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Network Working Group                                         E. StephanRequest for Comments: 5644                                France TelecomCategory: Standards Track                                       L. Liang                                                    University of Surrey                                                               A. Morton                                                               AT&T Labs                                                            October 2009IP Performance Metrics (IPPM): Spatial and MulticastAbstract   The IETF has standardized IP Performance Metrics (IPPM) for measuring   end-to-end performance between two points.  This memo defines two new   categories of metrics that extend the coverage to multiple   measurement points.  It defines spatial metrics for measuring the   performance of segments of a source to destination path, and metrics   for measuring the performance between a source and many destinations   in multiparty communications (e.g., a multicast tree).Status of This Memo   This document specifies an Internet standards track protocol for the   Internet community, and requests discussion and suggestions for   improvements.  Please refer to the current edition of the "Internet   Official Protocol Standards" (STD 1) for the standardization state   and status of this protocol.  Distribution of this memo is unlimited.Copyright Notice   Copyright (c) 2009 IETF Trust and the persons identified as the   document authors.  All rights reserved.   This document is subject toBCP 78 and the IETF Trust's Legal   Provisions Relating to IETF Documents   (http://trustee.ietf.org/license-info) in effect on the date of   publication of this document.  Please review these documents   carefully, as they describe your rights and restrictions with respect   to this document.  Code Components extracted from this document must   include Simplified BSD License text as described in Section 4.e of   the Trust Legal Provisions and are provided without warranty as   described in the BSD License.   This document may contain material from IETF Documents or IETF   Contributions published or made publicly available before November   10, 2008.  The person(s) controlling the copyright in some of this   material may not have granted the IETF Trust the right to allowStephan, et al.             Standards Track                     [Page 1]

RFC 5644             Spatial and Multicast Metrics          October 2009   modifications of such material outside the IETF Standards Process.   Without obtaining an adequate license from the person(s) controlling   the copyright in such materials, this document may not be modified   outside the IETF Standards Process, and derivative works of it may   not be created outside the IETF Standards Process, except to format   it for publication as an RFC or to translate it into languages other   than English.Table of Contents1. Introduction and Scope ..........................................32. Terminology .....................................................43. Brief Metric Descriptions .......................................74. Motivations ....................................................105. Spatial Vector Metrics Definitions .............................126. Spatial Segment Metrics Definitions ............................197. One-to-Group Metrics Definitions ...............................278. One-to-Group Sample Statistics .................................309. Measurement Methods: Scalability and Reporting .................4010. Manageability Considerations ..................................4411. Security Considerations .......................................4912. Acknowledgments ...............................................5013. IANA Considerations ...........................................5014. References ....................................................5614.1. Normative References .....................................5614.2. Informative References ...................................57Stephan, et al.             Standards Track                     [Page 2]

RFC 5644             Spatial and Multicast Metrics          October 20091.  Introduction and Scope   IETF has standardized IP Performance Metrics (IPPM) for measuring   end-to-end performance between two points.  This memo defines two new   categories of metrics that extend the coverage to multiple   measurement points.  It defines spatial metrics for measuring the   performance of segments of a source to destination path, and metrics   for measuring the performance between a source and many destinations   in multiparty communications (e.g., a multicast tree).   The purpose of this memo is to define metrics to fulfill the new   requirements of measurement involving multiple measurement points.   Spatial metrics measure the performance of each segment along a path.   One-to-group metrics measure the performance for a group of users.   These metrics are derived from one-way end-to-end metrics, all of   which follow the IPPM framework [RFC2330].   This memo is organized as follows:Section 2 introduces new terms   that extend the original IPPM framework [RFC2330].Section 3 briefly   introduces the new metrics, andSection 4 motivates each metric   category.  Sections5 through8 develop each category of metrics with   definitions and statistics.  Then the memo discusses the impact of   the measurement methods on the scalability and proposes an   information model for reporting the measurements.  Finally, the memo   discusses security aspects related to measurement and registers the   metrics in the IANA IP Performance Metrics Registry [RFC4148].   The scope of this memo is limited to metrics using a single source   packet or stream, and observations of corresponding packets along the   path (spatial), at one or more destinations (one-to-group), or both.   Note that all the metrics defined herein are based on observations of   packets dedicated to testing, a process that is called active   measurement.  Passive measurement (for example, a spatial metric   based on the observation of user traffic) is beyond the scope of this   memo.1.1.  Requirements Language   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this   document are to be interpreted as described inRFC 2119 [RFC2119].Stephan, et al.             Standards Track                     [Page 3]

RFC 5644             Spatial and Multicast Metrics          October 20092.  Terminology2.1.  Naming of the Metrics   The names of the metrics, including capitalized letters, are as close   as possible of the names of the one-way end-to-end metrics they are   derived from.2.2.  Terms Defined Elsewhere   host:section 5 of RFC 2330   router:section 5 of RFC 2330   loss threshold:section 2.8.2 of RFC 2680   path:section 5 of RFC 2330   sample:section 11 of RFC 2330   singleton:section 11 of RFC 23302.3.  Routers Digest   The list of the routers on the path from the source to the   destination that act as points of interest, also referred to as the   routers digest.2.4.  Multiparty Metric   A metric is said to be multiparty if the topology involves more than   one measurement collection point.  All multiparty metrics designate a   set of hosts as "points of interest", where one host is the source   and other hosts are the measurement collection points.  For example,   if the set of points of interest is < 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.2.5.  Spatial Metric   A metric is said to be spatial if one of the hosts (measurement   collection points) involved is neither the source nor a destination   of the measured packet(s).  Such measurement hosts will usually be   routers that are members of the routers digest.Stephan, et al.             Standards Track                     [Page 4]

RFC 5644             Spatial and Multicast Metrics          October 20092.6.  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 more than one destination.   Thus, the topology of the communication group can be viewed as a   center-distributed or server-client topology with the source as the   center/server in the topology.2.7.  Points of Interest   Points of interest are the hosts (as per theRFC 2330 definition,   "hosts" include routing nodes) that are measurement collection   points, which are a sub-set of the set of hosts involved in the   delivery of the packets (in addition to the source itself).   For spatial metrics, points of interest are a (possibly arbitrary)   sub-set of all the routers involved in the path.   Points of interest of one-to-group metrics are the intended   destination hosts for packets from the source (in addition to the   source itself).                         Src                   Dst                         `.          ,-.                           `.      ,'   `......1                             `.   ;       :                               `. ;       :                                 ;         :...2                                 |         |                                 :         ;                                  :       ;....3                                  :       ;                                   `.   ,'                                     `-'.......I                 Figure 1: One-to-Group Points of Interest   A candidate point of interest for spatial metrics is a router from   the set of routers involved in the delivery of the packets from   source to destination.Stephan, et al.             Standards Track                     [Page 5]

RFC 5644             Spatial and Multicast Metrics          October 2009                         Src ------.           Hosts                                    \                                     `---X   --- 1                                         \                                          x                                         /                              .---------X   ---- 2                            /                           x                            ...                            `---X           ---- ...                                   \                                    \                                     \                                      X     ---- J                                       \                                        \                                         \                                          `---- Dst                Note: 'X' are nodes that are points of interest,                      'x' are nodes that are not points of interest                   Figure 2: Spatial Points of Interest2.8.  Reference Point   A reference point is defined as the server where the statistical   calculations will be carried out.  It is usually a centralized server   in the measurement architecture that is controlled by a network   operator, where measurement data can be collected for further   processing.  The reference point is distinctly different from hosts   at measurement collection points, where the actual measurements are   carried out (e.g., points of interest).2.9.  Vector   A vector is a set of singletons (single atomic results) comprised of   observations corresponding to a single source packet at different   hosts in a network.  For instance, if the one-way delay singletons   observed at N receivers for Packet P sent by the source Src are dT1,   dT2,..., dTN, then a vector V with N elements can be organized as   {dT1, dT2,..., dTN}.  The element dT1 is distinct from all others as   the singleton at receiver 1 in response to a packet sent from the   source at a specific time.  The complete vector gives information   over the dimension of space, a set of N receivers in this example.Stephan, et al.             Standards Track                     [Page 6]

RFC 5644             Spatial and Multicast Metrics          October 2009   The singleton elements of any vector are distinctly different from   each other in terms of their measurement collection point.  Different   vectors for common measurement points of interest are distinguished   by the source packet sending time.2.10.  Matrix   Several vectors form a matrix, which contains results observed over a   sampling interval at different places in a network at different   times.  For example, the one-way delay vectors V1={dT11, dT12,...,   dT1N}, V2={dT21, dT22,..., dT2N},..., Vm={dTm1, dTm2,..., dTmN} for   Packet P1, P2,...,Pm, form a one-way delay Matrix {V1, V2,...,Vm}.   The matrix organizes the vector information to present network   performance in both space and time.   A one-dimensional matrix (row) corresponds to a sample in simple   point-to-point measurement.   The relationship among singleton, sample, vector, and matrix is   illustrated in Figure 3.                 points of        singleton                 interest           /       samples(time)                  ,----.    ^      /                 /   R1.....|  / R1dT1   R1dT2   R1dT3 ... R3dTk \                /         \ | |                                   |               ;  R2........| |  R2dT1   R2dT2   R2dT3 ... R3dTk  |          Src  |           || |                                   |               |      R3....| |  R3dT1   R3dT2   R3dT3 ... R3dTk  |               |           || |                                   |               :           ;| |                                   |                \         / | |                                   |                 \  Rn......|  \ RndT1   RndT2   RndT3 ... RndTk /                  `-----'   +-------------------------------------> time                                vector           matrix                               (space)      (time and space)     Figure 3: Relationship between Singletons, Samples, Vectors, and                                  Matrix3.  Brief Metric Descriptions   The metrics for spatial and one-to-group measurement are based on the   source-to-destination, or end-to-end metrics defined by IETF in   [RFC2679], [RFC2680], [RFC3393], and [RFC3432].Stephan, et al.             Standards Track                     [Page 7]

RFC 5644             Spatial and Multicast Metrics          October 2009   This memo defines seven new spatial metrics using the [RFC2330]   framework of parameters, units of measure, and measurement   methodologies.  Each definition includes a section that describes   measurement constraints and issues, and provides guidance to increase   the accuracy of the results.   The spatial metrics are:   o  Type-P-Spatial-One-way-Delay-Vector divides the end-to-end Type-P-      One-way-Delay [RFC2679] into a spatial vector of one-way delay      singletons.   o  Type-P-Spatial-One-way-Packet-Loss-Vector divides an end-to-end      Type-P-One-way-Packet-Loss [RFC2680] into a spatial vector of      packet loss singletons.   o  Type-P-Spatial-One-way-ipdv-Vector divides an end-to-end Type-P-      One-way-ipdv into a spatial vector of ipdv (IP Packet Delay      Variation) singletons.   o  Using elements of the Type-P-Spatial-One-way-Delay-Vector metric,      a sample called Type-P-Segment-One-way-Delay-Stream collects one-      way delay metrics between two points of interest on the path over      time.   o  Likewise, using elements of the Type-P-Spatial-Packet-Loss-Vector      metric, a sample called Type-P-Segment-Packet-Loss-Stream collects      one-way delay metrics between two points of interest on the path      over time.   o  Using the Type-P-Spatial-One-way-Delay-Vector metric, a sample      called Type-P-Segment-ipdv-prev-Stream will be introduced to      compute ipdv metrics (using the previous packet selection      function) between two points of interest on the path over time.   o  Again using the Type-P-Spatial-One-way-Delay-Vector metric, a      sample called Type-P-Segment-ipdv-min-Stream will define another      set of ipdv metrics (using the minimum delay packet selection      function) between two points of interest on the path over time.   The memo also defines three one-to-group metrics to measure the one-   way performance between a source and a group of receivers.  They are:   o  Type-P-One-to-group-Delay-Vector which collects the set of Type-P-      One-way-Delay singletons between one sender and N receivers;Stephan, et al.             Standards Track                     [Page 8]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  Type-P-One-to-group-Packet-Loss-Vector which collects the set of      Type-P-One-way-Packet-Loss singletons between one sender and N      receivers; and   o  Type-P-One-to-group-ipdv-Vector which collects the set of Type-P-      One-way-ipdv singletons between one sender and N receivers.   Finally, based on the one-to-group vector metrics listed above,   statistics are defined to capture single receiver performance, group   performance, and the relative performance for a multiparty   communication:   o  Using the Type-P-One-to-group-Delay-Vector, a metric called Type-      P-One-to-group-Receiver-n-Mean-Delay, or RnMD, presents the mean      of delays between one sender and a single receiver 'n'.  From this      metric, three additional metrics are defined to characterize the      mean delay over the entire group of receivers during the same time      interval:      *  Type-P-One-to-group-Mean-Delay, or GMD, presents the mean of         delays;      *  Type-P-One-to-group-Range-Mean-Delay, or GRMD, presents the         range of mean delays; and      *  Type-P-One-to-group-Max-Mean-Delay, or GMMD, presents the         maximum of mean delays.   o  Using the Type-P-One-to-group-Packet-Loss-Vector, a metric called      Type-P-One-to-group-Receiver-n-Loss-Ratio, or RnLR, captures the      packet loss ratio between one sender and a single receiver 'n'.      Based on this definition, two more metrics are defined to      characterize packet loss over the entire group during the same      time interval:      *  Type-P-One-to-group-Loss-Ratio, or GLR, captures the overall         packet loss ratio for the entire group of receivers; and      *  Type-P-One-to-group-Range-Loss-Ratio, or GRLR, presents the         comparative packet loss ratio during the test interval between         one sender and N receivers.   o  Using the Type-P-One-to-group-Packet-Loss-Vector, a metric called      Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio, or RnCLR, computes      a packet loss ratio using the maximum number of packets received      at any receiver.Stephan, et al.             Standards Track                     [Page 9]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  Using Type-P-One-to-group-ipdv-Vector, a metric called Type-P-One-      to-group-Range-Delay-Variation, or GRDV, presents the range of      delay variation between one sender and a group of receivers.4.  Motivations   All existing IPPM metrics are defined for end-to-end (source-to-   destination) measurement of point-to-point paths.  It is logical to   extend them to multiparty situations such as one-to-one trajectory   metrics and one-to-multipoint metrics.4.1.  Motivations for Spatial Metrics   Spatial metrics are needed for:   o  Decomposing the performance of an inter-domain path to quantify      the per-AS (Autonomous System) contribution to the end-to-end      performance.   o  Traffic engineering and troubleshooting, which benefit from      spatial views of one-way delay and ipdv consumption, or      identification of the path segment where packets were lost.   o  Monitoring the decomposed performance of a multicast tree based on      MPLS point-to-multipoint communications.   o  Dividing end-to-end metrics, so that some segment measurements can      be re-used and help measurement systems reach large-scale      coverage.  Spatial measures could characterize the performance of      an intra-domain segment and provide an elementary piece of      information needed to estimate inter-domain performance to another      destination using Spatial Composition metrics [SPATIAL].4.2.  Motivations for One-to-group Metrics   While the node-to-node-based spatial measures can provide very useful   data in the view of each connection, we also need measures to present   the performance of a multiparty communication topology.  A simple   point-to-point metric cannot completely describe the multiparty   situation.  New one-to-group metrics assess performance of the   multiple paths for further statistical analysis.  The new metrics are   named one-to-group performance metrics, and they are based on the   unicast metrics defined in IPPM RFCs.  One-to-group metrics are one-   way metrics from one source to a group of destinations or receivers.   The metrics are helpful for judging the overall performance of a   multiparty communications network and for describing the performance   variation across a group of destinations.Stephan, et al.             Standards Track                    [Page 10]

RFC 5644             Spatial and Multicast Metrics          October 2009   One-to-group performance metrics are needed for:   o  Designing and engineering multicast trees and MPLS point-to-      multipoint Label Switched Paths (LSPs).   o  Evaluating and controlling the quality of multicast services,      including inter-domain multicast.   o  Presenting and evaluating the performance requirements for      multiparty communications and overlay multicast.   To understand the packet transfer performance between one source and   any one receiver in the multiparty communication group, we need to   collect instantaneous end-to-end metrics, or singletons.  This gives   a very detailed view into the performance of each branch of the   multicast tree, and can provide clear and helpful information for   engineers to identify the branch with problems in a complex   multiparty routing tree.   The one-to-group metrics described in this memo introduce the   multiparty topology into the IPPM framework, and they describe the   performance delivered to a group receiving packets from the same   source.  The concept extends the "path" of the point-to-point   measurement to "path tree" to cover one-to-many topologies.  If   applied to one-to-one topology, the one-to-group metrics provide   exactly the same results as the corresponding one-to-one metrics.4.3.  Discussion on Group-to-One and Group-to-Group Metrics   We note that points of interest can also be selected to define   measurements on group-to-one and group-to-group topologies.  These   topologies are beyond the scope of this memo, because they would   involve multiple packets launched from different sources.  However,   this section gives some insights on these two cases.   The measurements for group-to-one topology can be easily derived from   the one-to-group measurement.  The measurement point is the host that   is acting as a receiver while all other hosts act as sources in this   case.   The group-to-group communication topology has no obvious focal point:   the sources and the measurement collection points can be anywhere.   However, it is possible to organize the problem by applying   measurements in one-to-group or group-to-one topologies for each host   in a uniform way (without taking account of how the realStephan, et al.             Standards Track                    [Page 11]

RFC 5644             Spatial and Multicast Metrics          October 2009   communication might be carried out).  For example, one group of hosts   < ha, hb, hc, ..., hn > might act as sources to send data to another   group of hosts < Ha, Hb, Hc, ..., Hm >, and they can be organized   into n sets of points of interest for one-to-group communications:   < ha, Ha, Hb, Hc, ..., Hm >, < hb, Ha, Hb, Hc, ..., Hm >, <hc, Ha,   Hb, Hc, ..., Hm >, ..., < hn, Ha, Hb, Hc, ..., Hm >.5.  Spatial Vector Metrics Definitions   This section defines vectors for the spatial decomposition of end-to-   end singleton metrics over a path.   Spatial vector metrics are based on the decomposition of standard   end-to-end metrics defined by the IPPM WG in [RFC2679], [RFC2680],   [RFC3393], and [RFC3432].   The spatial vector definitions are coupled with the corresponding   end-to-end metrics.  Measurement methodology aspects are common to   all the vectors defined and are consequently discussed in a common   section.5.1.  A Definition for Spatial One-Way Delay Vector   This section is coupled with the definition of Type-P-One-way-Delay   insection 3 of [RFC2679].  When a parameter from the definition in   [RFC2679] is re-used in this section, the first instance will be   tagged with a trailing asterisk.   Sections3.5 to3.8 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 measurements MUST respect them, especially   those related to methodology, clock, uncertainties, and reporting.5.1.1.  Metric Name   Type-P-Spatial-One-way-Delay-Vector5.1.2.  Metric Parameters   o  Src*, the IP address of the sender.   o  Dst*, the IP address of the receiver.   o  i, an integer in the ordered list <1,2,...,n> of routers in the      path.Stephan, et al.             Standards Track                    [Page 12]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  Hi, a router of the routers digest.   o  T*, a time, the sending (or initial observation) time for a      measured packet.   o  dT*, a delay, the one-way delay for a measured packet.   o  dTi, a delay, the one-way delay for a measured packet from the      source to router Hi.   o  <dT1,... dTi,... dTn> a list of n delay singletons.   o  Type-P*, the specification of the packet type.   o  <H1, H2,..., Hn> the routers digest.5.1.3.  Metric Units   The value of Type-P-Spatial-One-way-Delay-Vector is a sequence of   times (a real number in the dimension of seconds with sufficient   resolution to convey the results).5.1.4.  Definition   Given a Type-P packet sent by the Src at wire-time (first bit) T to   the receiver Dst on the path <H1, H2,..., Hn>.  There is a 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 for each Hi of the path, T+dTi is   either a real number corresponding to the wire-time the packet passes   (last bit received) Hi, or undefined if the packet does not pass Hi   within a specified loss threshold* time.   Type-P-Spatial-One-way-Delay-Vector metric is defined for the path   <Src, H1, H2,..., Hn, Dst> as the sequence of values   <T,dT1,dT2,...,dTn,dT>.5.1.5.  Discussion   Some specific issues that may occur are as follows:   o  the delay singletons "appear" to decrease: dTi > dTi+1.  This may      occur despite being physically impossible with the definition      used.Stephan, et al.             Standards Track                    [Page 13]

RFC 5644             Spatial and Multicast Metrics          October 2009      *  This is frequently due to a measurement clock synchronization         issue.  This point is discussed insection 3.7.1 "Errors or         uncertainties related to Clocks" of [RFC2679].  Consequently,         the values of delays measured at multiple routers may not match         the order of those routers on the path.      *  The actual order of routers on the path may change due to         reconvergence (e.g., recovery from a link failure).      *  The location of the measurement collection point in the device         influences the result.  If the packet is not observed directly         on the input interface, the delay includes buffering time and         consequently an uncertainty due to the difference between         'wire-time' and 'host time'.5.2.  A Definition for Spatial Packet Loss Vector   This section is coupled with the definition of Type-P-One-way-Packet-   Loss.  When a parameter fromsection 2 of [RFC2680] is used in this   section, the first instance will be tagged with a trailing asterisk.   Sections2.5 to2.8 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 MUST respect them, especially those   related to methodology, clock, uncertainties, and reporting.   The following sections define the spatial loss vector, adapt some of   the points above, and introduce points specific to spatial loss   measurement.5.2.1.  Metric Name   Type-P-Spatial-Packet-Loss-Vector5.2.2.  Metric Parameters   o  Src*, the IP address of the sender.   o  Dst*, the IP address of the receiver.   o  i, an integer in the ordered list <1,2,...,n> of routers in the      path.   o  Hi, a router of the routers digest.   o  T*, a time, the sending time for a measured packet.Stephan, et al.             Standards Track                    [Page 14]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  dTi, a delay, the one-way delay for a measured packet from the      source to host Hi.   o  <dT1,..., dTn>, list of n delay singletons.   o  Type-P*, the specification of packet type.   o  <H1, H2,..., Hn>, the routers digest.   o  <L1, L2, ...,Ln>, a list of Boolean values.5.2.3.  Metric Units   The value of Type-P-Spatial-Packet-Loss-Vector is a sequence of   Boolean values.5.2.4.  Definition   Given a Type-P packet sent by the Src at time T to the receiver Dst   on the path <H1, H2, ..., Hn>.  For the sequence of times <T+dT1,T+   dT2,..., T+dTi, ...,T+dTn> the packet passes in <H1, H2, ..., Hi,   ..., Hn>, define the Type-P-Packet-Loss-Vector metric as the sequence   of values <T, L1, L2, ..., Ln> such that for each Hi of the path, a   value of 0 for Li means that dTi is a finite value, and a value of 1   means that dTi is undefined.5.2.5.  Discussion   Some specific issues that may occur are as follows:   o  The result might include the sequence of values 1,0.  Although      this appears physically impossible (a packet is lost, then re-      appears later on the path):      *  The actual routers on the path may change due to reconvergence         (e.g., recovery from a link failure).      *  The order of routers on the path may change due to         reconvergence.      *  A packet may not be observed in a router due to some buffer or         CPU overflow at the measurement collection point.5.3.  A Definition for Spatial One-Way ipdv Vector   When a parameter fromsection 2 of [RFC3393] (the definition of Type-   P-One-way-ipdv) is used in this section, the first instance will be   tagged with a trailing asterisk.Stephan, et al.             Standards Track                    [Page 15]

RFC 5644             Spatial and Multicast Metrics          October 2009   The following sections define the spatial ipdv vector, adapt some of   the points above, and introduce points specific to spatial ipdv   measurement.5.3.1.  Metric Name   Type-P-Spatial-One-way-ipdv-Vector5.3.2.  Metric Parameters   o  Src*, the IP address of the sender.   o  Dst*, the IP address of the receiver.   o  i, an integer in the ordered list <1,2,...,n> of routers in the      path.   o  Hi, a router of the routers digest.   o  T1*, a time, the sending time for a first measured packet.   o  T2*, a time, the sending time for a second measured packet.   o  dT*, a delay, the one-way delay for a measured packet.   o  dTi, a delay, the one-way delay for a measured packet from the      source to router Hi.   o  Type-P*, the specification of the packet type.   o  P1, the first packet sent at time T1.   o  P2, the second packet sent at time T2.   o  <H1, H2,..., Hn>, the routers digest.   o  <T1,dT1.1, dT1.2,..., dT1.n,dT1>, the Type-P-Spatial-One-way-      Delay-Vector for a packet sent at time T1.   o  <T2,dT2.1, dT2.2,..., dT2.n,dT2>, the Type-P-Spatial-One-way-      Delay-Vector for a packet sent at time T2.   o  L*, a packet length in bits.  The packets of a Type-P packet      stream from which the Type-P-Spatial-One-way-Delay-Vector metric      is taken MUST all be of the same length.Stephan, et al.             Standards Track                    [Page 16]

RFC 5644             Spatial and Multicast Metrics          October 20095.3.3.  Metric Units   The value of Type-P-Spatial-One-way-ipdv-Vector is a sequence of   times (a real number in the dimension of seconds with sufficient   resolution to convey the results).5.3.4.  Definition   Given P1 the Type-P packet sent by the sender Src at wire-time (first   bit) T1 to the receiver Dst. Given <T1, dT1.1, dT1.2,..., dT1.n, dT1>   the Type-P-Spatial-One-way-Delay-Vector of P1 over the sequence of   routers <H1, H2,..., Hn>.   Given P2 the Type-P packet sent by the sender Src at wire-time (first   bit) T2 to the receiver Dst. Given <T2, dT2.1, dT2.2,..., dT2.n, dT2>   the Type-P-Spatial-One-way-Delay-Vector of P2 over the same path.   The Type-P-Spatial-One-way-ipdv-Vector metric is defined as the   sequence of values <T1, T2, dT2.1-dT1.1, dT2.2-dT1.2 ,..., dT2.n-   dT1.n, dT2-dT1> such that for each Hi of the sequence of routers <H1,   H2,..., Hn>, dT2.i-dT1.i is either a real number if the packets P1   and P2 pass Hi at wire-time (last bit) dT1.i and dT2.i respectively,   or undefined if at least one of them never passes Hi (and the   respective one-way delay is undefined).  The T1,T2* pair indicates   the inter-packet emission interval and dT2-dT1 is ddT* the Type-P-   One-way-ipdv.5.4.  Spatial Methodology   The methodology, reporting specifications, and uncertainties   specified insection 3 of [RFC2679] apply to each point of interest   (or measurement collection point), Hi, measuring an element of a   spatial delay vector.   Likewise, the methodology, reporting specifications, and   uncertainties specified insection 2 of [RFC2680] apply to each point   of interest, Hi, measuring an element of a spatial packet loss   vector.   Sections3.5 to3.7 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 MUST respect the methodology, clock,   uncertainties, and reporting aspects given there.Stephan, et al.             Standards Track                    [Page 17]

RFC 5644             Spatial and Multicast Metrics          October 2009   Generally, for a given Type-P packet of length L at a specific Hi,   the methodology for spatial vector metrics may proceed as follows:   o  At each Hi, points of interest/measurement collection points      prepare to capture the packet sent at time T, record a timestamp      Ti', and determine the internal delay correction dTi' (seesection3.7.1.  "Errors or uncertainties related to Clocks" of [RFC2679]);   o  Each Hi extracts the path ordering information from the packet      (e.g., time-to-live (TTL));   o  Each Hi computes the corrected wire-time from Src to Hi: Ti = Ti'      - dTi'.  This arrival time is undefined if the packet is not      detected after the 'loss threshold' duration;   o  Each Hi extracts the timestamp T from the packet;   o  Each Hi computes the one-way delay from Src to Hi: dTi = Ti - T;   o  The reference point gathers the result of each Hi and arranges      them according to the path ordering information received to build      the Type-P spatial one-way vector (e.g., Type-P-Spatial-One-way-      Delay-Vector metric <T, dT1, dT2,..., dTn, dT>) over the path      <Src, H1, H2,..., Hn, Dst> at time T.5.4.1.  Packet Loss Detection   In a pure end-to-end measurement, packet losses are detected by the   receiver only.  A packet is lost when Type-P-One-way-Delay is   undefined or very large (see sections2.4 and2.5 of [RFC2680] andsection 3.5 of [RFC2680]).  A packet is deemed lost by the receiver   after a duration that starts at the time the packet is sent.  This   timeout value is chosen by a measurement process.  It determines the   threshold between recording a long packet transfer time as a finite   value or an undefined value.   In a spatial measurement, packet losses may be detected at several   measurement collection points.  Depending on the consistency of the   packet loss detections among the points of interest, a packet may be   considered as lost at one point despite having a finite delay at   another, or it may be observed by the last measurement collection   point of the path but considered lost by Dst.   There is a risk of misinterpreting such results: has the path   changed?  Did the packet arrive at the destination or was it lost on   the very last link?Stephan, et al.             Standards Track                    [Page 18]

RFC 5644             Spatial and Multicast Metrics          October 2009   The same concern applies to one-way delay measures: a delay measured   may be computed as infinite by one observation point but as a real   value by another one, or may be measured as a real value by the last   observation point of the path but designated as undefined by Dst.   The observation/measurement collection points and the destination   SHOULD use consistent methods to detect packets losses.  The methods   and parameters must be systematically reported to permit careful   comparison and to avoid introducing any confounding factors in the   analysis.5.4.2.  Routers Digest   The methodology given above relies on knowing the order of the   router/measurement collection points on the path [RFC2330].   Path instability might cause a test packet to be observed more than   once by the same router, resulting in the repetition of one or more   routers in the routers digest.   For example, repeated observations may occur during rerouting phases   that introduce temporary micro loops.  During such an event, the   routers digest for a packet crossing Ha and Hb may include the   pattern <Hb, Ha, Hb, Ha, Hb>, meaning that Ha ended the computation   of the new path before Hb and that the initial path was from Ha to   Hb, and that the new path is from Hb to Ha.   Consequently, duplication of routers in the routers digest of a   vector MUST be identified before computation of statistics to avoid   producing corrupted information.6.  Spatial Segment Metrics Definitions   This section defines samples to measure the performance of a segment   of a path over time.  The definitions rely on the matrix of the   spatial vector metrics defined above.   First, this section defines a sample of one-way delay, Type-P-   Segment-One-way-Delay-Stream, and a sample of packet loss, Type-P-   Segment-Packet-Loss-Stream.   Then, it defines two different samples of ipdv: Type-P-Segment-ipdv-   prev-Stream uses the current and previous packets as the selection   function, and Type-P-Segment-ipdv-min-Stream uses the minimum delay   as one of the selected packets in every pair.Stephan, et al.             Standards Track                    [Page 19]

RFC 5644             Spatial and Multicast Metrics          October 20096.1.  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 routers on a path.  Since it is very close semantically to   the metric Type-P-One-way-Delay-Poisson-Stream defined insection 4   of [RFC2679], sections4.5 to4.8 of [RFC2679] are integral parts of   the definition text below.6.1.1.  Metric Name   Type-P-Segment-One-way-Delay-Stream6.1.2.  Metric Parameters   o  Src, the IP address of the sender.   o  Dst, the IP address of the receiver.   o  Type-P, the specification of the packet type.   o  i, an integer in the ordered list <1,2,...,n> of routers in the      path.   o  k, an integer that orders the packets sent.   o  a and b, two integers where b > a.   o  Hi, a router of the routers digest.   o  <H1,..., Ha, ..., Hb, ...., Hn>, the routers digest.   o  <T1, T2, ..., Tm>, a list of times.6.1.3.  Metric Units   The value of a Type-P-Segment-One-way-Delay-Stream is a pair of:      A list of times <T1, T2, ..., Tm>; and      A sequence of delays.6.1.4.  Definition   Given two routers, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,   ..., Hn>, and the matrix of Type-P-Spatial-One-way-Delay-Vector for   the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :Stephan, et al.             Standards Track                    [Page 20]

RFC 5644             Spatial and Multicast Metrics          October 2009      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>;      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>;      ...      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.   We define the sample Type-P-Segment-One-way-Delay-Stream as the   sequence <dT1.ab, dT2.ab, ..., dTk.ab, ..., dTm.ab> such that for   each time Tk, 'dTk.ab' is either the real number 'dTk.b - dTk.a', if   the packet sent at the time Tk passes Ha and Hb, or is undefined if   this packet never passes Ha or (inclusive) never passes Hb.6.1.5.  Discussion   Some specific issues that may occur are as follows:   o  the delay singletons "appear" to decrease: dTi > DTi+1, and is      discussed insection 5.1.5.      *  This could also occur when the clock resolution of one         measurement collection point is larger than the minimum delay         of a path.  For example, the minimum delay of a 500 km path         through optical fiber facilities is 2.5 ms, but the measurement         collection point has a clock resolution of 8 ms.   The metric SHALL be invalid for times < T1 , T2, ..., Tm-1, Tm> if   the following conditions occur:   o  Ha or Hb disappears from the path due to some routing change.   o  The order of Ha and Hb changes in the path.6.2.  A Definition of a Sample of Packet Loss of a Segment of the Path   This metric defines a sample of packet loss over time between a pair   of routers of a path.  Since it is very close semantically to the   metric Type-P-Packet-loss-Stream defined insection 3 of [RFC2680],   sections3.5 to3.8 of [RFC2680] are integral parts of the definition   text below.6.2.1.  Metric Name   Type-P-Segment-Packet-Loss-StreamStephan, et al.             Standards Track                    [Page 21]

RFC 5644             Spatial and Multicast Metrics          October 20096.2.2.  Metric Parameters   o  Src, the IP address of the sender.   o  Dst, the IP address of the receiver.   o  Type-P, the specification of the packet type.   o  k, an integer that orders the packets sent.   o  n, an integer that orders the routers on the path.   o  a and b, two integers where b > a.   o  <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the routers digest.   o  Hi, a router of the routers digest.   o  <T1, T2, ..., Tm>, a list of times.   o  <L1, L2, ..., Ln>, a list of Boolean values.6.2.3.  Metric Units   The value of a Type-P-Segment-Packet-Loss-Stream is a pair of:      The list of times <T1, T2, ..., Tm>; and      A sequence of Boolean values.6.2.4.  Definition   Given two routers, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,   ..., Hn> and the matrix of Type-P-Spatial-Packet-Loss-Vector for the   packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :      <T1, L1.1, L1.2,..., L1.a, ..., L1.b, ..., L1.n, L>,      <T2, L2.1, L2.2,..., L2.a, ..., L2.b, ..., L2.n, L>,      ...,      <Tm, Lm.1, Lm.2,..., Lma, ..., Lm.b, ..., Lm.n, L>.   We define the value of the sample Type-P-Segment-Packet-Loss-Stream   from Ha to Hb as the sequence of Booleans <L1.ab, L2.ab,..., Lk.ab,   ..., Lm.ab> such that for each Tk:Stephan, et al.             Standards Track                    [Page 22]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  A value of Lk of 0 means that Ha and Hb observed the packet sent      at time Tk (both Lk.a and Lk.b have a value of 0).   o  A value of Lk of 1 means that Ha observed the packet sent at time      Tk (Lk.a has a value of 0) and that Hb did not observe the packet      sent at time Tk (Lk.b has a value of 1).   o  The value of Lk is undefined when neither Ha nor Hb observed the      packet (both Lk.a and Lk.b have a value of 1).6.2.5.  Discussion   Unlike Type-P-Packet-loss-Stream, Type-P-Segment-Packet-Loss-Stream   relies on the stability of the routers digest.  The metric SHALL be   invalid for times < T1 , T2, ..., Tm-1, Tm> if the following   conditions occur:   o  Ha or Hb disappears from the path due to some routing change.   o  The order of Ha and Hb changes in the path.   o  Lk.a or Lk.b is undefined.   o  Lk.a has the value 1 (not observed) and Lk.b has the value 0      (observed).   o  L has the value 0 (the packet was received by Dst) and Lk.ab has      the value 1 (the packet was lost between Ha and Hb).6.3.  A Definition of a Sample of ipdv of a Segment Using the Previous      Packet Selection Function   This metric defines a sample of ipdv [RFC3393] over time between a   pair of routers using the previous packet as the selection function.6.3.1.  Metric Name   Type-P-Segment-ipdv-prev-Stream6.3.2.  Metric Parameters   o  Src, the IP address of the sender.   o  Dst, the IP address of the receiver.   o  Type-P, the specification of the packet type.   o  k, an integer that orders the packets sent.Stephan, et al.             Standards Track                    [Page 23]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  n, an integer that orders the routers on the path.   o  a and b, two integers where b > a.   o  <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the routers 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.6.3.3.  Metric Units   The value of a Type-P-Segment-ipdv-prev-Stream is a pair of:      The list of <T1, T2, ..., Tm-1, Tm>; and      A list of pairs of interval of times and delays;6.3.4.  Definition   Given two routers, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,   ..., Hn> and the matrix of Type-P-Spatial-One-way-Delay-Vector for   the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,      ...      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.   We define the Type-P-Segment-ipdv-prev-Stream as the sequence of   packet time pairs and delay variations   <(T1, T2 , dT2.ab - dT1.ab) ,...,   (Tk-1, Tk, dTk.ab - dTk-1.ab), ...,   (Tm-1, Tm, dTm.ab - dTm-1.ab)>   For any pair, Tk, Tk-1 in k=1 through m, the difference dTk.ab - dTk-   1.ab is undefined if:   o  the delay dTk.a or the delay dTk-1.a is undefined, OR   o  the delay dTk.b or the delay dTk-1.b is undefined.Stephan, et al.             Standards Track                    [Page 24]

RFC 5644             Spatial and Multicast Metrics          October 20096.3.5.  Discussion   This metric belongs to the family of inter-packet delay variation   metrics (IPDV in uppercase) whose results are extremely sensitive to   the inter-packet interval in practice.   The inter-packet interval of an end-to-end IPDV metric is under the   control of the source (ingress point of interest).  In contrast, the   inter-packet interval of a segment IPDV metric is not under the   control the ingress point of interest of the measure, Ha.  The   interval will certainly vary if there is delay variation between the   Source and Ha.  Therefore, the ingress inter-packet interval must be   known at Ha in order to fully comprehend the delay variation between   Ha and Hb.6.4.  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 routers on a path using the minimum delay as one of the   selected packets in every pair.6.4.1.  Metric Name   Type-P-Segment-One-way-ipdv-min-Stream6.4.2.  Metric Parameters   o  Src, the IP address of the sender.   o  Dst, the IP address of the receiver.   o  Type-P, the specification of the packet type.   o  k, an integer that orders the packets sent.   o  i, an integer that identifies a packet sent.   o  n, an integer that orders the routers on the path.   o  a and b, two integers where b > a.   o  <H1, H2, ..., Ha, ..., Hb, ...,Hn>, the routers 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.Stephan, et al.             Standards Track                    [Page 25]

RFC 5644             Spatial and Multicast Metrics          October 20096.4.3.  Metric Units   The value of a Type-P-Segment-One-way-ipdv-min-Stream is a pair of:      The list of <T1, T2, ..., Tm-1, Tm>; and      A list of times.6.4.4.  Definition   Given two routers, Ha and Hb, of the path <H1, H2,..., Ha, ..., Hb,   ..., Hn> and the matrix of Type-P-Spatial-One-way-Delay-Vector for   the packets sent from Src to Dst at times <T1, T2, ..., Tm-1, Tm> :      <T1, dT1.1, dT1.2, ..., dT1.a, ..., dT1.b,..., dT1.n, dT1>,      <T2, dT2.1, dT2.2, ..., dT2.a, ..., dT2.b,..., dT2.n, dT2>,      ...      <Tm, dTm.1, dTm.2, ..., dTm.a, ..., dTm.b,..., dTm.n, dTm>.   We define the Type-P-Segment-One-way-ipdv-min-Stream as the sequence   of times <dT1.ab - min(dTi.ab) ,..., dTk.ab - min(dTi.ab), ...,   dTm.ab - min(dTi.ab)> where:   o  min(dTi.ab) is the minimum value of the tuples (dTk.b - dTk.a);   o  for each time Tk, dTk.ab is undefined if dTk.a or (inclusive)      dTk.b is undefined, or the real number (dTk.b - dTk.a) is      undefined.6.4.5.  Discussion   This metric belongs to the family of packet delay variation metrics   (PDV).  PDV distributions have less sensitivity to inter-packet   interval variations than IPDV values, as discussed above.   In principle, the PDV distribution reflects the variation over many   different inter-packet intervals, from the smallest inter-packet   interval, up to the length of the evaluation interval, Tm - T1.   Therefore, when delay variation occurs and disturbs the packet   spacing observed at Ha, the PDV results will likely compare favorably   to a PDV measurement where the source is Ha and the destination is   Hb, because a wide range of spacings are reflected in any PDV   distribution.Stephan, et al.             Standards Track                    [Page 26]

RFC 5644             Spatial and Multicast Metrics          October 20097.  One-to-Group Metrics Definitions   This section defines performance metrics between a source and a group   of receivers.7.1.  A Definition for One-to-Group Delay   This section defines a metric for one-way delay between a source and   a group of receivers.7.1.1.  Metric Name   Type-P-One-to-group-Delay-Vector7.1.2.  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 times.   o  Type-P, the specification of the packet type.   o  Gr, the receiving group identifier.  The parameter Gr is the      multicast group address if the measured packets are transmitted      over IP multicast.  This parameter is to differentiate the      measured traffic from other unicast and multicast traffic.  It is      OPTIONAL for this metric to avoid losing any generality, i.e., to      make the metric also applicable to unicast measurement where there      is only one receiver.7.1.3.  Metric Units   The value of a Type-P-One-to-group-Delay-Vector is a set of Type-P-   One-way-Delay singletons [RFC2679], that is a sequence of times (a   real number in the dimension of seconds with sufficient resolution to   convey the results).7.1.4.  Definition   Given a Type-P packet sent by the source Src at time T, and the N   hosts { Recv1,...,RecvN } which receive the packet at the time {   T+dT1,...,T+dTn }, or the packet does not pass a receiver within a   specified loss threshold time, then the Type-P-One-to-group-Delay-Stephan, et al.             Standards Track                    [Page 27]

RFC 5644             Spatial and Multicast Metrics          October 2009   Vector is defined as the set of the Type-P-One-way-Delay singletons   between Src and each receiver with value of { dT1, dT2,...,dTn },   where any of the singletons may be undefined if the packet did not   pass the corresponding receiver within a specified loss threshold   time.7.2.  A Definition for One-to-Group Packet Loss7.2.1.  Metric Name   Type-P-One-to-group-Packet-Loss-Vector7.2.2.  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  Type-P, the specification of the packet type.   o  Gr, the receiving group identifier, OPTIONAL.7.2.3.  Metric Units   The value of a Type-P-One-to-group-Packet-Loss-Vector is a set of   Type-P-One-way-Packet-Loss singletons [RFC2680].   o  T, time the source packet was sent.   o  L1,...,LN a list of Boolean values.7.2.4.  Definition   Given a Type-P packet sent by the source Src at T and the N hosts,   Recv1,...,RecvN, the Type-P-One-to-group-Packet-Loss-Vector is   defined as a set of the Type-P-One-way-Packet-Loss singletons between   Src and each of the receivers:   {T, <L1=0|1>,<L2=0|1>,..., <LN=0|1>},   where the Boolean value 0|1 depends on receiving the packet at a   particular receiver within a loss threshold time.Stephan, et al.             Standards Track                    [Page 28]

RFC 5644             Spatial and Multicast Metrics          October 20097.3.  A Definition for One-to-Group ipdv7.3.1.  Metric Name   Type-P-One-to-group-ipdv-Vector7.3.2.  Metric Parameters   o  Src, the IP address of a host acting as the source.   o  Recv1,..., RecvN, the IP addresses of the N hosts acting as      receivers.   o  T1, a time.   o  T2, a time.   o  ddT1, ...,ddTn, a list of times.   o  Type-P, the specification of the packet type.   o  F, a selection function non-ambiguously defining the two packets      from the stream selected for the metric.   o  Gr, the receiving group identifier.  The parameter Gr is the      multicast group address if the measured packets are transmitted      over IP multicast.  This parameter is to differentiate the      measured traffic from other unicast and multicast traffic.  It is      OPTIONAL in the metric to avoid losing any generality, i.e., to      make the metric also applicable to unicast measurement where there      is only one receiver.7.3.3.  Metric Units   The value of a Type-P-One-to-group-ipdv-Vector is a set of Type-P-   One-way-ipdv singletons [RFC3393].7.3.4.  Definition   Given a Type-P packet stream, Type-P-One-to-group-ipdv-Vector is   defined for two packets transferred from the source Src to the N   hosts {Recv1,...,RecvN }, which are selected by the selection   function F as the difference between the value of the Type-P-One-to-   group-Delay-Vector from Src to { Recv1,..., RecvN } at time T1 and   the value of the Type-P-One-to-group-Delay-Vector from Src to {   Recv1,...,RecvN } at time T2.  T1 is the wire-time at which Src sentStephan, et al.             Standards Track                    [Page 29]

RFC 5644             Spatial and Multicast Metrics          October 2009   the first bit of the first packet, and T2 is the wire-time at which   Src sent the first bit of the second packet.  This metric is derived   from the Type-P-One-to-group-Delay-Vector metric.   For a set of real numbers {ddT1,...,ddTn}, the Type-P-One-to-group-   ipdv-Vector from Src to { Recv1,...,RecvN } at T1, T2 is   {ddT1,...,ddTn} means that Src sent two packets, the first at wire-   time T1 (first bit), and the second at wire-time T2 (first bit) and   the packets were received by { Recv1,...,RecvN } at wire-time {dT1+   T1,...,dTn+T1}(last bit of the first packet), and at wire-time {dT'1+   T2,...,dT'n+T2} (last bit of the second packet), and that {dT'1-   dT1,...,dT'n-dTn} ={ddT1,...,ddTn}.   For any pair of selected packets, the difference dT'n-dTn is   undefined if:   o  the delay dTn to Receiver n is undefined, OR   o  the delay dT'n to Receiver n is undefined.8.  One-to-Group Sample Statistics   The one-to-group metrics defined above are directly achieved by   collecting relevant unicast one-way metrics measurements results and   by gathering them per group of receivers.  They produce network   performance information that guides engineers toward potential   problems that may have happened on any branch of a multicast routing   tree.   The results of these metrics are not directly usable to present the   performance of a group because each result is made of a huge number   of singletons that are difficult to read and analyze.  As an example,   delays are not comparable because the distance between receiver and   sender differs.  Furthermore, they don't capture relative performance   situations in a multiparty communication.   From the performance point of view, the multiparty communication   services not only require the support of absolute performance   information but also information on "relative performance".   "Relative performance" means the difference between absolute   performance of all users.  Directly using the one-way metrics cannot   present the relative performance situation.  However, if we use the   variations of all users' one-way parameters, we can have new metrics   to measure the difference of the absolute performance and hence   provide the threshold value of relative performance that a multiparty   service might demand.  A very good example of the high relative   performance requirement is online gaming.  A very small difference in   delay might result in failure in the game.  We have to use multicast-Stephan, et al.             Standards Track                    [Page 30]

RFC 5644             Spatial and Multicast Metrics          October 2009   specific statistic metrics to define the relative delay required by   online gaming.  There are many other services, e.g., online biding,   online stock market, etc., that require multicast metrics in order to   evaluate the network against their requirements.  Therefore, we can   see the importance of new, multicast specific, statistic metrics to   feed this need.   We might also use some one-to-group statistic conceptions to present   and report the group performance and relative performance to save the   report transmission bandwidth.  Statistics have been defined for One-   way metrics in corresponding RFCs.  They provide the foundation of   definition for performance statistics.  For instance, there are   definitions for minimum and maximum one-way delay in [RFC2679].   However, there is a dramatic difference between the statistics for   one-to-one communications and for one-to-many communications.  The   former one only has statistics over the time dimension while the   later one can have statistics over both time and space dimensions.   This space dimension is introduced by the Matrix concept as   illustrated in Figure 4.  For a Matrix M, each row is a set of one-   way singletons spreading over the time dimension and each column is   another set of One-way singletons spreading over the space dimension.            Receivers             Space               ^             1 |    / R1dT1   R1dT2     R1dT3 ... R1dTk \               |   |                                     |             2 |   |  R2dT1   R2dT2     R2dT3 ... R2dTk  |               |   |                                     |             3 |   |  R3dT1   R3dT2     R3dT3 ... R3dTk  |             . |   |                                     |             . |   |                                     |             . |   |                                     |             n |    \ RndT1   RndT2     RndT3 ... RndTk /               +--------------------------------------------> time              T0                         Figure 4: Matrix M (n*m)   In Matrix M, each element is a one-way delay singleton.  Each column   is a delay vector.  It contains the one-way delays of the same packet   observed at n points of interest.  It implies the geographical factor   of the performance within a group.  Each row is a set of one-way   delays observed during a sampling interval at one of the points of   interest.  It presents the delay performance at a receiver over the   time dimension.Stephan, et al.             Standards Track                    [Page 31]

RFC 5644             Spatial and Multicast Metrics          October 2009   Therefore, one can either calculate statistics by rows over the space   dimension or by columns over the time dimension.  It's up to the   operators or service providers in which dimension they are   interested.  For example, a TV broadcast service provider might want   to know the statistical performance of each user in a long-term run   to make sure their services are acceptable and stable.  While for an   online gaming service provider, he might be more interested in   knowing if all users are served fairly by calculating the statistics   over the space dimension.  This memo does not intend to recommend   which of the statistics are better than the others.   To save the report transmission bandwidth, each point of interest can   send statistics in a pre-defined time interval to the reference point   rather than sending every one-way singleton it observed.  As long as   an appropriate time interval is decided, appropriate statistics can   represent the performance in a certain accurate scale.  How to decide   the time interval and how to bootstrap all points of interest and the   reference point depend on applications.  For instance, applications   with a lower transmission rate can have the time interval be longer,   and ones with higher transmission rate can have the time interval be   shorter.  However, this is out of the scope of this memo.   Moreover, after knowing the statistics over the time dimension, one   might want to know how these statistics are distributed over the   space dimension.  For instance, a TV broadcast service provider had   the performance Matrix M and calculated the one-way delay mean over   the time dimension to obtain a delay Vector as {V1,V2,..., VN}.  He   then calculated the mean of all the elements in the Vector to see   what level of delay he has served to all N users.  This new delay   mean gives information on how well the service has been delivered to   a group of users during a sampling interval in terms of delay.  It   requires twice as much calculation to have this statistic over both   time and space dimensions.  These kinds of statistics are referred to   as 2-level statistics to distinguish them from 1-level statistics   calculated over either space or time dimension.  It can be easily   proven that no matter over which dimension a 2-level statistic is   calculated first, the results are the same.  That is, one can   calculate the 2-level delay mean using the Matrix M by having the   1-level delay mean over the time dimension first and then calculate   the mean of the obtained vector to find out the 2-level delay mean.   Or, he can do the 1-level statistic calculation over the space   dimension first and then have the 2-level delay mean.  Both results   will be exactly the same.  Therefore, when defining a 2-level   statistic, there is no need to specify the order in which the   calculation is executed.Stephan, et al.             Standards Track                    [Page 32]

RFC 5644             Spatial and Multicast Metrics          October 2009   Many statistics can be defined for the proposed one-to-group metrics   over the space dimension, the time dimension, or both.  This memo   treats the case where a stream of packets from the Source results in   a sample at each of the Receivers in the Group, and these samples are   each summarized with the usual statistics employed in one-to-one   communication.  New statistic definitions are presented, which   summarize the one-to-one statistics over all the Receivers in the   Group.8.1.  Discussion on the Impact of Packet Loss on Statistics   Packet loss does have effects on one-way metrics and their   statistics.  For example, a lost packet can result in an infinite   one-way delay.  It is easy to handle the problem by simply ignoring   the infinite value in the metrics and in the calculation of the   corresponding statistics.  However, the packet loss has such a strong   impact on the statistics calculation for the one-to-group metrics   that it can not be solved by the same method used for one-way   metrics.  This is due to the complexity of building a matrix, which   is needed for calculation of the statistics proposed in this memo.   The situation is that measurement results obtained by different end   users might have different packet loss pattern.  For example, for   User1, packet A was observed to be lost.  And for User2, packet A was   successfully received, but packet B was lost.  If the method to   overcome the packet loss for one-way metrics is applied, the two   singleton sets reported by User1 and User2 will be different in terms   of the transmitted packets.  Moreover, if User1 and User2 have a   different number of lost packets, the size of the results will be   different.  Therefore, for the centralized calculation, the reference   point will not be able to use these two results to build up the group   Matrix and cannot calculate the statistics.  The extreme situation   being the case when no packets arrive at any user.  One of the   possible solutions is to replace the infinite/undefined delay value   by the average of the two adjacent values.  For example, if the   result reported by User1 is { R1dT1 R1dT2 R1dT3 ...  R1dTK-1 UNDEF   R1dTK+1...  R1MD } where "UNDEF" is an undefined value, the reference   point can replace it by R1dTK = {(R1dTK-1)+( R1dTK+1)}/2.  Therefore,   this result can be used to build up the group Matrix with an   estimated value R1dTK.  There are other possible solutions, such as   using the overall mean of the whole result to replace the infinite/   undefined value, and so on.  However, this is out of the scope of   this memo.   For the distributed calculation, the reported statistics might have   different "weight" to present the group performance, which is   especially true for delay and ipdv relevant metrics.  For example,Stephan, et al.             Standards Track                    [Page 33]

RFC 5644             Spatial and Multicast Metrics          October 2009   User1 calculates the Type-P-Finite-One-way-Delay-Mean R1MD as shown   in Figure 7 without any packet loss, and User2 calculates the R2MD   with N-2 packet loss.  The R1MD and R2MD should not be treated with   equal weight because R2MD was calculated only based on two delay   values in the whole sample interval.  One possible solution is to use   a weight factor to mark every statistic value sent by users and use   this factor for further statistic calculation.8.2.  General Metric Parameters   o  Src, the IP address of a host.   o  G, the receiving group identifier.   o  N, the number of Receivers (Recv1, Recv2, ...  RecvN).   o  T, a time (start of test interval).   o  Tf, a time (end of test interval).   o  K, the number of packets sent from the source during the test      interval.   o  J[n], the number of packets received at a particular Receiver, n,      where 1<=n<=N.   o  lambda, a rate in reciprocal seconds (for Poisson Streams).   o  incT, the nominal duration of inter-packet interval, first bit to      first bit (for Periodic Streams).   o  T0, a time that MUST be selected at random from the interval [T,      T+I] to start generating packets and taking measurements (for      Periodic Streams).   o  TstampSrc, the wire-time of the packet as measured at MP(Src) (the      Source Measurement Point).   o  TstampRecv, the wire-time of the packet as measured at MP(Recv),      assigned to packets that arrive within a "reasonable" time.   o  Tmax, a maximum waiting time for packets at the destination, set      sufficiently long to disambiguate packets with long delays from      packets that are discarded (lost); thus, the distribution of delay      is not truncated.   o  dT, shorthand notation for a one-way delay singleton value.Stephan, et al.             Standards Track                    [Page 34]

RFC 5644             Spatial and Multicast Metrics          October 2009   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.8.3.  One-to-Group Delay Statistics   This section defines the overall one-way delay statistics for a   receiver and for an entire group as illustrated by the matrix below.      Recv    /----------- Sample -------------\   Stats      Group Stat       1      R1dT1   R1dT2     R1dT3 ... R1dTk    R1MD  \                                                          |       2      R2dT1   R2dT2     R2dT3 ... R2dTk    R2MD   |                                                          |       3      R3dT1   R3dT2     R3dT3 ... R3dTk    R3MD    > Group Delay       .                                                  |       .                                                  |       .                                                  |       n      RndT1   RndT2     RndT3 ... RndTk    RnMD  /                                                 Receiver-n                                                   Delay                     Figure 5: One-to-Group Mean Delay   Statistics are computed on the finite one-way delays of the matrix   above.   All one-to-group delay statistics are expressed in seconds with   sufficient resolution to convey three significant digits.8.3.1.  Type-P-One-to-group-Receiver-n-Mean-Delay   This section defines Type-P-One-to-group-Receiver-n-Mean-Delay, the   Delay Mean, at each Receiver N, also named RnMD.   We obtain the value of Type-P-One-way-Delay singleton for all packets   sent during the test interval at each Receiver (Destination), as per   [RFC2679].  For each packet that arrives within Tmax of its sending   time, TstampSrc, the one-way delay singleton (dT) will be the finite   value TstampRecv[i] - TstampSrc[i] in units of seconds.  Otherwise,   the value of the singleton is Undefined.Stephan, et al.             Standards Track                    [Page 35]

RFC 5644             Spatial and Multicast Metrics          October 2009                           J[n]                           ---                      1    \           RnMD =    --- *  >  TstampRecv[i] - TstampSrc[i]                     J[n]  /                           ---                           i = 1           Note:  RnMD value is Undefined when J[n] = 0 for all n.            Figure 6: Type-P-One-to-group-Receiver-n-Mean-Delay   where all packets i= 1 through J[n] have finite singleton delays.8.3.2.  Type-P-One-to-group-Mean-Delay   This section defines Type-P-One-to-group-Mean-Delay, the Mean one-way   Delay calculated over the entire Group, also named GMD.                                         N                                        ---                                   1    \                            GMD =  - *   >   RnMD                                   N    /                                        ---                                        n = 1                 Figure 7: Type-P-One-to-group-Mean-Delay   Note that the Group Mean Delay can also be calculated by summing the   finite one-way delay singletons in the matrix, and dividing by the   number of finite one-way delay singletons.8.3.3.   Type-P-One-to-group-Range-Mean-Delay   This section defines a metric for the Range of Mean Delays over all N   receivers in the Group (R1MD, R2MD...RnMD).   Type-P-One-to-group-Range-Mean-Delay = GRMD = max(RnMD) - min(RnMD)8.3.4.  Type-P-One-to-group-Max-Mean-Delay   This section defines a metric for the Maximum of Mean Delays over all   N receivers in the Group (R1MD, R2MD,...RnMD).   Type-P-One-to-group-Max-Mean-Delay = GMMD = max(RnMD)Stephan, et al.             Standards Track                    [Page 36]

RFC 5644             Spatial and Multicast Metrics          October 20098.4.  One-to-Group Packet Loss Statistics   This section defines the overall one-way loss statistics for a   receiver and for an entire group as illustrated by the matrix below.    Recv    /----------- Sample ----------\   Stats     Group Stat      1      R1L1   R1L2     R1L3 ... R1Lk     R1LR \                                                     |      2      R2L1   R2L2     R2L3 ... R2Lk     R2LR  |                                                     |      3      R3L1   R3L2     R3L3 ... R3Lk     R3LR   > Group Loss Ratio      .                                              |      .                                              |      .                                              |      n      RnL1   RnL2     RnL3 ... RnLk     RnLR /                                           Receiver-n                                           Loss Ratio                     Figure 8: One-to-Group Loss Ratio   Statistics are computed on the sample of Type-P-One-way-Packet-Loss   [RFC2680] of the matrix above.   All loss ratios are expressed in units of packets lost to total   packets sent.8.4.1.  Type-P-One-to-group-Receiver-n-Loss-Ratio   Given a Matrix of loss singletons as illustrated above, determine the   Type-P-One-way-Packet-Loss-Average for the sample at each receiver,   according to the definitions and method of [RFC2680].  The Type-P-   One-way-Packet-Loss-Average and the Type-P-One-to-group-Receiver-n-   Loss-Ratio, also named RnLR, are equivalent metrics.  In terms of the   parameters used here, these metrics definitions can be expressed as                                           K                                          ---                                     1    \                             RnLR =  - *   >   RnLk                                     K    /                                          ---                                         k = 1            Figure 9: Type-P-One-to-group-Receiver-n-Loss-RatioStephan, et al.             Standards Track                    [Page 37]

RFC 5644             Spatial and Multicast Metrics          October 20098.4.2.  Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio   Usually, the number of packets sent is used in the denominator of   packet loss ratio metrics.  For the comparative metrics defined here,   the denominator is the maximum number of packets received at any   receiver for the sample and test interval of interest.  The numerator   is the sum of the losses at receiver n.   The Comparative Loss Ratio, also named, RnCLR, is defined as                                  K                                 ---                                 \                                  >   Ln(k)                                 /                                 ---                                 k=1            RnCLR =  -----------------------------                              /    K         \                              |   ---        |                              |   \          |                      K - Min |    >   Ln(k) |                              |   /          |                              |   ---        |                              \   k=1        / N            Note: Ln is a set of one-way loss values at receiver n.                  There is one value for each of the K packets sent.         Figure 10: Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio8.4.3.  Type-P-One-to-group-Loss-Ratio   Type-P-One-to-group-Loss-Ratio, the overall Group Loss Ratio, also   named GLR, is defined as:                                         K,N                                         ---                                   1     \                            GLR = --- *   >   Ln(k)                                  K*N    /                                         ---                                        k,n = 1                 Figure 11: Type-P-One-to-group-Loss-RatioStephan, et al.             Standards Track                    [Page 38]

RFC 5644             Spatial and Multicast Metrics          October 2009   Where the sum includes all of the Loss singletons, Ln(k), over the N   receivers and K packets sent, in a ratio with the total packets over   all receivers.8.4.4.  Type-P-One-to-group-Range-Loss-Ratio   The One-to-group Loss Ratio Range is defined as:   Type-P-One-to-group-Range-Loss-Ratio = max(RnLR) - min(RnLR)   It is most effective to indicate the range by giving both the maximum   and minimum loss ratios for the Group, rather than only reporting the   difference between them.8.5.  One-to-group Delay Variation Statistics   This section defines one-way delay variation (DV) statistics for an   entire group as illustrated by the matrix below.    Recv    /------------- Sample --------------\   Stats     1      R1ddT1   R1ddT2     R1ddT3 ... R1ddTk   R1DV  \                                                           |     2      R2ddT1   R2ddT2     R2ddT3 ... R2ddTk   R2DV   |                                                           |     3      R3ddT1   R3ddT2     R3ddT3 ... R3ddTk   R3DV    > Group Stat     .                                                     |     .                                                     |     .                                                     |     n      RnddT1   RnddT2     RnddT3 ... RnddTk   RnDV  /           Figure 12: One-to-group Delay Variation Matrix (DVMa)   Statistics are computed on the sample of Type-P-One-way-ipdv   singletons of the group delay variation matrix above where RnddTk is   the Type-P-One-way-ipdv singleton evaluated at Receiver n for the   packet k and where RnDV is the point-to-point one-way packet delay   variation for Receiver n.   All One-to-group delay variation statistics are expressed in seconds   with sufficient resolution to convey three significant digits.8.5.1.  Type-P-One-to-group-Range-Delay-Variation   This section defines a metric for the Range of Delay Variation over   all N receivers in the Group.Stephan, et al.             Standards Track                    [Page 39]

RFC 5644             Spatial and Multicast Metrics          October 2009   Maximum DV and minimum DV over all receivers summarize the   performance over the Group (where DV is a point-to-point metric).   For each receiver, the DV is usually expressed as the 1-10^(-3)   quantile of one-way delay minus the minimum one-way delay.   Type-P-One-to-group-Range-Delay-Variation = GRDV =   = max(RnDV) - min(RnDV) for all n receivers   This range is determined from the minimum and maximum values of the   point-to-point one-way IP Packet Delay Variation for the set of   Destinations in the group and a population of interest, using the   Packet Delay Variation expressed as the 1-10^-3 quantile of one-way   delay minus the minimum one-way delay.  If a more demanding service   is considered, one alternative is to use the 1-10^-5 quantile, and in   either case, the quantile used should be recorded with the results.   Both the minimum and the maximum delay variation are recorded, and   both values are given to indicate the location of the range.9.  Measurement Methods: Scalability and Reporting   Virtually all the guidance on measurement processes supplied by the   earlier IPPM RFCs (such as [RFC2679] and [RFC2680]) for one-to-one   scenarios is applicable here in the spatial and multiparty   measurement scenario.  The main difference is that the spatial and   multiparty configurations require multiple points of interest where a   stream of singletons will be collected.  The amount of information   requiring storage grows with both the number of metrics and the   points of interest, so the scale of the measurement architecture   multiplies the number of singleton results that must be collected and   processed.   It is possible that the architecture for results collection involves   a single reference point with connectivity to all the points of   interest.  In this case, the number of points of interest determines   both storage capacity and packet transfer capacity of the host acting   as the reference point.  However, both the storage and transfer   capacity can be reduced if the points of interest are capable of   computing the summary statistics that describe each measurement   interval.  This is consistent with many operational monitoring   architectures today, where even the individual singletons may not be   stored at each point of interest.   In recognition of the likely need to minimize the form of the results   for storage and communication, the Group metrics above have been   constructed to allow some computations on a per-Receiver basis.  ThisStephan, et al.             Standards Track                    [Page 40]

RFC 5644             Spatial and Multicast Metrics          October 2009   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).9.1.  Computation Methods   The scalability issue can be raised when there are thousands of   points of interest in a group who are trying to send back the   measurement results to the reference point for further processing and   analysis.  The points of interest can send either the whole measured   sample or only the calculated statistics.  The former is a   centralized statistic calculation method and the latter is a   distributed statistic calculation method.  The sample should include   all metrics parameters, the values, and the corresponding sequence   numbers.  The transmission of the whole sample can cost much more   bandwidth than the transmission of the statistics that should include   all statistic parameters specified by policies and the additional   information about the whole sample, such as the size of the sample,   the group address, the address of the point of interest, the ID of   the sample session, and so on.  Apparently, the centralized   calculation method can require much more bandwidth than the   distributed calculation method when the sample size is big.  This is   especially true when the measurement has a very large number of the   points of interest.  It can lead to a scalability issue at the   reference point by overloading the network resources.   The distributed calculation method can save much more bandwidth and   mitigate issues arising from scalability at the reference point side.   However, it may result in a loss of information.  As not all measured   singletons are available for building up the group matrix, the real   performance over time can be hidden from the result.  For example,   the loss pattern can be missed by simply accepting the loss ratio.   This tradeoff between bandwidth consumption and information   acquisition has to be taken into account when designing the   measurement approach.   One possible solution could be to transmit the statistic parameters   to the reference point first to obtain the general information of the   group performance.  If detailed results are required, the reference   point should send the requests to the points of interest, which could   be particular ones or the whole group.  This procedure can happen in   the off peak time and can be well scheduled to avoid delivery of too   many points of interest at the same time.  Compression techniques can   also be used to minimize the bandwidth required by the transmission.   This could be a measurement protocol to report the measurement   results.  However, this is out of the scope of this memo.Stephan, et al.             Standards Track                    [Page 41]

RFC 5644             Spatial and Multicast Metrics          October 20099.2.  Measurement   To prevent any bias in the result, the configuration of a one-to-many   measure must take into consideration that more packets will be routed   than sent (copies of a packet sent are expected to arrive at many   destination points) and select a test packet rate that will not   impact the network performance.9.3.  Effect of Time and Space Aggregation Order on Stats   This section presents the impact of the aggregation order on the   scalability of the reporting and of the computation.  It makes the   hypothesis that receivers are not co-located and that results are   gathered in a point of reference for further usages.   Multimetric samples are represented in a matrix as illustrated below      Point of      Interest        1      R1S1   R1S1     R1S1 ... R1Sk    \                                                 |        2      R2S1   R2S2     R2S3 ... R2Sk     |                                                 |        3      R3S1   R3S2     R3S3 ... R3Sk      >  Sample over Space        .                                        |        .                                        |        .                                        |        n      RnS1   RnS2     RnS3 ... RnSk    /               S1M    S2M      S3M  ... SnM     Stats over Space               \-------------  ------------/                             \/                 Stats over Space and Time       Figure 13: Impact of Space Aggregation on Multimetrics Stats   Two methods are available to compute statistics on a matrix:   o  Method 1: The statistic metric is computed over time and then over      space; or   o  Method 2: The statistic metric is computed over space and then      over time.Stephan, et al.             Standards Track                    [Page 42]

RFC 5644             Spatial and Multicast Metrics          October 2009   These two methods differ only by the order of the aggregation.  The   order does not impact the computation resources required.  It does   not change the value of the result.  However, it impacts severely the   minimal volume of data to report:   o  Method 1: Each point of interest periodically computes statistics      over time to lower the volume of data to report.  They are      reported to the reference point for subsequent computations over      the spatial dimension.  This volume no longer depends on the      number of samples.  It is only proportional to the computation      period.   o  Method 2: The volume of data to report is proportional to the      number of samples.  Each sample, RiSi, must be reported to the      reference point for computing statistic over space and statistic      over time.  The volume increases with the number of samples.  It      is proportional to the number of test packets;   Method 2 has severe drawbacks in terms of security and dimensioning:   o  Increasing the rate of the test packets may result in a Denial of      Service (DoS) toward the points of reference;   o  The dimensioning of a measurement system is quite impossible to      validate because any increase of the rate of the test packets will      increase the bandwidth requested to collect the raw results.   The computation period over time period (commonly named the   aggregation period) provides the reporting side with a control of   various collecting aspects such as bandwidth, computation, and   storage capacities.  So this document defines metrics based on method   1.9.3.1.  Impact on Spatial Statistics   Two methods are available to compute spatial statistics:   o  Method 1: Spatial segment metrics and statistics are preferably      computed over time for each points of interest;   o  Method 2: Vectors metrics are intrinsically instantaneous space      metrics, which must be reported using Method 2 whenever      instantaneous metrics information is needed.Stephan, et al.             Standards Track                    [Page 43]

RFC 5644             Spatial and Multicast Metrics          October 20099.3.2.  Impact on One-to-Group Statistics   Two methods are available to compute group statistics:   o  Method 1: Figure 5 and Figure 8 illustrate the method.  The one-      to-one statistic is computed per interval of time before the      computation of the mean over the group of receivers.   o  Method 2: Figure 13 presents the second method.  The metric is      computed over space and then over time.10.  Manageability Considerations   This section defines the reporting of all the metrics introduced in   the document.   Information models of spatial metrics and of one-to-group metrics are   similar except that points of interests of spatial vectors MUST be   ordered.   The complexity of the reporting relies on the number of points of   interest.10.1.  Reporting Spatial Metric   The reporting of spatial metrics shares a lot of aspects withRFC2679 andRFC 2680.  New ones are common to all the definitions and   are mostly related to the reporting of the path and of methodology   parameters that may bias raw results analysis.  This section presents   these specific parameters and then lists exhaustively the parameters   that SHOULD be reported.10.1.1.  Path   End-to-end metrics can't determine the path of the measure despite   the fact that IPPM RFCs recommend it be reported (seesection 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 routers of the path participating to the   instantaneous measure.10.1.2.  Host Order   A spatial vector MUST order the points of interest according to their   order in the path.  The ordering MAY be based on information from the   TTL in IPv4, the Hop Limit in IPv6, or the corresponding information   in MPLS.Stephan, et al.             Standards Track                    [Page 44]

RFC 5644             Spatial and Multicast Metrics          October 2009   The report of a spatial vector MUST include the ordered list of the   hosts involved in the instantaneous measure.10.1.3.  Timestamping Bias   The location of the point of interest inside a node influences the   timestamping skew and accuracy.  As an example, consider that some   internal machinery delays the timestamping up to three milliseconds;   then the minimal uncertainty reported be 3 ms if the internal delay   is unknown at the time of the timestamping.   The report of a spatial vector MUST include the uncertainty of the   timestamping compared to wire-time.10.1.4.  Reporting Spatial One-Way Delay   The reporting includes information to report for one-way delay assection 3.6 of [RFC2679].  The same applies for packet loss and ipdv.10.2.  Reporting One-to-Group Metric   All reporting rules described in [RFC2679] and [RFC2680] apply to the   corresponding One-to-group metrics.  The following are specific   parameters that SHOULD be reported.10.2.1.  Path   As suggested by [RFC2679] and [RFC2680], the path traversed by the   packet SHOULD be reported, if possible.  For One-to-group metrics,   the path tree between the source and the destinations or the set of   paths between the source and each destination SHOULD be reported.   The path tree might not be as valuable as individual paths because an   incomplete path might be difficult to identify in the path tree.  For   example, how many points of interest are reached by a packet   traveling along an incomplete path?10.2.2.  Group Size   The group size SHOULD be reported as one of the critical management   parameters.  One-to-group metrics, unlike spatial metrics, don't   require the ordering of the points of interests because group members   receive the packets in parallel.10.2.3.  Timestamping Bias   It is the same as described insection 10.1.3.Stephan, et al.             Standards Track                    [Page 45]

RFC 5644             Spatial and Multicast Metrics          October 200910.2.4.  Reporting One-to-group One-way Delay   It is the same as described insection 10.1.4.10.2.5.  Measurement Method   As explained insection 9, the measurement method will have impact on   the analysis of the measurement result.  Therefore, it SHOULD be   reported.10.3.  Metric Identification   IANA assigns each metric defined by the IPPM WG a unique identifier   as per [RFC4148] in the IANA-IPPM-METRICS-REGISTRY-MIB.10.4.  Information Model   This section presents the elements of information and the usage of   the information reported for network performance analysis.  It is out   of the scope of this section to define how the information is   reported.   The information model is built with pieces of information introduced   and explained in the sections of [RFC2679] , [RFC2680] , [RFC3393],   and [RFC3432] that define the IPPM metrics and from any of the   sections named "Reporting the metric" , "Methodology", and "Errors   and Uncertainties" whenever they exist in these documents.   The following are the elements of information taken from end-to-end   metrics definitions referred to in this memo and from spatial and   multicast metrics it defines:   o  Packet_type, the Type-P of test packets (Type-P).   o  Packet_length, a packet length in bits (L).   o  Src_host, the IP address of the sender.   o  Dst_host, the IP address of the receiver.   o  Hosts_series: <H1, H2,..., Hn>, a list of points of interest      participating in the instantaneous measure.  They are routers in      the case of spatial metrics or receivers in the case of one-to-      group metrics.   o  Loss_threshold, the threshold of infinite delay.Stephan, et al.             Standards Track                    [Page 46]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  Systematic_error, constant delay between wire-time and      timestamping.   o  Calibration_error, maximal uncertainty.   o  Src_time, the sending time for a measured packet.   o  Dst_time, the receiving time for a measured packet.   o  Result_status, an indicator of usability of a result 'Resource      exhaustion' 'infinite', 'lost'.   o  Delays_series, <dT1,..., dTn>, a list of delays.   o  Losses_series, <B1, B2, ..., Bi, ..., Bn>, a list of Boolean      values (spatial) or a set of Boolean values (one-to-group).   o  Result_status_series, a list of results status.   o  dT, a delay.   o  Singleton_number, a number of singletons.   o  Observation_duration, an observation duration.   o  metric_identifier.   The following is the information of each vector that SHOULD be   available to compute samples:   o  Packet_type;   o  Packet_length;   o  Src_host, the sender of the packet;   o  Dst_host, the receiver of the packet, apply only for spatial      vectors;   o  Hosts_series, not ordered for one-to-group;   o  Src_time, the sending time for the measured packet;   o  dT, the end-to-end one-way delay for the measured packet, apply      only for spatial vectors;   o  Delays_series, apply only for delays and ipdv vector, not ordered      for one-to-group;Stephan, et al.             Standards Track                    [Page 47]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  Losses_series, apply only for packets loss vector, not ordered for      one-to-group;   o  Result_status_series;   o  Observation_duration, the difference between the time of the last      singleton and the time of the first singleton.   Following is the context information (measure, points of interests)   that SHOULD be available to compute samples:   o  Loss threshold;   o  Systematic error, constant delay between wire-time and      timestamping;   o  Calibration error, maximal uncertainty.   A spatial or a one-to-group sample is a collection of singletons   giving the performance from the sender to a single point of interest.   The following is the information that SHOULD be available for each   sample to compute statistics:   o  Packet_type;   o  Packet_length;   o  Src_host, the sender of the packet;   o  Dst_host, the receiver of the packet;   o  Start_time, the sending time of the first packet;   o  Delays_series, apply only for delays and ipdv samples;   o  Losses_series, apply only for packets loss samples;   o  Result_status_series;   o  Observation_duration, the difference between the time of the last      singleton of the last sample and the time of the first singleton      of the first sample.   The following is the context information (measure, points of   interests) that SHOULD be available to compute statistics:   o  Loss threshold;Stephan, et al.             Standards Track                    [Page 48]

RFC 5644             Spatial and Multicast Metrics          October 2009   o  Systematic error, constant delay between wire-time and      timestamping;   o  Calibration error, maximal uncertainty;   The following is the information of each statistic that SHOULD be   reported:   o  Result;   o  Start_time;   o  Duration;   o  Result_status;   o  Singleton_number, the number of singletons on which the statistic      is computed;11.  Security Considerations   Spatial and one-to-group metrics are defined on the top of end-to-end   metrics.  Security considerations discussed in the one-way delay   metrics definitions of [RFC2679], in packet loss metrics definitions   of [RFC2680] and in IPDV metrics definitions of [RFC3393] and   [RFC3432] apply to metrics defined in this memo.   Someone may spoof the identity of a point of interest identity and   intentionally send corrupt results in order to remotely orient the   traffic engineering decisions.   A point of interest could intentionally corrupt its results in order   to remotely orient the traffic engineering decisions.11.1.  Spatial Metrics   Malicious generation of packets that systematically match the hash   function used to detect the packets may lead to a DoS attack toward   the point of reference.   Spatial measurement results carry the performance of individual   segments of the path and the identity of nodes.  An attacker may   infer from this information the points of weakness of a network   (e.g., congested node) that would require the least amount of   additional attacking traffic to exploit.  Therefore, monitoring   information should be carried in a way that prevents unintendedStephan, et al.             Standards Track                    [Page 49]

RFC 5644             Spatial and Multicast Metrics          October 2009   recipients from inspecting the measurement reports.  A   straightforward solution is to restrict access to the reports using   encrypted sessions or secured networks.11.2.  One-to-Group Metrics   Reporting of measurement results from a huge number of probes may   overload reference point resources (network, network interfaces,   computation capacities, etc.).   The configuration of a measurement must take into consideration that   implicitly more packets will be routed than sent and select a test   packet rate accordingly.  Collecting statistics from a huge number of   probes may overload any combination of the network to which the   measurement controller is attached, measurement controller network   interfaces, and measurement controller computation capacities.   One-to-group metric measurements should consider using source   authentication protocols, standardized in the MSEC group, to avoid   fraud packet in the sampling interval.  The test packet rate could be   negotiated before any measurement session to avoid denial-of-service   attacks.   A point of interest could intentionally degrade its results in order   to remotely increase the quality of the network on the branches of   the multicast tree to which it is connected.12.  Acknowledgments   Lei would like to acknowledge Professor Zhili Sun from CCSR,   University of Surrey, for his instruction and helpful comments on   this work.13.  IANA Considerations   Metrics defined in this memo have been registered in the IANA IPPM   METRICS REGISTRY as described in the initial version of the registry   [RFC4148]:   IANA has registered the following metrics in the IANA-IPPM-METRICS-   REGISTRY-MIB:   ietfSpatialOneWayDelayVector OBJECT-IDENTITY      STATUS current      DESCRIPTIONStephan, et al.             Standards Track                    [Page 50]

RFC 5644             Spatial and Multicast Metrics          October 2009         "Type-P-Spatial-One-way-Delay-Vector"      REFERENCE         "RFC 5644, section 5.1."      := { ianaIppmMetrics 52 }   ietfSpatialPacketLossVector OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-Spatial-Packet-Loss-Vector"      REFERENCE         "RFC 5644, section 5.2."      := { ianaIppmMetrics 53 }   ietfSpatialOneWayIpdvVector OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-Spatial-One-way-ipdv-Vector"      REFERENCE         "RFC 5644, section 5.3."      := { ianaIppmMetrics 54 }   ietfSegmentOneWayDelayStream OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-Segment-One-way-Delay-Stream"      REFERENCE         "RFC 5644, section 6.1."Stephan, et al.             Standards Track                    [Page 51]

RFC 5644             Spatial and Multicast Metrics          October 2009      := { ianaIppmMetrics 55 }   ietfSegmentPacketLossStream OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-Segment-Packet-Loss-Stream"      REFERENCE         "RFC 5644, section 6.2."      := { ianaIppmMetrics 56 }   ietfSegmentIpdvPrevStream OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-Segment-ipdv-prev-Stream"      REFERENCE         "RFC 5644, section 6.3."      := { ianaIppmMetrics 57 }   ietfSegmentIpdvMinStream OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-Segment-ipdv-min-Stream"      REFERENCE         "RFC 5644, section 6.4."      := { ianaIppmMetrics 58 }   -- One-to-group metrics   ietfOneToGroupDelayVector OBJECT-IDENTITYStephan, et al.             Standards Track                    [Page 52]

RFC 5644             Spatial and Multicast Metrics          October 2009      STATUS current      DESCRIPTION         "Type-P-One-to-group-Delay-Vector"      REFERENCE         "RFC 5644, section 7.1."      := { ianaIppmMetrics 59 }   ietfOneToGroupPacketLossVector OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Packet-Loss-Vector"      REFERENCE         "RFC 5644, section 7.2."      := { ianaIppmMetrics 60 }   ietfOneToGroupIpdvVector OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-ipdv-Vector"      REFERENCE         "RFC 5644, section 7.3."      := { ianaIppmMetrics 61 }   -- One to group statistics   --   ietfOnetoGroupReceiverNMeanDelay OBJECT-IDENTITY      STATUS currentStephan, et al.             Standards Track                    [Page 53]

RFC 5644             Spatial and Multicast Metrics          October 2009      DESCRIPTION         "Type-P-One-to-group-Receiver-n-Mean-Delay"      REFERENCE         "RFC 5644, section 8.3.1."      := { ianaIppmMetrics 62 }   ietfOneToGroupMeanDelay OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Mean-Delay"      REFERENCE         "RFC 5644, section 8.3.2."      := { ianaIppmMetrics 63 }   ietfOneToGroupRangeMeanDelay OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Range-Mean-Delay"      REFERENCE         "RFC 5644, section 8.3.3."      := { ianaIppmMetrics 64 }   ietfOneToGroupMaxMeanDelay OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Max-Mean-Delay"      REFERENCEStephan, et al.             Standards Track                    [Page 54]

RFC 5644             Spatial and Multicast Metrics          October 2009         "RFC 5644, section 8.3.4."      := { ianaIppmMetrics 65 }   ietfOneToGroupReceiverNLossRatio OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Receiver-n-Loss-Ratio"      REFERENCE         "RFC 5644, section 8.4.1."      := { ianaIppmMetrics 66 }   --   ietfOneToGroupReceiverNCompLossRatio OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Receiver-n-Comp-Loss-Ratio"      REFERENCE         "RFC 5644, section 8.4.2."      := { ianaIppmMetrics 67 }   ietfOneToGroupLossRatio OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Loss-Ratio"      REFERENCE         "RFC 5644, section 8.4.3."      := { ianaIppmMetrics 68 }Stephan, et al.             Standards Track                    [Page 55]

RFC 5644             Spatial and Multicast Metrics          October 2009   --   ietfOneToGroupRangeLossRatio OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Range-Loss-Ratio"      REFERENCE         "RFC 5644, section 8.4.4."      := { ianaIppmMetrics 69 }   ietfOneToGroupRangeDelayVariation OBJECT-IDENTITY      STATUS current      DESCRIPTION         "Type-P-One-to-group-Range-Delay-Variation"      REFERENCE         "RFC 5644, section 8.5.1."      := { ianaIppmMetrics 70 }   --14.  References14.1.  Normative References   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate              Requirement Levels",BCP 14,RFC 2119, March 1997.   [RFC2679]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way              Delay Metric for IPPM",RFC 2679, September 1999.   [RFC2680]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way              Packet Loss Metric for IPPM",RFC 2680, September 1999.   [RFC3393]  Demichelis, C. and P. Chimento, "IP Packet Delay Variation              Metric for IP Performance Metrics (IPPM)",RFC 3393,              November 2002.Stephan, et al.             Standards Track                    [Page 56]

RFC 5644             Spatial and Multicast Metrics          October 2009   [RFC4148]  Stephan, E., "IP Performance Metrics (IPPM) Metrics              Registry",BCP 108,RFC 4148, August 2005.14.2.  Informative References   [RFC2330]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,              "Framework for IP Performance Metrics",RFC 2330,              May 1998.   [RFC3432]  Raisanen, V., Grotefeld, G., and A. Morton, "Network              performance measurement with periodic streams",RFC 3432,              November 2002.   [SPATIAL]  Morton, A. and E. Stephan, "Spatial Composition of              Metrics", Work in Progress, June 2009.Authors' Addresses   Stephan Emile   France Telecom Division R&D   2 avenue Pierre Marzin   Lannion  F-22307   France   Fax:   +33 2 96 05 18 52   EMail: emile.stephan@orange-ftgroup.com   Lei Liang   CCSR, University of Surrey   Guildford   Surrey  GU2 7XH   UK   Fax:   +44 1483 683641   EMail: L.Liang@surrey.ac.uk   Al Morton   200 Laurel Ave. South   Middletown, NJ  07748   USA   Phone: +1 732 420 1571   EMail: acmorton@att.comStephan, et al.             Standards Track                    [Page 57]

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