Network Working Group E. Stephan
Request for Comments: 5644 France Telecom
Category: Standards Track L. Liang
University of Surrey
A. Morton
AT&T Labs
October 2009
IP Performance Metrics (IPPM): Spatial and Multicast
Abstract
The IETF has standardized IP Performance Metrics (IPPM) for measuring
endtoend 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.
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Contributions published or made publicly available before November
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material may not have granted the IETF Trust the right to allow
Stephan, et al. Standards Track [Page 1]
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modifications of such material outside the IETF Standards Process.
Without obtaining an adequate license from the person(s) controlling
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Table of Contents
1. Introduction and Scope ..........................................3
2. Terminology .....................................................4
3. Brief Metric Descriptions .......................................7
4. Motivations ....................................................10
5. Spatial Vector Metrics Definitions .............................12
6. Spatial Segment Metrics Definitions ............................19
7. OnetoGroup Metrics Definitions ...............................27
8. OnetoGroup Sample Statistics .................................30
9. Measurement Methods: Scalability and Reporting .................40
10. Manageability Considerations ..................................44
11. Security Considerations .......................................49
12. Acknowledgments ...............................................50
13. IANA Considerations ...........................................50
14. References ....................................................56
14.1. Normative References .....................................56
14.2. Informative References ...................................57
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1. Introduction and Scope
IETF has standardized IP Performance Metrics (IPPM) for measuring
endtoend 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.
Onetogroup metrics measure the performance for a group of users.
These metrics are derived from oneway endtoend 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, and Section 4 motivates each metric
category. Sections 5 through 8 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 (onetogroup), 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 in RFC 2119 [RFC2119].
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2. Terminology
2.1. Naming of the Metrics
The names of the metrics, including capitalized letters, are as close
as possible of the names of the oneway endtoend 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 2330
2.3. 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>, ..., .
For the purposes of this memo (reflecting the scope of a single
source), the only multiparty metrics are onetogroup 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.
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2.6. OnetoGroup Metric
A metric is said to be onetogroup 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
centerdistributed or serverclient topology with the source as the
center/server in the topology.
2.7. Points of Interest
Points of interest are the hosts (as per the RFC 2330 definition,
"hosts" include routing nodes) that are measurement collection
points, which are a subset 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)
subset of all the routers involved in the path.
Points of interest of onetogroup 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: OnetoGroup 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.
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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 Interest
2.8. 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 oneway 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.
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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 oneway delay vectors V1={dT11, dT12,...,
dT1N}, V2={dT21, dT22,..., dT2N},..., Vm={dTm1, dTm2,..., dTmN} for
Packet P1, P2,...,Pm, form a oneway delay Matrix {V1, V2,...,Vm}.
The matrix organizes the vector information to present network
performance in both space and time.
A onedimensional matrix (row) corresponds to a sample in simple
pointtopoint 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
Matrix
3. Brief Metric Descriptions
The metrics for spatial and onetogroup measurement are based on the
sourcetodestination, or endtoend metrics defined by IETF in
[RFC2679], [RFC2680], [RFC3393], and [RFC3432].
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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 TypePSpatialOnewayDelayVector divides the endtoend TypeP
OnewayDelay [RFC2679] into a spatial vector of oneway delay
singletons.
o TypePSpatialOnewayPacketLossVector divides an endtoend
TypePOnewayPacketLoss [RFC2680] into a spatial vector of
packet loss singletons.
o TypePSpatialOnewayipdvVector divides an endtoend TypeP
Onewayipdv into a spatial vector of ipdv (IP Packet Delay
Variation) singletons.
o Using elements of the TypePSpatialOnewayDelayVector metric,
a sample called TypePSegmentOnewayDelayStream collects one
way delay metrics between two points of interest on the path over
time.
o Likewise, using elements of the TypePSpatialPacketLossVector
metric, a sample called TypePSegmentPacketLossStream collects
oneway delay metrics between two points of interest on the path
over time.
o Using the TypePSpatialOnewayDelayVector metric, a sample
called TypePSegmentipdvprevStream 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 TypePSpatialOnewayDelayVector metric, a
sample called TypePSegmentipdvminStream 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 onetogroup metrics to measure the one
way performance between a source and a group of receivers. They are:
o TypePOnetogroupDelayVector which collects the set of TypeP
OnewayDelay singletons between one sender and N receivers;
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o TypePOnetogroupPacketLossVector which collects the set of
TypePOnewayPacketLoss singletons between one sender and N
receivers; and
o TypePOnetogroupipdvVector which collects the set of TypeP
Onewayipdv singletons between one sender and N receivers.
Finally, based on the onetogroup 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 TypePOnetogroupDelayVector, a metric called Type
POnetogroupReceivernMeanDelay, 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:
* TypePOnetogroupMeanDelay, or GMD, presents the mean of
delays;
* TypePOnetogroupRangeMeanDelay, or GRMD, presents the
range of mean delays; and
* TypePOnetogroupMaxMeanDelay, or GMMD, presents the
maximum of mean delays.
o Using the TypePOnetogroupPacketLossVector, a metric called
TypePOnetogroupReceivernLossRatio, 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:
* TypePOnetogroupLossRatio, or GLR, captures the overall
packet loss ratio for the entire group of receivers; and
* TypePOnetogroupRangeLossRatio, or GRLR, presents the
comparative packet loss ratio during the test interval between
one sender and N receivers.
o Using the TypePOnetogroupPacketLossVector, a metric called
TypePOnetogroupReceivernCompLossRatio, or RnCLR, computes
a packet loss ratio using the maximum number of packets received
at any receiver.
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o Using TypePOnetogroupipdvVector, a metric called TypePOne
togroupRangeDelayVariation, 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 endtoend (sourceto
destination) measurement of pointtopoint paths. It is logical to
extend them to multiparty situations such as onetoone trajectory
metrics and onetomultipoint metrics.
4.1. Motivations for Spatial Metrics
Spatial metrics are needed for:
o Decomposing the performance of an interdomain path to quantify
the perAS (Autonomous System) contribution to the endtoend
performance.
o Traffic engineering and troubleshooting, which benefit from
spatial views of oneway 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 pointtomultipoint communications.
o Dividing endtoend metrics, so that some segment measurements can
be reused and help measurement systems reach largescale
coverage. Spatial measures could characterize the performance of
an intradomain segment and provide an elementary piece of
information needed to estimate interdomain performance to another
destination using Spatial Composition metrics [SPATIAL].
4.2. Motivations for Onetogroup Metrics
While the nodetonodebased 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
pointtopoint metric cannot completely describe the multiparty
situation. New onetogroup metrics assess performance of the
multiple paths for further statistical analysis. The new metrics are
named onetogroup performance metrics, and they are based on the
unicast metrics defined in IPPM RFCs. Onetogroup 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.
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Onetogroup performance metrics are needed for:
o Designing and engineering multicast trees and MPLS pointto
multipoint Label Switched Paths (LSPs).
o Evaluating and controlling the quality of multicast services,
including interdomain 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 endtoend 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 onetogroup 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 pointtopoint
measurement to "path tree" to cover onetomany topologies. If
applied to onetoone topology, the onetogroup metrics provide
exactly the same results as the corresponding onetoone metrics.
4.3. Discussion on GrouptoOne and GrouptoGroup Metrics
We note that points of interest can also be selected to define
measurements on grouptoone and grouptogroup 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 grouptoone topology can be easily derived from
the onetogroup measurement. The measurement point is the host that
is acting as a receiver while all other hosts act as sources in this
case.
The grouptogroup 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 onetogroup or grouptoone topologies for each host
in a uniform way (without taking account of how the real
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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 onetogroup communications:
< ha, Ha, Hb, Hc, ..., Hm >, < hb, Ha, Hb, Hc, ..., Hm >, , ..., < hn, Ha, Hb, Hc, ..., Hm >.
5. Spatial Vector Metrics Definitions
This section defines vectors for the spatial decomposition of endto
end singleton metrics over a path.
Spatial vector metrics are based on the decomposition of standard
endtoend metrics defined by the IPPM WG in [RFC2679], [RFC2680],
[RFC3393], and [RFC3432].
The spatial vector definitions are coupled with the corresponding
endtoend 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 OneWay Delay Vector
This section is coupled with the definition of TypePOnewayDelay
in section 3 of [RFC2679]. When a parameter from the definition in
[RFC2679] is reused in this section, the first instance will be
tagged with a trailing asterisk.
Sections 3.5 to 3.8 of [RFC2679] give requirements and applicability
statements for endtoend oneway delay measurements. They are
applicable to each point of interest, Hi, involved in the measure.
Spatial oneway delay measurements MUST respect them, especially
those related to methodology, clock, uncertainties, and reporting.
5.1.1. Metric Name
TypePSpatialOnewayDelayVector
5.1.2. 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.
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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 oneway delay for a measured packet.
o dTi, a delay, the oneway delay for a measured packet from the
source to router Hi.
o a list of n delay singletons.
o TypeP*, the specification of the packet type.
o the routers digest.
5.1.3. Metric Units
The value of TypePSpatialOnewayDelayVector 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 TypeP packet sent by the Src at wiretime (first bit) T to
the receiver Dst on the path . There is a sequence
of values such that dT is the TypeP
OnewayDelay from Src to Dst, and for each Hi of the path, T+dTi is
either a real number corresponding to the wiretime the packet passes
(last bit received) Hi, or undefined if the packet does not pass Hi
within a specified loss threshold* time.
TypePSpatialOnewayDelayVector metric is defined for the path
as the sequence of values
.
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.
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* This is frequently due to a measurement clock synchronization
issue. This point is discussed in section 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
'wiretime' and 'host time'.
5.2. A Definition for Spatial Packet Loss Vector
This section is coupled with the definition of TypePOnewayPacket
Loss. When a parameter from section 2 of [RFC2680] is used in this
section, the first instance will be tagged with a trailing asterisk.
Sections 2.5 to 2.8 of [RFC2680] give requirements and applicability
statements for endtoend oneway 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
TypePSpatialPacketLossVector
5.2.2. Metric Parameters
o Src*, the IP address of the sender.
o Dst*, the IP address of the receiver.
o i, an integer 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.
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o dTi, a delay, the oneway delay for a measured packet from the
source to host Hi.
o , list of n delay singletons.
o TypeP*, the specification of packet type.
o , the routers digest.
o , a list of Boolean values.
5.2.3. Metric Units
The value of TypePSpatialPacketLossVector is a sequence of
Boolean values.
5.2.4. Definition
Given a TypeP packet sent by the Src at time T to the receiver Dst
on the path . For the sequence of times the packet passes in , define the TypePPacketLossVector metric as the sequence
of values 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 OneWay ipdv Vector
When a parameter from section 2 of [RFC3393] (the definition of Type
POnewayipdv) is used in this section, the first instance will be
tagged with a trailing asterisk.
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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
TypePSpatialOnewayipdvVector
5.3.2. 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 oneway delay for a measured packet.
o dTi, a delay, the oneway delay for a measured packet from the
source to router Hi.
o TypeP*, 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 , the routers digest.
o , the TypePSpatialOneway
DelayVector for a packet sent at time T1.
o , the TypePSpatialOneway
DelayVector for a packet sent at time T2.
o L*, a packet length in bits. The packets of a TypeP packet
stream from which the TypePSpatialOnewayDelayVector metric
is taken MUST all be of the same length.
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5.3.3. Metric Units
The value of TypePSpatialOnewayipdvVector 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 TypeP packet sent by the sender Src at wiretime (first
bit) T1 to the receiver Dst. Given
the TypePSpatialOnewayDelayVector of P1 over the sequence of
routers .
Given P2 the TypeP packet sent by the sender Src at wiretime (first
bit) T2 to the receiver Dst. Given
the TypePSpatialOnewayDelayVector of P2 over the same path.
The TypePSpatialOnewayipdvVector metric is defined as the
sequence of values such that for each Hi of the sequence of routers , dT2.idT1.i is either a real number if the packets P1
and P2 pass Hi at wiretime (last bit) dT1.i and dT2.i respectively,
or undefined if at least one of them never passes Hi (and the
respective oneway delay is undefined). The T1,T2* pair indicates
the interpacket emission interval and dT2dT1 is ddT* the TypeP
Onewayipdv.
5.4. Spatial Methodology
The methodology, reporting specifications, and uncertainties
specified in section 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 in section 2 of [RFC2680] apply to each point
of interest, Hi, measuring an element of a spatial packet loss
vector.
Sections 3.5 to 3.7 of [RFC3393] give requirements and applicability
statements for endtoend Oneway ipdv measurements. They are
applicable to each point of interest, Hi, involved in the measure.
Spatial Oneway ipdv measurement MUST respect the methodology, clock,
uncertainties, and reporting aspects given there.
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Generally, for a given TypeP 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' (see section
3.7.1. "Errors or uncertainties related to Clocks" of [RFC2679]);
o Each Hi extracts the path ordering information from the packet
(e.g., timetolive (TTL));
o Each Hi computes the corrected wiretime 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 oneway 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 TypeP spatial oneway vector (e.g., TypePSpatialOneway
DelayVector metric ) over the path
at time T.
5.4.1. Packet Loss Detection
In a pure endtoend measurement, packet losses are detected by the
receiver only. A packet is lost when TypePOnewayDelay is
undefined or very large (see sections 2.4 and 2.5 of [RFC2680] and
section 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?
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The same concern applies to oneway 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 , 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 oneway delay, TypeP
SegmentOnewayDelayStream, and a sample of packet loss, TypeP
SegmentPacketLossStream.
Then, it defines two different samples of ipdv: TypePSegmentipdv
prevStream uses the current and previous packets as the selection
function, and TypePSegmentipdvminStream uses the minimum delay
as one of the selected packets in every pair.
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6.1. A Definition of a Sample of OneWay Delay of a Segment of the Path
This metric defines a sample of oneway delays over time between a
pair of routers on a path. Since it is very close semantically to
the metric TypePOnewayDelayPoissonStream defined in section 4
of [RFC2679], sections 4.5 to 4.8 of [RFC2679] are integral parts of
the definition text below.
6.1.1. Metric Name
TypePSegmentOnewayDelayStream
6.1.2. Metric Parameters
o Src, the IP address of the sender.
o Dst, the IP address of the receiver.
o TypeP, 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 , the routers digest.
o , a list of times.
6.1.3. Metric Units
The value of a TypePSegmentOnewayDelayStream is a pair of:
A list of times ; and
A sequence of delays.
6.1.4. Definition
Given two routers, Ha and Hb, of the path , and the matrix of TypePSpatialOnewayDelayVector for
the packets sent from Src to Dst at times :
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;
;
...
.
We define the sample TypePSegmentOnewayDelayStream as the
sequence 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 in section 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, ..., Tm1, 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 TypePPacketlossStream defined in section 3 of [RFC2680],
sections 3.5 to 3.8 of [RFC2680] are integral parts of the definition
text below.
6.2.1. Metric Name
TypePSegmentPacketLossStream
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6.2.2. Metric Parameters
o Src, the IP address of the sender.
o Dst, the IP address of the receiver.
o TypeP, 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 , the routers digest.
o Hi, a router of the routers digest.
o , a list of times.
o , a list of Boolean values.
6.2.3. Metric Units
The value of a TypePSegmentPacketLossStream is a pair of:
The list of times ; and
A sequence of Boolean values.
6.2.4. Definition
Given two routers, Ha and Hb, of the path and the matrix of TypePSpatialPacketLossVector for the
packets sent from Src to Dst at times :
,
,
...,
.
We define the value of the sample TypePSegmentPacketLossStream
from Ha to Hb as the sequence of Booleans such that for each Tk:
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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 TypePPacketlossStream, TypePSegmentPacketLossStream
relies on the stability of the routers digest. The metric SHALL be
invalid for times < T1 , T2, ..., Tm1, 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
TypePSegmentipdvprevStream
6.3.2. Metric Parameters
o Src, the IP address of the sender.
o Dst, the IP address of the receiver.
o TypeP, the specification of the packet type.
o k, an integer that orders the packets sent.
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o n, an integer that orders the routers on the path.
o a and b, two integers where b > a.
o , the routers digest.
o , a list of times.
o , a
TypePSpatialOnewayDelayVector.
6.3.3. Metric Units
The value of a TypePSegmentipdvprevStream is a pair of:
The list of ; and
A list of pairs of interval of times and delays;
6.3.4. Definition
Given two routers, Ha and Hb, of the path and the matrix of TypePSpatialOnewayDelayVector for
the packets sent from Src to Dst at times :
,
,
...
.
We define the TypePSegmentipdvprevStream as the sequence of
packet time pairs and delay variations
<(T1, T2 , dT2.ab  dT1.ab) ,...,
(Tk1, Tk, dTk.ab  dTk1.ab), ...,
(Tm1, Tm, dTm.ab  dTm1.ab)>
For any pair, Tk, Tk1 in k=1 through m, the difference dTk.ab  dTk
1.ab is undefined if:
o the delay dTk.a or the delay dTk1.a is undefined, OR
o the delay dTk.b or the delay dTk1.b is undefined.
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6.3.5. Discussion
This metric belongs to the family of interpacket delay variation
metrics (IPDV in uppercase) whose results are extremely sensitive to
the interpacket interval in practice.
The interpacket interval of an endtoend IPDV metric is under the
control of the source (ingress point of interest). In contrast, the
interpacket 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 interpacket 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
TypePSegmentOnewayipdvminStream
6.4.2. Metric Parameters
o Src, the IP address of the sender.
o Dst, the IP address of the receiver.
o TypeP, 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 , the routers digest.
o , a list of times.
o , a
TypePSpatialOnewayDelayVector.
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6.4.3. Metric Units
The value of a TypePSegmentOnewayipdvminStream is a pair of:
The list of ; and
A list of times.
6.4.4. Definition
Given two routers, Ha and Hb, of the path and the matrix of TypePSpatialOnewayDelayVector for
the packets sent from Src to Dst at times :
,
,
...
.
We define the TypePSegmentOnewayipdvminStream as the sequence
of times 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 interpacket
interval variations than IPDV values, as discussed above.
In principle, the PDV distribution reflects the variation over many
different interpacket intervals, from the smallest interpacket
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.
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7. OnetoGroup Metrics Definitions
This section defines performance metrics between a source and a group
of receivers.
7.1. A Definition for OnetoGroup Delay
This section defines a metric for oneway delay between a source and
a group of receivers.
7.1.1. Metric Name
TypePOnetogroupDelayVector
7.1.2. Metric Parameters
o Src, the IP address of a host acting as the source.
o Recv1,..., RecvN, the IP addresses of the N hosts acting as
receivers.
o T, a time.
o dT1,...,dTn a list of times.
o TypeP, 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 TypePOnetogroupDelayVector is a set of TypeP
OnewayDelay 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 TypeP 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 TypePOnetogroupDelay
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Vector is defined as the set of the TypePOnewayDelay 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 OnetoGroup Packet Loss
7.2.1. Metric Name
TypePOnetogroupPacketLossVector
7.2.2. Metric Parameters
o Src, the IP address of a host acting as the source.
o Recv1,..., RecvN, the IP addresses of the N hosts acting as
receivers.
o T, a time.
o TypeP, the specification of the packet type.
o Gr, the receiving group identifier, OPTIONAL.
7.2.3. Metric Units
The value of a TypePOnetogroupPacketLossVector is a set of
TypePOnewayPacketLoss singletons [RFC2680].
o T, time the source packet was sent.
o L1,...,LN a list of Boolean values.
7.2.4. Definition
Given a TypeP packet sent by the source Src at T and the N hosts,
Recv1,...,RecvN, the TypePOnetogroupPacketLossVector is
defined as a set of the TypePOnewayPacketLoss singletons between
Src and each of the receivers:
{T, ,,..., },
where the Boolean value 01 depends on receiving the packet at a
particular receiver within a loss threshold time.
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7.3. A Definition for OnetoGroup ipdv
7.3.1. Metric Name
TypePOnetogroupipdvVector
7.3.2. Metric Parameters
o Src, the IP address of a host acting as the source.
o Recv1,..., RecvN, the IP addresses of the N hosts acting as
receivers.
o T1, a time.
o T2, a time.
o ddT1, ...,ddTn, a list of times.
o TypeP, the specification of the packet type.
o F, a selection function nonambiguously 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 TypePOnetogroupipdvVector is a set of TypeP
Onewayipdv singletons [RFC3393].
7.3.4. Definition
Given a TypeP packet stream, TypePOnetogroupipdvVector 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 TypePOneto
groupDelayVector from Src to { Recv1,..., RecvN } at time T1 and
the value of the TypePOnetogroupDelayVector from Src to {
Recv1,...,RecvN } at time T2. T1 is the wiretime at which Src sent
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the first bit of the first packet, and T2 is the wiretime at which
Src sent the first bit of the second packet. This metric is derived
from the TypePOnetogroupDelayVector metric.
For a set of real numbers {ddT1,...,ddTn}, the TypePOnetogroup
ipdvVector 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 wiretime T2 (first bit) and
the packets were received by { Recv1,...,RecvN } at wiretime {dT1+
T1,...,dTn+T1}(last bit of the first packet), and at wiretime {dT'1+
T2,...,dT'n+T2} (last bit of the second packet), and that {dT'1
dT1,...,dT'ndTn} ={ddT1,...,ddTn}.
For any pair of selected packets, the difference dT'ndTn is
undefined if:
o the delay dTn to Receiver n is undefined, OR
o the delay dT'n to Receiver n is undefined.
8. OnetoGroup Sample Statistics
The onetogroup metrics defined above are directly achieved by
collecting relevant unicast oneway 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 oneway metrics cannot
present the relative performance situation. However, if we use the
variations of all users' oneway 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
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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 onetogroup 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 oneway delay in [RFC2679].
However, there is a dramatic difference between the statistics for
onetoone communications and for onetomany 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 Oneway 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 oneway delay singleton. Each column
is a delay vector. It contains the oneway 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 oneway
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.
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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 longterm 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 predefined time interval to the reference point
rather than sending every oneway 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 oneway 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 2level statistics to distinguish them from 1level statistics
calculated over either space or time dimension. It can be easily
proven that no matter over which dimension a 2level statistic is
calculated first, the results are the same. That is, one can
calculate the 2level delay mean using the Matrix M by having the
1level delay mean over the time dimension first and then calculate
the mean of the obtained vector to find out the 2level delay mean.
Or, he can do the 1level statistic calculation over the space
dimension first and then have the 2level delay mean. Both results
will be exactly the same. Therefore, when defining a 2level
statistic, there is no need to specify the order in which the
calculation is executed.
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Many statistics can be defined for the proposed onetogroup 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 onetoone
communication. New statistic definitions are presented, which
summarize the onetoone 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 oneway metrics and their
statistics. For example, a lost packet can result in an infinite
oneway 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 onetogroup metrics
that it can not be solved by the same method used for oneway
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 oneway 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 ... R1dTK1 UNDEF
R1dTK+1... R1MD } where "UNDEF" is an undefined value, the reference
point can replace it by R1dTK = {(R1dTK1)+( 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,
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User1 calculates the TypePFiniteOnewayDelayMean R1MD as shown
in Figure 7 without any packet loss, and User2 calculates the R2MD
with N2 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 interpacket 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 wiretime of the packet as measured at MP(Src) (the
Source Measurement Point).
o TstampRecv, the wiretime 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 oneway delay singleton value.
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o L, shorthand notation for a oneway 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 oneway delay variation singleton
value.
8.3. OnetoGroup Delay Statistics
This section defines the overall oneway 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 /
Receivern
Delay
Figure 5: OnetoGroup Mean Delay
Statistics are computed on the finite oneway delays of the matrix
above.
All onetogroup delay statistics are expressed in seconds with
sufficient resolution to convey three significant digits.
8.3.1. TypePOnetogroupReceivernMeanDelay
This section defines TypePOnetogroupReceivernMeanDelay, the
Delay Mean, at each Receiver N, also named RnMD.
We obtain the value of TypePOnewayDelay 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 oneway delay singleton (dT) will be the finite
value TstampRecv[i]  TstampSrc[i] in units of seconds. Otherwise,
the value of the singleton is Undefined.
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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: TypePOnetogroupReceivernMeanDelay
where all packets i= 1 through J[n] have finite singleton delays.
8.3.2. TypePOnetogroupMeanDelay
This section defines TypePOnetogroupMeanDelay, the Mean oneway
Delay calculated over the entire Group, also named GMD.
N

1 \
GMD =  * > RnMD
N /

n = 1
Figure 7: TypePOnetogroupMeanDelay
Note that the Group Mean Delay can also be calculated by summing the
finite oneway delay singletons in the matrix, and dividing by the
number of finite oneway delay singletons.
8.3.3. TypePOnetogroupRangeMeanDelay
This section defines a metric for the Range of Mean Delays over all N
receivers in the Group (R1MD, R2MD...RnMD).
TypePOnetogroupRangeMeanDelay = GRMD = max(RnMD)  min(RnMD)
8.3.4. TypePOnetogroupMaxMeanDelay
This section defines a metric for the Maximum of Mean Delays over all
N receivers in the Group (R1MD, R2MD,...RnMD).
TypePOnetogroupMaxMeanDelay = GMMD = max(RnMD)
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8.4. OnetoGroup Packet Loss Statistics
This section defines the overall oneway 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 /
Receivern
Loss Ratio
Figure 8: OnetoGroup Loss Ratio
Statistics are computed on the sample of TypePOnewayPacketLoss
[RFC2680] of the matrix above.
All loss ratios are expressed in units of packets lost to total
packets sent.
8.4.1. TypePOnetogroupReceivernLossRatio
Given a Matrix of loss singletons as illustrated above, determine the
TypePOnewayPacketLossAverage for the sample at each receiver,
according to the definitions and method of [RFC2680]. The TypeP
OnewayPacketLossAverage and the TypePOnetogroupReceivern
LossRatio, 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: TypePOnetogroupReceivernLossRatio
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8.4.2. TypePOnetogroupReceivernCompLossRatio
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 oneway loss values at receiver n.
There is one value for each of the K packets sent.
Figure 10: TypePOnetogroupReceivernCompLossRatio
8.4.3. TypePOnetogroupLossRatio
TypePOnetogroupLossRatio, the overall Group Loss Ratio, also
named GLR, is defined as:
K,N

1 \
GLR =  * > Ln(k)
K*N /

k,n = 1
Figure 11: TypePOnetogroupLossRatio
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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. TypePOnetogroupRangeLossRatio
The Onetogroup Loss Ratio Range is defined as:
TypePOnetogroupRangeLossRatio = 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. Onetogroup Delay Variation Statistics
This section defines oneway 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: Onetogroup Delay Variation Matrix (DVMa)
Statistics are computed on the sample of TypePOnewayipdv
singletons of the group delay variation matrix above where RnddTk is
the TypePOnewayipdv singleton evaluated at Receiver n for the
packet k and where RnDV is the pointtopoint oneway packet delay
variation for Receiver n.
All Onetogroup delay variation statistics are expressed in seconds
with sufficient resolution to convey three significant digits.
8.5.1. TypePOnetogroupRangeDelayVariation
This section defines a metric for the Range of Delay Variation over
all N receivers in the Group.
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Maximum DV and minimum DV over all receivers summarize the
performance over the Group (where DV is a pointtopoint metric).
For each receiver, the DV is usually expressed as the 110^(3)
quantile of oneway delay minus the minimum oneway delay.
TypePOnetogroupRangeDelayVariation = GRDV =
= max(RnDV)  min(RnDV) for all n receivers
This range is determined from the minimum and maximum values of the
pointtopoint oneway 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 110^3 quantile of oneway
delay minus the minimum oneway delay. If a more demanding service
is considered, one alternative is to use the 110^5 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 onetoone
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 perReceiver basis. This
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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.
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9.2. Measurement
To prevent any bias in the result, the configuration of a onetomany
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 colocated 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.
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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.
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9.3.2. Impact on OnetoGroup Statistics
Two methods are available to compute group statistics:
o Method 1: Figure 5 and Figure 8 illustrate the method. The one
toone 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 onetogroup 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 with RFC
2679 and RFC 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
Endtoend metrics can't determine the path of the measure despite
the fact that IPPM RFCs recommend it be reported (see section 3.8.4
of [RFC2679]). Spatial metrics vectors provide this path. The
report of a spatial vector MUST include the points of interests
involved: the subset 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.
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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 wiretime.
10.1.4. Reporting Spatial OneWay Delay
The reporting includes information to report for oneway delay as
section 3.6 of [RFC2679]. The same applies for packet loss and ipdv.
10.2. Reporting OnetoGroup Metric
All reporting rules described in [RFC2679] and [RFC2680] apply to the
corresponding Onetogroup 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 Onetogroup 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. Onetogroup 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 in section 10.1.3.
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10.2.4. Reporting Onetogroup Oneway Delay
It is the same as described in section 10.1.4.
10.2.5. Measurement Method
As explained in section 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 IANAIPPMMETRICSREGISTRYMIB.
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 endtoend
metrics definitions referred to in this memo and from spatial and
multicast metrics it defines:
o Packet_type, the TypeP of test packets (TypeP).
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: , 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 oneto
group metrics.
o Loss_threshold, the threshold of infinite delay.
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o Systematic_error, constant delay between wiretime 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, , a list of delays.
o Losses_series, , a list of Boolean
values (spatial) or a set of Boolean values (onetogroup).
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 onetogroup;
o Src_time, the sending time for the measured packet;
o dT, the endtoend oneway delay for the measured packet, apply
only for spatial vectors;
o Delays_series, apply only for delays and ipdv vector, not ordered
for onetogroup;
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o Losses_series, apply only for packets loss vector, not ordered for
onetogroup;
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 wiretime and
timestamping;
o Calibration error, maximal uncertainty.
A spatial or a onetogroup 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;
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o Systematic error, constant delay between wiretime 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 onetogroup metrics are defined on the top of endtoend
metrics. Security considerations discussed in the oneway 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 unintended
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recipients from inspecting the measurement reports. A
straightforward solution is to restrict access to the reports using
encrypted sessions or secured networks.
11.2. OnetoGroup 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.
Onetogroup 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 denialofservice
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 IANAIPPMMETRICS
REGISTRYMIB:
ietfSpatialOneWayDelayVector OBJECTIDENTITY
STATUS current
DESCRIPTION
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"TypePSpatialOnewayDelayVector"
REFERENCE
"RFC 5644, section 5.1."
:= { ianaIppmMetrics 52 }
ietfSpatialPacketLossVector OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSpatialPacketLossVector"
REFERENCE
"RFC 5644, section 5.2."
:= { ianaIppmMetrics 53 }
ietfSpatialOneWayIpdvVector OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSpatialOnewayipdvVector"
REFERENCE
"RFC 5644, section 5.3."
:= { ianaIppmMetrics 54 }
ietfSegmentOneWayDelayStream OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSegmentOnewayDelayStream"
REFERENCE
"RFC 5644, section 6.1."
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:= { ianaIppmMetrics 55 }
ietfSegmentPacketLossStream OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSegmentPacketLossStream"
REFERENCE
"RFC 5644, section 6.2."
:= { ianaIppmMetrics 56 }
ietfSegmentIpdvPrevStream OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSegmentipdvprevStream"
REFERENCE
"RFC 5644, section 6.3."
:= { ianaIppmMetrics 57 }
ietfSegmentIpdvMinStream OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSegmentipdvminStream"
REFERENCE
"RFC 5644, section 6.4."
:= { ianaIppmMetrics 58 }
 Onetogroup metrics
ietfOneToGroupDelayVector OBJECTIDENTITY
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STATUS current
DESCRIPTION
"TypePOnetogroupDelayVector"
REFERENCE
"RFC 5644, section 7.1."
:= { ianaIppmMetrics 59 }
ietfOneToGroupPacketLossVector OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupPacketLossVector"
REFERENCE
"RFC 5644, section 7.2."
:= { ianaIppmMetrics 60 }
ietfOneToGroupIpdvVector OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupipdvVector"
REFERENCE
"RFC 5644, section 7.3."
:= { ianaIppmMetrics 61 }
 One to group statistics

ietfOnetoGroupReceiverNMeanDelay OBJECTIDENTITY
STATUS current
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DESCRIPTION
"TypePOnetogroupReceivernMeanDelay"
REFERENCE
"RFC 5644, section 8.3.1."
:= { ianaIppmMetrics 62 }
ietfOneToGroupMeanDelay OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupMeanDelay"
REFERENCE
"RFC 5644, section 8.3.2."
:= { ianaIppmMetrics 63 }
ietfOneToGroupRangeMeanDelay OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupRangeMeanDelay"
REFERENCE
"RFC 5644, section 8.3.3."
:= { ianaIppmMetrics 64 }
ietfOneToGroupMaxMeanDelay OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupMaxMeanDelay"
REFERENCE
Stephan, et al. Standards Track [Page 54]
RFC 5644 Spatial and Multicast Metrics October 2009
"RFC 5644, section 8.3.4."
:= { ianaIppmMetrics 65 }
ietfOneToGroupReceiverNLossRatio OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupReceivernLossRatio"
REFERENCE
"RFC 5644, section 8.4.1."
:= { ianaIppmMetrics 66 }

ietfOneToGroupReceiverNCompLossRatio OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupReceivernCompLossRatio"
REFERENCE
"RFC 5644, section 8.4.2."
:= { ianaIppmMetrics 67 }
ietfOneToGroupLossRatio OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupLossRatio"
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 OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupRangeLossRatio"
REFERENCE
"RFC 5644, section 8.4.4."
:= { ianaIppmMetrics 69 }
ietfOneToGroupRangeDelayVariation OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePOnetogroupRangeDelayVariation"
REFERENCE
"RFC 5644, section 8.5.1."
:= { ianaIppmMetrics 70 }

14. References
14.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2679] Almes, G., Kalidindi, S., and M. Zekauskas, "A Oneway
Delay Metric for IPPM", RFC 2679, September 1999.
[RFC2680] Almes, G., Kalidindi, S., and M. Zekauskas, "A Oneway
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 F22307
France
Fax: +33 2 96 05 18 52
EMail: emile.stephan@orangeftgroup.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.com
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