Network Working Group                                         E. Stephan
Internet-Draft                                            France Telecom
Intended status: Informational                                  L. Liang
Expires: April 25, September 2, 2007                          University of Surrey
                                                               A. Morton
                                                               AT&T Labs
                                                        October 22, 2006
                                                           March 1, 2007

        IP Performance Metrics (IPPM) for spatial and multicast
                    draft-ietf-ippm-multimetrics-02
                    draft-ietf-ippm-multimetrics-03

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Copyright Notice

   Copyright (C) The Internet Society (2006). IETF Trust (2007).

Abstract

   The IETF IP Performance Metrics (IPPM) working group has standardized
   metrics for measuring end-to-end performance between 2 points.  This
   memo defines 2 sets of metrics to extend these end-to-end ones.  It
   defines spatial metrics for measuring the performance of segments
   along a path and metrics for measuring the performance of a group of
   users in multiparty communications.

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3  4
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  5  6
     2.1.  Multiparty metric  . . . . . . . . . . . . . . . . . . . .  5  6
     2.2.  Spatial metric . . . . . . . . . . . . . . . . . . . . . .  5  6
     2.3.  Spatial metric points of interest  . . . . . . . . . . . .  5  6
     2.4.  One-to-group metric  . . . . . . . . . . . . . . . . . . .  5  6
     2.5.  One-to-group metric points of interest . . . . . . . . . .  5  6
     2.6.  Reference point  . . . . . . . . . . . . . . . . . . . . .  5  6
     2.7.  Vector . . . . . . . . . . . . . . . . . . . . . . . . . .  6  7
     2.8.  Matrix . . . . . . . . . . . . . . . . . . . . . . . . . .  6  7
   3.  Motivations for spatial and one-to-group metrics . . . . . . .  7  8
     3.1.  spatial metrics  . . . . . . . . . . . . . . . . . . . . .  7  8
     3.2.  One-to-group metrics . . . . . . . . . . . . . . . . . . .  8  9
     3.3.  Discussion on Group-to-one and Group-to-group metrics  . .  9 10
   4.  Spatial metrics definitions  . . . . . . . . . . . . . . . . .  9 10
     4.1.  A Definition for Spatial One-way Delay Vector  . . . . . . 10
     4.2.  A Definition of a sample of One-way Delay of a sub path  . 12 13
     4.3.  A Definition for Spatial One-way Packet Loss Vector  . . . 15 16
     4.4.  A Definition for Spatial One-way Jitter Vector . . . . . . 16 17
     4.5.  Pure Passive Metrics . . . . . . . . . . . . . . . . . . . 18 19
     4.6.  Discussion on spatial statistics . . . . . . . . . . . . . 20 21
   5.  One-to-group metrics definitions . . . . . . . . . . . . . . . 20 21
     5.1.  A Definition for one-to-group One-way Delay  . . . . . . . 20 21
     5.2.  A Definition for one-to-group One-way Packet Loss  . . . . 21 22
     5.3.  A Definition for one-to-group One-way Jitter . . . . . . . 21
     5.4. 22
   6.  One-to-Group Sample Statistics . . . . . . . . . . . . . . . . 24
     6.1.  Discussion on one-to-group the Impact of packet loss on statistics  . . 26
     6.2.  General Metric Parameters  . . . . . . . . 23
   6.  Extension from one-to-one to one-to-many measurement . . . . . 26 . . . 27
     6.3.  One-to-Group one-way Delay Statistics  . . . . . . . . . . 28
     6.4.  One-to-Group one-way Loss Statistics . . . . . . . . . . . 31
     6.5.  One-to-Group one-way Delay Variation Statistics  . . . . . 33
   7.  Open issues  Measurement Methods: Scaleability and Reporting  . . . . . . . 33
     7.1.  Computation methods  . . . . . . . . . . . . . . . . . . 27
   8.  Security Considerations . 34
     7.2.  Measurement  . . . . . . . . . . . . . . . . . . . 27
   9.  Acknowledgments . . . . 35
     7.3.  effect of  Time and Space Aggregation Order on Group
           Stats  . . . . . . . . . . . . . . . . . . . . . . . 27
   10. IANA . . . 35
     7.4.  effect of  Time and Space Aggregation Order on Spatial
           Stats  . . . . . . . . . . . . . . . . . . . . . . . . . . 37
   8.  Open issues  . . . . . . . . . . . . . . . . . . . . . . . . . 37
   9.  Security Considerations  . . . . . . . . . . . . . . . . . . . 37
     9.1.  passive measurement  . . 27
   11. References . . . . . . . . . . . . . . . . . 37
     9.2.  one-to-group metric  . . . . . . . . . 28
     11.1. Normative References . . . . . . . . . . 37
   10. Acknowledgments  . . . . . . . . . 28
     11.2. Informative References . . . . . . . . . . . . . . 37
   11. IANA Considerations  . . . . 28
   Authors' Addresses . . . . . . . . . . . . . . . . . 38
   12. References . . . . . . . 29
   Intellectual Property and Copyright Statements . . . . . . . . . . 30

1.  Introduction

   The metrics specified in this memo are built on notions introduced
   and discussed in the IPPM Framework document, RFC 2330 . . . . . . . . . 42
     12.1. Normative References . . . . . . . . . . . . . . . . . . . 42
     12.2. Informative References . . . . . . . . . . . . . . . . . . 43
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 43
   Intellectual Property and Copyright Statements . . . . . . . . . . 45

1.  Introduction

   The metrics specified in this memo are built on notions introduced
   and discussed in the IPPM Framework document, RFC 2330 [RFC2330].
   The reader should be familiar with these documents.

   This memo makes use of definitions of end-to-end One-way Delay
   Metrics defined in the RFC 2679 [RFC2679] to define metrics for
   decomposition of end-to-end one-way delays measurements.

   This memo makes use of definitions of end-to-end One-way Packet loss
   Metrics defined in the RFC 2680 [RFC2680] to define metrics for
   decomposition of end-to-end one-way packet loss measurements.

   The IPPM WG defined a framework for metric definitions and end-to-end
   measurements:

   o  A general framework for defining performance metrics, described in
      the Framework for IP Performance Metrics, RFC 2330 Metrics [RFC2330];

   o  A One-way Active Measurement Protocol Requirements, RFC 3763 Requirements [RFC3763];

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

   o  An IP Performance Metrics Registry , RFC 4148 [RFC4148];

   It specified a set of end-to-end metrics, which conform to this
   framework:

   o  The IPPM Metrics for Measuring Connectivity, RFC 2678 Connectivity [RFC2678];

   o  The One-way Delay Metric for IPPM, RFC 2679 IPPM [RFC2679];

   o  The One-way Packet Loss Metric for IPPM, RFC 2680 IPPM [RFC2680];

   o  The Round-trip Delay Metric for IPPM, RFC 2681 IPPM [RFC2681];

   o  A Framework for Defining Empirical Bulk Transfer Capacity Metrics
      RFC 3148
      [RFC3148];

   o  One-way Loss Pattern Sample Metrics, RFC 3357 Metrics [RFC3357];

   o  IP Packet Delay Variation Metric for IPPM, RFC 3393 IPPM [RFC3393];

   o  Network performance measurement for periodic streams, RFC 3432 streams [RFC3432];

   o  Packet Reordering Metric for IPPM [Work [RFC4737][Work in progress];
   Based on these works, this memo defines 2 kinds of multi party
   metrics.

   Firstly it defines spatial metrics:

   o  A 'sample', called Type-P-Spatial-One-way-Delay-Vector, will be
      introduced to divide an end-to-end Type-P-One-way-Delay in a
      spatial sequence of one-way delays.

   o  A 'sample', called Type-P-Spatial-One-way-Packet-Loss-Vector, will
      be introduced to divide an end-to-end Type-P-One-way-Packet-Loss
      in a spatial sequence of packet loss.

   o  Using the Type-P-Spatial-One-way-Delay-Vector metric, a 'sample',
      called Type-P-Spatial-One-way-Jitter-Vector, will be introduced to
      divide an end-to-end Type-P-One-way-ipdv in a spatial sequence of
      jitter.

   o  Using the Type-P-Spatial-One-way-Delay-Vector metric, a 'sample',
      called Type-P-subpath-One-way-Delay-Stream, will be introduced to
      define the one-way-delay between a pair of host of the path.  This
      metric is similar to Type-P-One-way-Delay-Stream.

   o  Using Type-P-subpath-One-way-Delay-Stream, a 'sample' Type-P-
      Passive-One-way-Delay-Stream will be introduced to define passive
      metrics.  These metrics are designed for pure passive measurement
      methodology as introduced by PSAMP WG.

   Then it defines one-to-group metrics.

   o  Using one test packet sent from one sender to a group of
      receivers, a 'sample', called Type-P-one-to-group-One-way-Delay-
      Vector, will be introduced to define the list of Type-P-one-way-
      delay between this sender and the group of receivers.

   o  Using one test packet sent from one sender to a group of
      receivers, a 'sample', called Type-P-one-to-group-One-way-Packet-
      Loss-Vector, will be introduced to define the list of Type-P-One-
      way-Packet-Loss between this sender and the group of receivers

   o  Using one test packet sent from one sender to a group of
      receivers, a 'sample', called Type-P-one-to-group-One-way-Jitter-
      Vector, will be introduced to define the list of Type-P-One-way-
      ipdv between this sender and the group of receivers

   o  Then a discussion section presents the set of statistics that may
      be computed on the top of these metrics to present the QoS in a
      view of a group of users as well as the requirements of relative
      QoS on multiparty communications.

2.  Terminology

2.1.  Multiparty metric

   A metric is said to be multiparty if the definition involved more
   than two sources or destinations in the measurements.  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 >.

2.2.  Spatial metric

   A metric is said to be spatial if one of the hosts involved is
   neither the source nor the destination of the metered packet.

2.3.  Spatial metric points of interest

   Points of interest of a spatial metric are the routers or sibling in
   the path between source and destination (in addition to the source
   and the destination themself). themselves).

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.  One-to-group metric points of interest

   Points of interest of One-to-group metrics are the set of host
   destinations receiving packets from the source (in addition to the
   source itself).

2.6.  Reference point

   The centre/server in the one-to-group measurement that is controlled
   by network operators can be a very good reference point where
   measurement data can be collected for further processing although the
   actual measurements have to be carried out at all points of interest.
   I.e., the measurement points will be all clients/receivers while the
   reference point acts as source for the one-to-group metric.  Thus, we
   can define the reference point as the host while the statistic
   calculation will be carried out.

2.7.  Vector

   A group of singletons is the set of results of the observation of the
   behaviour of the same packet at different places of a network.

   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 time.  For instance, if One-way delay
   singletons abserved 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 orgnized organized as {dT1, dT2,..., dTN}.  The elements in
   one vector are singletons distinct with each other in terms of both
   measurement point and time.  Given the vector V as an example, the
   element dT1 is distinct from the rest by measured at receiver 1 at
   time T1.  Additional to a singleton, Vector gives information over a
   space dimension.

2.8.  Matrix

   Several vectors can orgnize organize form up a Matrix, which contains results
   observed in a sampling interval at different place of a network at
   different time.  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 corresponding corresponds to a sample.

   The relation among Singleton, Vector and Matrix can be shown in the
   following Fig Figure 1.

           one to group

                 one-to-group         Singleton
                                     /          Sample
         Src             Rcvr                  Recv ..............................
     ..................R1dT1
           .................... 1  R1dT1   R1dT2     R1dT3    R1dT4
            `:=-.._
           T   `._ ``-..__
                  `.      `-      `-... 2  R2dT1   R2dT2     R2dT3    R2dT4
                    `-.
                       `-.
                    `._R3dT1
                          `.... N  R3dT1   R3dT2     R3dT3    R3dT4

                                  Vector           Matrix
                                 (space)           (time)

         Figure 1. 1: Relation beween Singletons, vectors and matrix

3.  Motivations for spatial and one-to-group metrics

   All IPPM metrics are defined for end-to-end measurement.  These
   metrics provide very good guides for measurement in the pair
   communications.  However, further efforts should be put to define
   metrics for multiparty measurements such as one to one trajectory
   metrics and one to multipoint metrics.

3.1.  spatial metrics

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

   o  The PCE WG is extending existing protocols to permit remote path
      computation and path computation quality, including inter domain.
      One may say that in intra domain the decomposing  Decomposing the performance of a interdomain path is not whished.  However such decomposition is desirable in
      interdomain to qualify each per AS computation with contribution to the initial
      request. performance.  So
      it is necessary to define standard spatial metrics before going
      further in the computation of inter domain path with QoS
      constraint.

   o  Traffic engineering and troubleshooting applications require
      spatial views of the one-way delay consumption, identification of
      the location of the lost of packets and the decomposition of the
      jitter over the path.

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

   o  Composition of metrics is a need to scale in the measurement
      plane.  The definition of composition metrics is a work in
      progress [I-D.ietf-ippm-spatial-composition]; .  Spatial measure give typically the individual performance
      of an intra domain segment.  It is the elementary piece of
      information to exchange for measuring interdomain performance
      based on composition of metrics.

   o  The PSAMP WG defines capabilities to sample packets in a way to to
      support measurement.  [I-D.boschi-ipfix-reducing-redundancy];
      defines a method to collect packets information to measure the instantaneous spatial performance without injecting test traffic. measurement respecful of the IPPM framework
      [RFC2330].  Consequently it is urgent necessary to define a set of common
      spatial metrics for passive and active techniques which respect the IPPM
      framework [RFC2330].  This need is emphases by the fact that end-
      to-end spatial measurement involves the 2 techniques; techniques.

3.2.  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 in the view of a group
   with consideration that it involves a group of people rather than
   two.  As a consequence a simple one-way metric cannot describe the
   multi-connection situation.  We need some new metrics to collect
   performance of all the connections for further statistics analysis.
   A group of metrics are proposed in this stage named one-to-group
   performance metrics based on the unicast metrics defined in IPPM WG.
   One-to-group metrics are trying to composite one-way metrics from one
   source to a group of destinations to make up new metrics.  The
   compositions are necessary for judging the network performance of
   multiparty communications and can also be used to describe the
   difference of the QoS served among a group of 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 relative QoS requirements for
      the multiparty communications.

   To understand the connection situation between one source and any one
   receiver in the multiparty communication group, we need the
   collection of instantaneous end-to-end measures.  It will give us
   very detailed insight into each branch of the multicast tree in terms
   of end-to-end absolute QoS.  It can provide clear and helpful
   information for engineers to identify the connection with problems in
   a complex multiparty routing tree.

3.3.  Discussion on Group-to-one and Group-to-group

   The one-to-group metrics

   We note that points of interest can also be selected described in this memo introduce one-to-many
   concerns to the IPPM working group to measure the performance of a
   group of users who receiving data 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.  Nevertheless,
   applied to one-to-one communications they 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 and Group-to-group topologies.  These
   topologies are currently beyond the scope of this memo, because they
   would involve multiple packets launched from different sources.
   However, we can give some clues here on these two cases.

   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, we can hardly define the
   reference point and, therefore, have difficulty 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 metrics definitions

   Spatial decomposition metrics are based on standard end-to-end
   metrics.

   The definition of a spatial metric is coupled with the corresponding
   end-to-end metric.  The methodoly methodology is based on the measure of the
   same test packet and parameters of the corresponding end-to-end
   metric.

4.1.  A Definition for Spatial One-way Delay Vector

   This section is coupled with the definition of Type-P-One-way-Delay.
   When a parameter from section 3 of [RFC2679] is 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

             + Src*, the IP address of the sender.

             + Dst*, the IP address of the receiver.

             + i, An integer which ordered the hosts in the path.

             + Hi, exchange points of the path digest.

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

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

             + dT1,..., dTn a list of delay.

             + P*, the specification of the packet type.

             + <Src, H1, H2,..., Hn, Dst>, a path digest.

4.1.3.  Metric Units

   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
      to some clock synchronisation issue. this point is discussed in
      the section 3.7.1.  "Errors or uncertainties related to Clocks" of
      of [RFC2679];

   o  The location of the point of interest in the device influences the
      result (see [I-D.quittek-ipfix-middlebox]).
      result.  If the packet is not observed on the input interface the
      delay includes buffering time and consequently an uncertainty due
      to the difference between 'wire time' and 'host time';

4.1.6.  Interference with other test packet

   To avoid packet collision it is preferable to include a sequence
   number in the packet.

4.1.7.  loss threshold

   To determine if a dTi is defined or undefined it is necessary to
   define a period of time after which a packet is considered loss.

4.1.8.  Methodologies

   Section 3.6 of [RFC2679] gives methodologies for end-to-end one-way-
   delay measurements.  Most of them apply to each points interest Hi
   and are relevant to this section.

   Generally, for a given Type-P, in a given Hi, the methodology would
   proceed as follows:

   o  At each Hi, prepare to capture the packet sent a time T, take a
      timestamp Ti', determine the internal delay correction dTi',
      extract the timestamp T from the packet, then compute the one-way-
      delay from Src to Hi: dTi = Ti' - dTi' - T. The one-way delay is
      undefined (infinite) if the packet is not detected after the 'loss
      threshold' duration;
   o  Gather the set of dTi of each Hi and order them according to the
      path to build the Type-P-Spatial-One-way-Delay-Vector metric
      <T,dT1,dT2,...,dTn,dT> over the path <H1, H2,..., Hn>.

   It is out of the scope of this document to define how each Hi detects
   the packet.

4.1.9.  Reporting the metric

   Section 3.6 of [RFC2679] indicates the items to report.

4.1.10.  Path

   It is clear that a end-to-end Type-P-One-way-Delay can't determine
   the list of hosts the packet passes throught. through.  Section 3.8.4 of
   [RFC2679] says that the path traversed by the packet SHOULD be
   reported but is practically impossible to determine.

   This part of the job is provide by Type-P-Spatial-One-way-Delay-
   Vector metric because each points of interest Hi which capture the
   packet is part of the path.

4.2.  A Definition of a sample of One-way Delay of a sub path

   This metric is similar to the metric Type-P-One-way-Delay-Poisson-
   stream defined in [RFC2679] and to the metric Type-P-One-way-Delay-
   Periodic-Stream defined in [RFC3432].

   Nevertheless its definition differs because it is based of the
   division of end-to-end One-way delay using the metric Type-P-Spatial-
   One-way-Delay-Vector defined above.

   It aims is to define a sample of One-way-Delay between a pair of
   hosts of a path usable by active and passive measurements.

   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.
   Subpath one-way-delay measurement SHOULD be respectful of them,
   especially those related to methodology, clock, uncertainties and
   reporting.

4.2.1.  Metric Name

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

4.2.2.  Metric Parameters

             + Src*, the IP address of the sender.

             + Dst*, the IP address of the receiver.

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

             + k, An integer which orders the packets sent.

         + <Src, H1, H2,..., Hn, Dst>, a path digest.

             + 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 path must greater that Ha;

             + Hi, exchange points of the path digest.

             + dT1,..., dTn a list of delay.

             + P*, the specification of the packet type.

4.2.3.  Metric Units

   A sequence of pairs <Tk,dt>.

   T is one of time of the sequence T1...Tn;

   dt is a delay.

4.2.4.  Definition

   Given 2 hosts Ha and Hb of the path <Src, H1, H2,..., Hn, Dst>, given
   a flow of 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,dT1.1, dT1.2,..., dT1.n,dT1>.  We define the
   value of the sample Type-P-subpath-One-way-Delay-Stream as the
   sequence made up of the couples <Tk,dTk.b - dTk.a>. dTk.a is the
   delay between Src and Ha. dTk.b is the delay between Src and Hb.
   'dTk.b - dTk.a' is the one-way delay experienced by the packet sent
   at the time Tk by Src when going from Ha to Hb.

4.2.5.  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 to clock synchronisation 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 minimun 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 (see [I-D.quittek-ipfix-middlebox]).
      result.  If the packet is not observed on the input interface the
      delay includes buffering time and consequently an uncertainty due
      to the difference between 'wire time' and 'host time';

   o  dTk.b may be observed and not dTk.a.

   o  Tk is unknown if the flow is made of end user packets, that is
      pure passive measure.  In this case Tk may be forced to Tk+dTk.a.
      This motivate separate metrics names for pure passive measurement
      or specific reporting information.

   o  Pure passive measure should consider packets of the same size and
      of the same Type-P.

4.2.6.  Interference with other packet

4.2.7.  loss threshold

   To determine if a dTi is defined or undefined it is necessary to
   define a period of time after which a packet is considered loss.

4.2.8.  Methodologies

   Both active and passive method should discussed.

4.2.9.  Reporting the metric

   Section 3.6 of [RFC2679] indicates the items to report.

4.2.10.  Path

4.3.  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 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, uncertainities uncertainties and
   reporting.

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

4.3.1.  Metric Name

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

4.3.2.  Metric Parameters

           + Src*, the IP address of the sender.

           + Dst*, the IP address of the receiver.

           + i, An integer which ordered the hosts in the path.

           + Hi, exchange points of the path digest.

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

           + dT1,..., dTn, dT, a list of delay.

           + P*, the specification of the packet type.

           + <Src, H1, H2,..., Hn, Dst>, a path digest.

           + B1, B2, ..., Bi, ..., Bn, a list of boolean Boolean values.

4.3.3.  Metric Units

   A sequence of boolean Boolean values.

4.3.4.  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> the packet passes <H1, H2 ..., Hn,
   Dst>,

   Type-P-One-way-Packet-Lost-Vector metric is defined as the sequence
   of values <B1, B2, ..., Bn> such that for each Hi of the path, a
   value of Bi of 0 means that dTi is a finite value, and a value of 1
   means that dTi is undefined.

4.3.5.  Discussion

   Following are specific issues wich which may occur:

   o  the result includes the sequence 1,0.  This case means that the
      packet was seen by a host but not by it successor on the path;

   o

   The location of the meter in the device influences the result:

   o  Even if the packet is received by a device, it may be not observed
      by a meter located after a buffer;

4.3.6.  Reporting

   Section in progress.

4.4.  A Definition for Spatial One-way Jitter 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.

   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 them,
   especially those related to methodology, clock, uncertainities uncertainties and
   reporting.

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

4.4.1.  Metric Name

   Type-P-Spatial-One-way-Jitter-Vector

4.4.2.  Metric Parameters

             + Src*, the IP address of the sender.

             + Dst*, the IP address of the receiver.

             + i, An integer which ordered the hosts in the path.

             + Hi, exchange points of the path digest.

             + T1*, the time the first packet was sent.

             + T2*, the time the second packet was sent.

             + P, the specification of the packet type.

             + P1, the first packet sent at time T1.

             + P2, the second packet sent at time T2.

             + <Src, H1, H2,..., Hn, Dst>, a path digest.

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

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

             + 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.

4.4.3.  Metric Units

   A sequence of times.

4.4.4.  Definition

   Given 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 the path <H1,
   H2,..., Hn>.

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

4.4.5.  Sections in progress

   See sections 3.5 to 3.7 of [RFC3393].

4.5.  Pure Passive Metrics

   Spatial metrics may be measured without injecting test traffic as
   described in [I-D.boschi-ipfix-reducing-redundancy] . traffic.

4.5.1.  Discussion on Passive measurement

   One might says that most of the operational issues occur in the last
   mile and that consequently such measure are less useful than active
   measuremeent.
   measurement.  Nevertheless they are usable for network TE and
   interdomain QoS monitoring, and composition of metric.

   Such a technique have some limitations that are discussed below.

4.5.1.1.  Passive One way delay

   As the packet is not a test packet, it does not include the time it
   was sent.

   Consequently a point of interest Hi ignores the time the packet was
   send.  So It is not possible to measure the delay between Src and Hi
   in the same manner it is not possible to measure the delay betwwen Hi
   and Dst.

4.5.1.2.  Passive Packet loss

   The packet is not a test packet, so it does not include a sequence
   number.

   Packet lost measurement doe not require time synchronization and
   require only one point of observation.  Nevertheless it requires the
   point of interest Hi to be expecting the packet.  Practically Hi may
   not detect a lost of packet that occurs between Src and Hi.

   A point of interest Hi ignores the time the packet is send because
   the packet does not carry the time it was injected in the network.
   So a probe Hi can not compute dTi.

   An alternative to these issues consist in considering sample spatial
   One-way delay that T is the time when H1 (the first passive probe of
   the path) observed the packet.

4.5.2.  Reporting and composition

   To avoid misunderstanding and to address specific reporting
   constraint a proposal consists in defining distinct metrics for pure
   passive measurement based on the definition above.

   It is crucial to know the methodologie methodologies used because of the
   difference of method of detection (expecting Seq++); because of the
   difference of source of time (H1 vs Src) and because of the
   difference of
   behavior behaviour of the source (Poisson/unknown).

4.5.3.  naming and registry

   Having distinct metrics identifiers for spatial metrics and passive
   spatial metrics in the [RFC4148] will avoid interoperabily interoperability issues
   especially during composition of metrics.

4.5.4.  Passive One way delay metrics

4.5.5.  Passive One way PacketLoss metrics

4.5.6.  Passive One way jitter metrics

4.6.  Discussion on spatial statistics

   Do we define min, max, avg of spatial 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.

5.  One-to-group metrics definitions

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

5.1.1.  Metric Name

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

5.1.2.  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 group address (optional).  The parameter Gr is
      the multicast group address if the measured packets are
      transmitted by multicast.  This parameter is to identify 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.

5.1.3.  Metric Units

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

5.1.4.  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 is
   defined as the set of the Type-P-One-way-Delay singleton between Src
   and each receiver with value of { dT1, dT2,...,dTn }.

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

5.2.1.  Metric Name

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

5.2.2.  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 group address (optional).

5.2.3.  Metric Units

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

5.2.4.  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 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>}.

5.3.  A Definition for one-to-group One-way Jitter

5.3.1.  Metric Name

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

5.3.2.  Metric Parameters

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

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

           + T1, a time.

           + T2, a time.

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

           + P, the specification of the packet type.

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

    + Gr, the multicast group address (optional)

5.3.3.  Metric Units

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

5.3.4.  Definition

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

   Therefore, for a set of real number {ddT1,...,ddTn},Type-P-one- to-
   group-One-way-Jitter-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}.

5.4.  Discussion on one-to-group statistics

6.  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 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 be directly used to
   conveniently present the performance in terms of a group and neither
   to identify the relative performance situation.

   One may say that no matter how many people join the communication,
   the connections can still be treated as a set of one-to-one
   connection.  However, we might not describe a multiparty
   communication by a set of one-way measurement metrics because of the
   difficulty for understanding and the lack of convenience.  For
   instance, an engineer might not describe the connections of a
   multiparty online conference in terms of one-to-group one-way delay
   for user A and B, B and C, and C and A because people might be
   confused.  If there are more users in the same communication, the
   description might be very long.  And he might use the one-way metrics
   with worst and the best value to give users an idea of the
   performance range of the service they are providing.  But it is not
   clear enough and might not be accurate in a large multiparty
   communication scenario.

   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 worse difference in delay will might result in
   failure in the game.  We have to use the new 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.,
   need a rule that require multicast metrics in order to judge
   evaluate the relative performance requirement. network against their requirements.  Therefore, we can
   see the importance of new 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 FRCs.  They provide the foundation of
   definition for performance statistics.  For instance, there are
   definitions for minimum and maximum One-way delay in [RFC2679] and
   One-way delay mean in [I-D.ietf-ippm-spatial-composition]. [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 dimension and space dimention. dimensions.
   This space dimension is introduced by the Matrix concept.  For a concept as
   illustrated in Figure 7.  For a Matrix M
   shown in the Fig. 2, each row is a set of One-way
   singletons spreading over the space time dimension and each colume column is
   another set of One-way singletons spreading over the time space dimension.

   (preamble)

            Receivers
             Space
               ^
             1 |    / R1dT1   R1dT2     R1dT3 ... R3dTk \
               | dT11, dT12,..., dT1N   |                                     | dT21, dT22,..., dT2N
             2 |   |                 :  R2dT1   R2dT2     R2dT3 ... R3dTk  |
               |                 :   |                                     | dTm1, dTm2,..., dTmN
             3 |   |  R3dT1   R3dT2     R3dT3 ... R3dTk  |
             . |   |                                     |
             . |   |                                     |
             . |   |                                     |
             n |    \ RndT1   RndT2     RndT3 ... RndTk /

   Fig. 2
               +--------------------------------------------> time
              T0

                         Figure 7: Matrix M (m*N) (n*m)

   In Matrix M, each element is a One-way delay singleton.  Each row column
   is a delay vector contains the One-way delays of the same packet
   observed at N M points of interest.  It implies the geographical factor
   of the performance within a group.  Each colume 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 columes 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 farely fairly by calculating the statistics over the space
   dimension.  This memo does not intent intend to recommend which of the
   statistics are better than the other.

   To save the report transmission bandwidth, each point of interest can
   send statistics in a pre-defined time interval to the reference point
   rather than sending every One-way singleton it observed.  As long as
   an appropriate time interval is decided, appropriate stantistics 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 dimention 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, it there is no need to specify in which
   procedure the calculation should follow.

   There are many

   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 one-to-group metrics
   over either the space dimension or the time dimension or both.  In this memo, we define one-to-group mean and one-to-group
   variation over the space dimension.  These statistics are offered
   mostly to be illustrative of what could be done.

   One-to-group mean are trying to measure  This
   memo treats the overall performance for a
   multicast group associated to one source.  It is case where a reflection stream of packets from the
   absolute performance of Source
   results in a multiparty communication service when we
   treat all receivers as one customer.  It can also present the trend
   of the absolute performance of all receivers, i.e., it shows that
   most sample at each of the receivers Receivers in the multiparty communication service trend
   to receive an absolute performance close to Group, and these
   samples are each summarized with the mean.

   One-to-group variation streams usual statistics employed in
   one-to-one communication.  New statistic definitions are trying to measure how presented,
   which summarize the
   performance varies among one-to-one statistics over all of the users Receivers in a multicast group
   associated to one source.
   the Group.

6.1.  Discussion on the Impact of packet loss on statistics

   The word "variation" in this memo is packet loss does have effects on one-way metrics and their
   statistics.  For example, the
   population standard deviation. lost packet can result an infinite one-
   way delay.  It reflects is easy to handle the relative
   performancesituation problem by simply ignoring the
   infinite value in a multiparty communication service, i.e., the
   level of metrics and in the difference between calculation of the absolute performanceof each
   receivers.

   Using
   corresponding statistics.  However, the one-to-group 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 jitter 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.

6.2.  General Metric Parameters

   o  Src, the IP address of a host

   o  G, the Group IP address

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

   o  T, a time (start of test interval)

   o  Tf, a time (end of test interval)

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

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

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

   o  T0, a time that MUST be selected at random from the interval [T,
      T+I] to start generating packets and taking measurements (for
      Periodic Streams)

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

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

   o  Tmax, a maximum waiting time for packets at the destination, set
      sufficiently long to disambiguate packets with long delays from
      packets that are discarded (lost), thus the distribution of delay
      is not truncated

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

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

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

6.3.  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 entire 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 8: One-to-GroupGroup 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).

6.3.1.  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.

6.3.2.  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 9: Type-P-Finite-One-way-Delay-Mean-Receiver-n

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

6.3.3.  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 10: 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.

6.3.4.  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)

6.3.5.  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)

6.4.  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 11: 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).

6.4.1.  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 12

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

6.4.2.  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 13: 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.

6.4.3.  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 14: Type-P-Comp-Loss-Ratio-Receiver-n

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

   There is are two delay variation (DV) statistics to summarize the
   performance over the Group: the maximum DV over all receivers and the
   range of DV over all receivers.

   The detailed definitions are T0 BE PROVIDED.

7.  Measurement Methods: Scaleability 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).

7.1.  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 one-to-group variation concepts, we so on.  Apparently, the centralized
   calculation method can have 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 clear understand 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.

7.2.  Measurement

   To prevent any biais 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.

7.3.  effect of  Time and Space Aggregation Order on Group Stats

   This section presents the performanceof a multiparty
   communication service in terms impact of its trend and range.  There can be
   mean the aggregation order on the
   scalability of the reporting and variation stream definitions for each of the three one-to-
   group metrics defined above.  We only present the definition of Type-
   P-one-to-group-One-way-Delay-Space-Mean computation.  It makes
   the hypothesis that receivers are managed remotly and Type-P-one-to-group- One-
   way-Delay-Space-Variation as examples in this memo.

5.4.1.  Type-P-one-to-group-One-way-Delay-Space-Mean

   Given a Type-P-one-to-group-One-way-Delay-Vector, not co-located.

   2 methods are available to compute group statistics:

      Figure 8and (Figure 11) illustrate the mean { dT1,
   dT2,...,dTN } for method method choosen: the packet from Src at
      one-to-one statistic is computed per interval of time T to { Recv1,...,RecvN
   }.

   For example, suppose we take a delay vector and before the results is:

      Delay_Vector = {dT1,...,dTN}

   Then
      computation of the mean over the group of receivers [method1];

      Figure 15 presents the second one, metric is computed over space dimension would be:

      Delay_Space_Mean = DsM = sum{dT1,...,dTN}/N

5.4.2.  Type-P-one-to-group-One-way-Delay-Variation-Stream

   Given a Type-P-one-to-group-One-way-Delay-Vector,
      and then over time [method2].

   They differ only by the variation {
   dT1, dT2,...,dTN } for order of the packet from Src at time T to {
   Recv1,...,RecvN }.

   We still take and of the above Delay_Vector space
   aggregation.  View as an a matrix this order is neutral as it does not
   impact the result, but the impact on a measurement deployement is
   critical.

      Recv

        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

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

           Figure 15: Impact of space aggregation on Group Stat

   In both cases the variation
   would be:

      Delay_Variation_Stream = {SUM[(dT1-DsM)^2,...,(dTN-
      DsM)^2)}/N)^(1/2)

6.  Extension from one-to-one volume of data to one-to-many measurement

   The above one-to-group metrics were defined report is proportional to compose measurement
   results the
   number of probes.  But there is a group of users who receive major difference between these 2
   methods:

      method2: In space and time aggregation mode the same volume of data from one
   source.  Moreover, this to
      collect is one proportionnal to the number of efforts test packets received;
      Each received packet RiSi triggers out a block of data that must
      be reported to introducing a common place for computing the one-to-
   many concern to stat over space;

      method1: In time and space aggregation mode the IPPM working group with respect volume of data to
      collect is proportionnal to the fact that
   all existing documents in period of aggregation, so it does
      not depend on the group are unicast oriented, which talk
   about only one-to-one single "path" number of packet received;

   Method 2 property has severe drawbacks in measurements.  This concept
   can be extended from the "path" to "path tree" to cover both one-to-
   one terms of security and one-to-many communications.  Actually,
   dimensionning:

      The increasing of the one-to-one
   communications can be viewed as a special case rate of one-to-many from the routing point test packets may result in a
      sort of view. DoS toward the computation points;

      The one-to-many communications build up dimensioning of a
   routing tree in measurement system is quite impossible to
      validate.

   The time agregation interval provides the networks and one-to-one can be viewed as reporting side with a
   special simplified tree without branches but only the "trunk".

   Therefore, the one-to-group metrics described in this memo can even
   be viewed
   control of various collecting aspects such as general metrics to measure the delay, jitter bandwidth and packet
   loss in IP networks.  When
   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 adress this need it applies is suggested firstly to one-to-one communications, limit the metrics will have N receivers while N equal to 1.  And
   number of test and the
   statistic metrics for one-to-one communications are exactly number of test packets per seconds.  Then
   reducing the one-
   to-group metrics themselves when calculated using size of the methods given.

7. sample over time to one packet give sample
   of singleton over space..

7.4.  effect of  Time and Space Aggregation Order on Spatial Stats

   TBD

8.  Open issues

8.

9.  Security Considerations

   Active measumrement: see measurement: (TODO: security section in considerations of owd pl, jitter
   rfcs applies (editor notes: add references).

9.1.  passive measurement: measurement

   The generation of packets which match systematically the hash
   function may lead to a DoS attack toward the collector.

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

   one-to-group metrics require collection detect the spoofing.

9.2.  one-to-group metric

   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 singletons which probes may overload any
   combination of the network the measurement controller is attach to.

9. to,
   measurement controller network interfaces and measurement controller
   computation capacities.

   one-to-group metrics:

10.  Acknowledgments

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

10.

11.  IANA Considerations

   Metrics defined in this memo will 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].

11. [RFC4148] :

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

   Spatial-One-way-Delay-Vector 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

   subpath-One-way-Delay-Stream OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      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-Packet-Loss-Vector OBJECT-IDENTITY
      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 4.3."

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

      := { ianaIppmMetrics nn } -- IANA assigns nn

   Spatial-One-way-Jitter-Vector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 4.4."

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

      := { ianaIppmMetrics nn } -- IANA assigns nn

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

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.1."

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

      := { ianaIppmMetrics nn } -- IANA assigns nn
   one-to-group-One-way-Packet-Loss-Vector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.2."

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

      := { ianaIppmMetrics nn } -- IANA assigns nn

   one-to-group-One-way-Jitter-Vector OBJECT-IDENTITY

      STATUS current

      DESCRIPTION

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

      REFERENCE

         "Reference "RFCyyyy, section 5.3."

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

      := { ianaIppmMetrics nn } -- IANA assigns nn

   One-to-Group-Mean-Delay 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 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 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 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 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

   --

12.  References

11.1.

12.1.  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.

11.2.

12.2.  Informative References

   [I-D.boschi-ipfix-reducing-redundancy]
              Boschi, E., "Reducing redundancy in IPFIX and PSAMP
              reports", draft-boschi-ipfix-reducing-redundancy-02 (work
              in progress), June 2006.

   [I-D.ietf-ippm-spatial-composition]
              Morton, A. and E. Stephan, "Spatial Composition of
              Metrics", draft-ietf-ippm-spatial-composition-01 (work in
              progress), June 2006.

   [I-D.quittek-ipfix-middlebox]
              Quittek, J., "Guidelines for IPFIX Implementations on
              Middleboxes", draft-quittek-ipfix-middlebox-00 (work in
              progress), February 2004.

   [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.

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-ft.com 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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