Delay Statistics

   This section defines the overall one-way delay statistics for an
   entire Group or receivers.  For example, we can define the group mean
   delay, as illustrated below.  This is a metric designed to summarize
   the whole matrix.

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

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

                     Figure 10: One-to-GroupGroup 5: One-to-Group Mean Delay

   where:

   R1dT1 is the Type-P-Finite-One-way-Delay singleton evaluated at
   Receiver 1 for packet 1.

   R1DM is the Type-P-Finite-One-way-Delay-Mean evaluated at Receiver 1
   for the sample of packets (1,...K).

   GMD is the mean of the sample means over all Receivers (1, ...N).

7.3.1.  Definition and Metric Units

   Using the parameters above, 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 a finite value in units of seconds.
   Otherwise, the value of the singleton is Undefined.

   For each packet [i] that has a finite One-way Delay at Receiver n (in
   other words, excluding packets which have undefined one-way delay):

   Type-P-Finite-One-way-Delay-Receiver-n-[i] =

   = TstampRecv[i] - TstampSrc[i]

   The units of Finite one-way delay are seconds, with sufficient
   resolution to convey 3 significant digits.

7.3.2.  Sample Mean Statistic

   This section defines the Sample Mean at each of N Receivers.

   Type-P-Finite-One-way-Delay-Mean-Receiver-n = RnDM =
                 J[n]
                  ---
            1     \
           --- *   >   Type-P-Finite-One-way-Delay-Receiver-n-[i]
           J[n]   /
                  ---
                 i = 1

           Figure 11: 6: Type-P-Finite-One-way-Delay-Mean-Receiver-n

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

7.3.3.  One-to-Group Mean Delay Statistic

   This section defines the Mean One-way Delay calculated over the
   entire Group (or Matrix).

   Type-P-One-to-Group-Mean-Delay = GMD =
                                     N
                                    ---
                               1    \
                               - *   >   RnDM
                               N    /
                                    ---
                                   n = 1

                 Figure 12: 7: Type-P-One-to-Group-Mean-Delay

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

7.3.4.  One-to-Group Range of Mean Delays

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

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

7.3.5.  One-to-Group Maximum of Mean Delays

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

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

7.4.  One-to-Group one-way Loss Statistics

   This section defines the overall 1-way loss statistics for an entire
   Group.  For example, we can define the group loss ratio, as
   illustrated below.  This is a metric designed to summarize the entire
   Matrix.

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

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

                     Figure 13: 8: One-to-Group Loss Ratio

   where:

   R1L1 is the Type-P-One-way-Loss singleton (L) evaluated at Receiver 1
   for packet 1.

   R1LR is the Type-P-One-way-Loss-Ratio evaluated at Receiver 1 for the
   sample of packets (1,...K).

   GLR is the loss ratio over all Receivers (1, ..., N).

7.4.1.  One-to-Group Loss Ratio

   The overall Group loss ratio id defined as

   Type-P-One-to-Group-Loss-Ratio =
                                     K,N
                                     ---
                               1     \
                            = --- *   >   L(k,n)
                              K*N    /
                                     ---
                                    k,n = 1

                                 Figure 14 9

   ALL Loss ratios are expressed in units of packets lost to total
   packets sent.

7.4.2.  One-to-Group Loss Ratio Range

   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, RnLR for receiver n, and the Type-P-One-
   way-Loss-Ratio illustrated above are equivalent metrics.  In terms of
   the parameters used here, these metrics definitions can be expressed
   as

   Type-P-One-way-Loss-Ratio-Receiver-n = RnLR =
                                     K
                                    ---
                               1    \
                               - *   >   RnLk
                               K    /
                                    ---
                                   k = 1

              Figure 15: 10: Type-P-One-way-Loss-Ratio-Receiver-n

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

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

7.4.3.  Comparative 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 is defined as

   Type-P-Comp-Loss-Ratio-Receiver-n = RnCLR =
                                    K
                                   ---
                                   \
                                    >   Ln(k)
                                   /
                                   ---
                                   k=1
                      = -----------------------------
                                /    K         \
                                |   ---        |
                                |   \          |
                        K - Min |    >   Ln(k) |
                                |   /          |
                                |   ---        |
                                \   k=1        / N

               Figure 16: 11: Type-P-Comp-Loss-Ratio-Receiver-n

7.5.  One-to-Group one-way Delay Variation Statistics

   There are two delay variation (DV) statistics that summarize the
   performance over the Group: the maximum DV over all receivers and the
   minimum DV over all receivers (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.

8.  Measurement Methods: Scaleability 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 measurement points where a
   stream of singletons will be collected.  The amount of information
   requiring storage grows with both the number of metrics and the
   number of measurement points, 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 aggregation point with connectivity to all the measurement
   points.  In this case, the number of measurement points determines
   both storage capacity and packet transfer capacity of the host acting
   as the aggregation point.  However, both the storage and transfer
   capacity can be reduced if the measurement points 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 measurement point.

   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.  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.  It is out of the scope of this memo.

8.2.  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.  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 samples represented 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 17: 12: Impact of space aggregation on multimetrics Stat

   2 methods are available to compute statistics on the resulting
   matrix:

   o  metric is computed over time and then over space;
   o  metric is computed over space and then over time.

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

   In both cases the volume of data to report is proportional to the
   number of probes.  But there is a major difference between these 2
   methods:

      method2: In space and time aggregation mode the volume of data to
      collect is proportional to the number of test packets received;
      Each received packet RiSi triggers out a block of data that must
      be reported to a common place for computing the stat over space;

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

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

      The increasing of the rate of the test packets may result in a
      sort of DoS toward the computation points;

      The dimensioning of a measurement system is quite impossible to
      validate.

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

   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.  Impact on group stats

   2 methods are available to compute group statistics:

   o  method1: Figure 10 5 andFigure 13 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: Figure 17 12 presents the second one, metric is computed
      over space and then over time.

8.3.2.  Impact on spatial stats

   2 methods are available to compute spatial statistics:

   o  method 1: spatial segment metrics and statistics are preferably
      computed over time by each points of interest;

   o  method 2: Vectors metrics are intrinsically instantaneous space
      metrics which must be reported using method2 whenever
      instantaneous metrics information is needed.

9.  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
   while avoiding repetitions.  The aim is to contribute to the work of
   the WG on the reporting and to satisfy IESG recommendation of
   gathering manageability considerations in a dedicated section.

   Data models of spatial and 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.  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.  Path

   End-to-end metrics can't determine the path of the measure despite
   IPPM RFCs recommend it to be reported (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.  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.  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.  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.  Reporting One-to-group metric

   All reporting rules described in RFC2679-80 apply to the
   corresponding One-to-group metrics RFC2679-80.  In addition, several
   new parameters are needed to report which are common to all the
   metrics and are presented here.

9.2.1.  Path

   As suggested by the RFC2679-80, the path traversed by the packet
   SHOULD be reported, if possible.  For One-to-group metrics, there is
   a path tree SHOULD be reported rather than A path.  This is even more
   impractical.  If, by anyway, partial information is available to
   report, it might not be as valuable as it is in the one-to-one case
   because the incomplete path might be difficult to identify its
   position in the path tree.  For example, how many points of interest
   are reached by the packet traveled through this incomplete path?
   However, the multicast path tree is normally more stable than
   unicast, which is dependant on multicast routing protocols.  For
   example, the PIM-SM protocol [RFC4601] initializes the multicast
   route before any data packets are sent to the receivers.

9.2.2.  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.  Timestamping bias

   It is the same as described in section 9.1.3.

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

   It is the same as described in section 9.1.4.

9.2.5.  Measurement method

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

9.3.  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.

   To avoid misunderstanding and to address specific reporting
   constraints, section [passive_metrics] of this memo gives distinct
   names to passive metrics and Section 13 requests a distinct metric
   identifier for each metrics the memo defines.

   As it is crucial for composition of metrics to know the methodology
   used (e.g. generation method, detection method...), the report of a
   metric result used in composition of metrics MUST always include its
   metric identifier.

9.4.  Reporting data model

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

   The data 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[RFC3393][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 the datamodel 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.  Open issues

   Do we define min, max, avg of for each segment metrics ?

      having the maximum loss metric value could be interesting.  Say,
      the segment between router A and B always contributes loss metric
      value of "1" means it could be the potential problem segment.

      Uploading dTi of each Hi consume a lot of bandwidth.  Computing
      statistics (min, max and avg) of dTi locally in each Hi reduce the
      bandwidth consumption.

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 multimetrics.

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.

11.2.  one-to-group metric

   The reporting of measurement results from a huge number of probes may
   overload the network the reference point is attach to, the reference
   point network interfaces and the reference point computation
   capacities.

   The configuration of a measure 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 attach 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.

12.  Acknowledgments

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

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 :

   Spatial-One-way-Delay-Vector

   ietfSpatialOneWayDelayVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 4.1."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   Spatial-Packet-Loss-Vector

   ietfSpatialPacketLossVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 4.2."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   Spatial-One-way-ipdv-Vector

   ietfSpatialOneWayIpdvVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 4.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   Spatial-Segment-One-way-Delay-Stream

   ietfSpatialSegmentOnewayDelayStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.1."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   Spatial-Segment-Packet-Loss-Stream

   ietfSpatialSegmentPacketLossStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.2."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn
   Spatial-Segment-One-way-ipdv-Stream

   ietfSpatialSegmentOneWayIpdvPrevStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Spatial-Segment-ipdv-Stream"

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

         "Reference "RFCyyyy, section 5.3."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   ietfSpatialSegmentOneWayIpdvMinStream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-Spatial-Segment-ipdv-minStream"

      REFERENCE

         "Reference "RFCyyyy, section 5.4."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   -- One-to-group metrics

   one-to-group-One-way-Delay-Vector

   ietfOneToGroupOneWayDelayVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.1." 6.1."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   one-to-group-One-way-Packet-Loss-Vector

   ietfOneToGroupOneWayPktLossVector OBJECT-IDENTITY
      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.2." 6.2."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   one-to-group-One-way-ipdv-Vector

   ietfOneToGroupOneWayIpdvVector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.3." 6.3."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   One-to-Group-Mean-Delay

   -- One to group statistics

   --

   ietfOneToGroupMeanDelay OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 6.3.3."
         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   One-to-Group-Range-Mean-Delay

   ietfOneToGroupRangeMeanDelay OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 6.3.4."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   One-to-Group-Max-Mean-Delay

   ietfOneToGroupMaxMeanDelay OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 6.3.5."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   One-to-Group-Loss-Ratio

   ietfOneToGroupLossRatio OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

         "Type-P-One-to-Group-Loss-Ratio"
      REFERENCE

         "Reference "RFCyyyy, section 6.4.1."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   --

   One-to-Group-Loss-Ratio-Range

   ietfOneToGroupLossRatioRange OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 6.4.2."

         -- RFC Ed.: replace yyyy with actual RFC number & remove this
         note

      := { ianaIppmMetrics nn } -- IANA assigns nn

   --

14.  References

14.1.  Normative References

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

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

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

   [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.

14.2.  Informative References

   [I-D.ietf-ippm-spatial-composition]
              Morton, A. and E. Stephan, "Spatial Composition of
              Metrics", draft-ietf-ippm-spatial-composition-05 (work in
              progress), November 2007.

   [RFC2678]  Mahdavi, J. and V. Paxson, "IPPM Metrics for Measuring
              Connectivity", RFC 2678, September 1999.

   [RFC2681]  Almes, G., Kalidindi, S., and M. Zekauskas, "A Round-trip
              Delay Metric for IPPM", RFC 2681, September 1999.

   [RFC3148]  Mathis, M. and M. Allman, "A Framework for Defining
              Empirical Bulk Transfer Capacity Metrics", RFC 3148,
              July 2001.

   [RFC3357]  Koodli, R. and R. Ravikanth, "One-way Loss Pattern Sample
              Metrics", RFC 3357, August 2002.

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

   [RFC3763]  Shalunov, S. and B. Teitelbaum, "One-way Active
              Measurement Protocol (OWAMP) Requirements", RFC 3763,
              April 2004.

   [RFC4656]  Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M.
              Zekauskas, "A One-way Active Measurement Protocol
              (OWAMP)", RFC 4656, September 2006.

   [RFC4737]  Morton, A., Ciavattone, L., Ramachandran, G., Shalunov,
              S., and J. Perser, "Packet Reordering Metrics", RFC 4737,
              November 2006.

   [passive_metrics]
              "", 2005.

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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