 1/draftietfippmmultimetrics11.txt 20090901 20:12:07.000000000 +0200
+++ 2/draftietfippmmultimetrics12.txt 20090901 20:12:07.000000000 +0200
@@ 1,21 +1,21 @@
Network Working Group E. Stephan
InternetDraft France Telecom
Intended status: Standards Track L. Liang
Expires: October 30, 2009 University of Surrey
+Expires: March 5, 2010 University of Surrey
A. Morton
AT&T Labs
 April 28, 2009
+ September 1, 2009
IP Performance Metrics (IPPM) for spatial and multicast
 draftietfippmmultimetrics11
+ draftietfippmmultimetrics12
Status of this Memo
This InternetDraft is submitted to IETF in full conformance with the
provisions of BCP 78 and BCP 79. 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 allow modifications of such material outside the
IETF Standards Process. Without obtaining an adequate license from
@@ 34,21 +34,21 @@
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use InternetDrafts as reference
material or to cite them other than as "work in progress."
The list of current InternetDrafts can be accessed at
http://www.ietf.org/ietf/1idabstracts.txt.
The list of InternetDraft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html.
 This InternetDraft will expire on October 30, 2009.
+ This InternetDraft will expire on March 5, 2010.
Copyright Notice
Copyright (c) 2009 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents in effect on the date of
publication of this document (http://trustee.ietf.org/licenseinfo).
Please review these documents carefully, as they describe your rights
@@ 72,30 +72,30 @@
Table of Contents
1. Introduction and Scope . . . . . . . . . . . . . . . . . . . . 4
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Brief Metric Descriptions . . . . . . . . . . . . . . . . . . 8
4. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . 10
5. Spatial vector metrics definitions . . . . . . . . . . . . . . 12
6. Spatial Segment Metrics Definitions . . . . . . . . . . . . . 19
7. Onetogroup metrics definitions . . . . . . . . . . . . . . . 24
 8. Onetogroup Sample Statistics . . . . . . . . . . . . . . . . 27
+ 8. Onetogroup Sample Statistics . . . . . . . . . . . . . . . . 28
9. Measurement Methods: Scalability and Reporting . . . . . . . . 37
 10. Manageability Considerations . . . . . . . . . . . . . . . . . 40
+ 10. Manageability Considerations . . . . . . . . . . . . . . . . . 41
11. Security Considerations . . . . . . . . . . . . . . . . . . . 45
 12. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 46
 13. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 46
 14. References . . . . . . . . . . . . . . . . . . . . . . . . . . 50
 14.1. Normative References . . . . . . . . . . . . . . . . . . 50
 14.2. Informative References . . . . . . . . . . . . . . . . . 51
 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 51
+ 12. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 47
+ 13. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 47
+ 14. References . . . . . . . . . . . . . . . . . . . . . . . . . . 51
+ 14.1. Normative References . . . . . . . . . . . . . . . . . . 51
+ 14.2. Informative References . . . . . . . . . . . . . . . . . 52
+ Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 52
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).
@@ 131,118 +131,120 @@
2.1. Naming of the metrics
The names of the metrics, including capitalization 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
 path digest: section 5 of RFC 2330

sample: section 11 of RFC 2330
singleton: section 11 of RFC 2330
2.3. Path Digest Hosts
+2.3. Routers Digest
 The list of the hosts on a path from the source to the destination,
 also referred to as the host path digest.
+ The list of the routers on the path from the source to the
+ destination which 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
 members of the path digest.
+ routers member of the routers digest.
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, 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 hosts involved in the path.
+ 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 host from the
 set of hosts involved in the delivery of the packets from source to
 destination.
+ 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.
Src . Hosts
\
 `X ... 1
+ `X  1
\
x
/
 .X .... 2
+ .X  2
/
x
 \
 `X .... 3
+ ...
+ `X  ...
\
\
\
 X .... J
+ X  J
\
\
\
` Dst
 Note: 'x' are nodes which are not points of interest
+ Note: 'X' are nodes which are points of interest,
+ 'x' are nodes which 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
@@ 299,37 +301,38 @@
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], [RFC3432].
+ [RFC2679], [RFC2680], [RFC3393], [RFC3432].
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
measurements 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 singletons.
+ 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
@@ 392,22 +396,23 @@
metrics and one to multipoint metrics.
4.1. Motivations for spatial metrics
Spatial metrics are needed for:
o Decomposing the performance of an interdomain path to quantify
the perAS 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
 of MPLS pointtomultipoint communications.
+ 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
[ID.ietfippmspatialcomposition].
4.2. Motivations for Onetogroup metrics
@@ 502,31 +507,31 @@
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 hosts in the
+ o i, an integer in the ordered list <1,2,...,n> of routers in the
path.
 o Hi, a host in the path digest.
+ 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 host Hi.
+ source to router Hi.
o a list of n delay singletons.
o TypeP*, the specification of the packet type.
 o , a path host digest.
+ 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
@@ 537,71 +542,70 @@
(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
+ o the delay singletons "appear" to decrease: dTi > dTi+1. This may
occur despite being physically impossible with the definition
used.
* This is frequently due to a measurement clock synchronization
issue. This point is discussed in the section 3.7.1. "Errors
or uncertainties related to Clocks" of [RFC2679].
 Consequently, the values of delays measured at multiple hosts
 may not match the order of those hosts on the path.
 * The actual order of hosts on the path may change due to
+ 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 TypePOnewayPacket
 Loss. When a parameter from the section 2 of [RFC2680] is used in
 this section, the first instance will be tagged with a trailing
 asterisk.
+ 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 hosts in the
+ 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 Hi, points of interest from the path digest.
o T*, a time, the sending time for a measured packet.
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 , a host path digest.
+ 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
@@ 611,89 +615,90 @@
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 hosts on the path may change due to reconvergence
+ * The actual routers on the path may change due to reconvergence
(e.g., recovery from a link failure).
 * The order of hosts on the path may change due to reconvergence.
 * A packet may not be observed in a host due to some buffer or
+ * 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.
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 hosts in the
+ o i, an integer in the ordered list <1,2,...,n> of routers in the
path.
 o Hi, a host of the path digest.
+ 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 host Hi.
+ source to router Hi.
o TypeP*, the specification of the packets type.
o P1, the first packet sent at time T1.
o P2, the second packet sent at time T2.
 o , a host path digest.
+ o , the routers digest.
o , the TypePSpatialOneway
DelayVector for packet sent at time T1.
o , the TypePSpatialOneway
DelayVector for packet sent at time T2.
o L*, a packet length in bits. The packets of a Type P packet
stream from which the TypePSpatialOnewayDelayVector metric
is taken MUST all be of the same length.
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 and
 its TypePSpatialOnewayDelayVector over the path .
+ its TypePSpatialOnewayDelayVector over the sequence of routers
+ .
Given P2 the TypeP packet sent by the sender Src at wiretime (first
bit) T2 to the receiver Dst and
its TypePSpatialOnewayDelayVector over the same path.
TypePSpatialOnewayipdvVector metric is defined as the sequence
of values such that for each Hi of the path , 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 TypePOnewayipdv.
+ dT1> 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 inter
+ packet emission interval and dT2dT1 is ddT* the TypePOnewayipdv.
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
@@ 751,91 +756,92 @@
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. Host Path Digest
+5.4.2. Routers Digest
 The methodology given above relies on knowing the order of the hosts/
 measurement collection points on the path [RFC2330].
+ 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 host, resulting in the repetition of one or more
 hosts in the Path Digest.
+ 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
 which introduce temporary micro loops. During such an event the host
 path 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.
+ which 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 hosts in the path digest of a vector
 MUST be identified before computation of statistics to avoid
+ 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.
Firstly this section defines a sample of oneway delay, TypeP
SegmentOnewayDelayStream, and a sample of packet loss, TypeP
segmentPacketLossStream.
Then it defines 2 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.
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 hosts 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.
+ 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 hosts in the
+ o i, an integer in the ordered list <1,2,...,n> of routers in the
path.
o k, an integer which orders the packets sent.
o a and b, two integers where b > a.
 o Hi, a host of the path digest.
 o , a host path digest.
+ 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 ;
A sequence of delays.
6.1.4. Definition
 Given 2 hosts, Ha and Hb, of the path , and the matrix of TypePSpatialOnewayDelayVector for the
 packets sent from Src to Dst at times :
+ Given two routers, Ha and Hb, of the the path , and the matrix of TypePSpatialOnewayDelayVector
+ for the packets sent from Src to Dst at times
+ :
;
;
...
.
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 time Tk passes Ha and Hb or undefined if this
packet never passes Ha or (inclusive) never passes Hb.
@@ 851,128 +857,126 @@
through optical fiber facilities is 2.5ms, but the measurement
collection point has a clock resolution of 8ms.
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 hosts of a path. Since it is very close semantically to the
+ 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
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 which orders the packets sent.
 o n, an integer which orders the hosts on the path.
+ o n, an integer which orders the routers on the path.
o a and b, two integers where b > a.
 o , a host path digest.
 o Hi, exchange points of the path digest.
+ 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:
A The list of times ;
A sequence of Boolean values.
6.2.4. Definition
 Given two hosts, Ha and Hb, of the path , and the matrix of TypePSpatialPacketLossVector for the
 packets sent from Src to Dst at times :
+ Given two routers, Ha and Hb, of the the path , and the matrix of TypePSpatialPacketLossVector for
+ the packets sent from Src to Dst at times :
,
,
...,
.
 We define the value of the sample TypePsegmentPacketLostStream
+ We define the value of the sample TypePsegmentPacketLossStream
from Ha to Hb as the sequence of Booleans such that for each Tk:
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 host path digest. The metric SHALL be
+ 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 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 hosts using the previous packet as the selection function.
+ 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 which orders the packets sent.
 o n, an integer which orders the hosts on the path.
+ o n, an integer which orders the routers on the path.
o a and b, two integers where b > a.
 o , the hosts path digest.
+ 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 ;
A list of pairs of interval of times and delays;
6.3.4. Definition
 Given two hosts, 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.
6.3.5. Discussion
@@ 987,51 +991,51 @@
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 hosts on a path using the minimum delay as one of the
+ 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 which orders the packets sent.
o i, an integer which identifies a packet sent.
 o n, an integer which orders the hosts on the path.
+ o n, an integer which orders the routers on the path.
o a and b, two integers where b > a.
 o , the host path digest.
 o , a list of times.
+ o , the routers digest.
+ o , a list of times.
o , a
TypePSpatialOnewayDelayVector.
6.4.3. Metric Units
The value of a TypePSegmentOnewayipdvminStream is a pair of:
The list of ;
A list of times.
6.4.4. Definition
 Given two hosts, 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:
@@ 1243,37 +1247,37 @@
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 Oneway
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 ... R3dTk \
+ 1  / R1dT1 R1dT2 R1dT3 ... R1dTk \
  
 2   R2dT1 R2dT2 R2dT3 ... R3dTk 
+ 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 contains the Oneway delays of the same packet
 observed at M points of interest. It implies the geographical factor
+ 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.
Therefore, one can either calculate statistics by rows over the space
dimension or by columns over the time dimension. It's up to the
operators or service provides which dimension they are interested in.
For example, a TV broadcast service provider might want to know the
statistical performance of each user in a long term run to make sure
@@ 1297,22 +1301,22 @@
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 good 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. This kind of statistics is referred to as
 2level statistics to distinguish them from 1level statistics
+ 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. I.e. 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 two 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.
@@ 1321,21 +1325,21 @@
over either the space dimension or the time dimension or both. This
memo treats the case where a stream of packets from the Source
results in a sample at each of the Receivers in the Group, and these
samples are each summarized with the usual statistics employed in
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
 The packet loss does have effects on oneway metrics and their
+ 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
@@ 1429,73 +1433,75 @@
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 3 significant digits.
8.3.1. TypePOnetogroupReceivernMeanDelay
This section defines TypePOnetogroupReceivernMeanDelay the
 Delay Mean at each Receiver N, also named RnDM.
+ 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.
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 =  * > RnDM
+ 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 (R1DM, R2DM,...RnDM).
+ receivers in the group (R1MD, R2MD...RnMD).
 TypePOnetogroupRangeMeanDelay = GRMD = max(RnDM)  min(RnDM)
+ 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 (R1DM, R2DM,...RnDM).
+ N receivers in the group (R1MD, R2MD,...RnMD).
 TypePOnetogroupMaxMeanDelay = GMMD = max(RnDM)
+ TypePOnetogroupMaxMeanDelay = GMMD = max(RnMD)
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 \

@@ 1534,56 +1541,65 @@

k = 1
Figure 9: TypePOnetogroupReceivernLossRatio
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.
+ 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 =  * > L(k,n)
+ GLR =  * > Ln(k)
K*N /

k,n = 1
Figure 11: TypePOnetogroupLossRatio
+ 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 max and
minimum loss ratios for the Group, rather than only reporting the
difference between them.
@@ 1688,57 +1703,55 @@
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 lost of information. As all measured
 singletons are not 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
+ 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 transit the statistic parameters to
 the reference point first to obtain the general information of the
+ 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.
9.2. Measurement
To prevent any bias in the result, the configuration of a onetomany
 measure must take in consideration that intrically more packets will
 to be routed than sent (copies of a packet sent are expected to
 arrive at many destination points) and selects a test packets rate
 that will not impact the network performance.
+ measure must take in consideration that more packets will to be
+ routed than sent (copies of a packet sent are expected to arrive at
+ many destination points) and selects a test packets 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.
Multimetrics samples are represented in a matrix as illustrated below

Point of
interest
1 R1S1 R1S1 R1S1 ... R1Sk \

2 R2S1 R2S2 R2S3 ... R2Sk 

3 R3S1 R3S2 R3S3 ... R3Sk > sample over space
. 
. 
. 
@@ 1799,114 +1812,112 @@
Two methods are available to compute group statistics:
o Method1: Figure 5 and Figure 8 illustrate the method chosen: the
onetoone statistic is computed per interval of time before the
computation of the mean over the group of receivers;
o Method2: Figure 13 presents the second one, metric is computed
over space and then over time.
10. Manageability Considerations
 Usually IPPM WG documents defines each metric reporting within its
 definition. This document defines the reporting of all the metrics
 introduced in a single section to provide consistent information, to
 avoid repetitions and to conform to IESG recommendation of gathering
 manageability considerations in a dedicated section.
+ This section defines the reporting of all the metrics introduced in
+ the document.
Information models of spatial metrics and of onetogroup metrics are
 similar excepted that points of interests of spatial vectors must be
+ similar excepted that points of interests of spatial vectors MUST be
ordered.
The complexity of the reporting relies on the number of points of
interests.
10.1. Reporting spatial metric
The reporting of spatial metrics shares a lot of aspects with
RFC267980. New ones are common to all the definitions and are
mostly related to the reporting of the path and of methodology
parameters that may bias raw results analysis. This section presents
these specific parameters and then lists exhaustively the parameters
 that shall be reported.
+ that SHOULD be reported.
10.1.1. Path
Endtoend metrics can't determine the path of the measure despite
IPPM RFCs recommend it to be reported (See Section 3.8.4 of
[RFC2679]). Spatial metrics vectors provide this path. The report
 of a spatial vector must include the points of interests involved:
 the sub set of the hosts of the path participating to the
+ 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. It is highly suggested to use the TTL in IPv4,
 the Hop Limit in IPv6 or the corresponding information in MPLS.
+ 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.
 The report of a spatial vector must include the ordered list of the
+ 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 3 milliseconds then
the minimal uncertainty reported be 3 ms if the internal delay is
unknown at the time of the timestamping.
 The report of a spatial vector must include the uncertainty of the
+ The report of a spatial vector MUST include the uncertainty of the
timestamping compared to wire time.
10.1.4. Reporting spatial Oneway Delay
The reporting includes information to report for onewaydelay as the
Section 3.6 of [RFC2679]. The same apply for packet loss and ipdv.
10.2. Reporting Onetogroup metric
All reporting rules described in [RFC2679] and [RFC2680] apply to the
corresponding Onetogroup metrics. Following are specific
 parameters that should be reported.
+ parameters that SHOULD be reported.
10.2.1. Path
As suggested by the [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.
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
travelling along an incomplete path?
10.2.2. Group size
 The group size should be reported as one of the critical management
+ 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.
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
+ the analysis of the measurement result. Therefore, it SHOULD be
reported.
10.3. Metric identification
IANA assigns each metric defined by the IPPM WG with a unique
identifier as per [RFC4148] in the IANAIPPMMETRICSREGISTRYMIB.
10.4. Information model
This section presents the elements of information and the usage of
@@ 1922,143 +1933,165 @@
Uncertainties".
Following are the elements of information taken from endtoend
metrics definitions referred 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_serie: , a list of points of interest;
+ o Hosts_serie: , a list of points of interest
+ participating to 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;
o Systematic_error: constant delay between wire time and
timestamping;
o Calibration_error: maximal uncertainty;
o Src_time, the sending time for a measured packet;
o Dst_time, the receiving time for a measured packet;
o Result_status : an indicator of usability of a result 'Resource
exhaustion' 'infinite', 'lost';
o Delays_serie: a list of delays;
o Losses_serie: , a list of Boolean values
(spatial) or a set of Boolean values (onetogroup);
o Result_status_serie: a list of results status;
o dT: a delay;
o Singleton_number: a number of singletons;
o Observation_duration: An observation duration;
o metric_identifier.
 Following is the information of each vector that should be available
+ Following is the information of each vector that SHOULD be available
to compute samples:
o Packet_type;
o Packet_length;
o Src_host, the sender of the packet;
o Dst_host, the receiver of the packet, apply only for spatial
vectors;
o Hosts_serie: not ordered for 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_serie: apply only for delays and ipdv vector, not ordered
for onetogroup;
o Losses_serie: apply only for packets loss vector, not ordered for
onetogroup;
o Result_status_serie;
o Observation_duration: the difference between the time of the last
singleton and the time of the first singleton.
o Following is the context information (measure, points of
 interests) that should be available to compute samples :
+ interests) that SHOULD be available to compute samples :
+
* Loss threshold;
* Systematic error: constant delay between wire time and
timestamping;
* Calibration error: maximal uncertainty;
A spatial or a onetogroup sample is a collection of singletons
giving the performance from the sender to a single point of interest.
 Following is the information that should be available for each sample
+ Following is the information that SHOULD be available for each sample
to compute statistics:
o Packet_type;
o Packet_length;
o Src_host, the sender of the packet;
o Dst_host, the receiver of the packet;
o Start_time, the sending time of the first packet;
o Delays_serie: apply only for delays and ipdv samples;
o Losses_serie: apply only for packets loss samples;
o Result_status_serie;
o Observation_duration: the difference between the time of the last
singleton of the last sample and the time of the first singleton
of the first sample.
o Following is the context information (measure, points of
 interests) that should be available to compute statistics :
+ interests) that SHOULD be available to compute statistics :
* Loss threshold;
* Systematic error: constant delay between wire time and
timestamping;
* Calibration error: maximal uncertainty;
 Following is the information of each statistic that should be
+ Following is the information of each statistic that SHOULD be
reported:
o Result;
o Start_time;
o Duration;
o Result_status;
o Singleton_number, the number of singletons the statistic is
computed on;
11. Security Considerations
Spatial and onetogroup metrics are defined on the top of endtoend
metrics. Security considerations discussed in 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.
11.1. Spatial metrics
+ 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.
 Malicious generation of packets with spoofing addresses may corrupt
 the results without any possibility to detect the spoofing.
+ 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 which match systematically 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) which would require the least amount of additional
+ attacking traffic to exploit. Therefore, monitoring information
+ should be carried in a way which prevents unintended recipients from
+ inspecting the measurement reports. A straight forward 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 ...).
The configuration of a measurement must take in consideration that
implicitly more packets will be routed than sent and selects a test
packets rate accordingly. Collecting statistics from a huge number
of probes may overload any combination of the network where the
measurement controller is attached to, measurement controller network
interfaces and measurement controller computation capacities.
Onetogroup metrics measurement should consider using source
authentication protocols, standardized in the MSEC group, to avoid
fraud packet in the sampling interval. The test packet rate could be
negotiated before any measurement session to avoid deny of service
attacks.
+ 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 it is connected to.
+
12. Acknowledgments
Lei would like to acknowledge Prof. Zhili Sun from CCSR, University
of Surrey, for his instruction and helpful comments on this work.
13. IANA Considerations
 Metrics defined in this memo Metrics defined in this memo are
 designed to be registered in the IANA IPPM METRICS REGISTRY as
 described in initial version of the registry [RFC4148] :
+ Metrics defined in this memo are designed to be registered in the
+ IANA IPPM METRICS REGISTRY as described in initial version of the
+ registry [RFC4148] :
IANA is asked to register the following metrics in the IANAIPPM
METRICSREGISTRYMIB :
ietfSpatialOneWayDelayVector OBJECTIDENTITY
STATUS current
DESCRIPTION
"TypePSpatialOnewayDelayVector"
REFERENCE
"Reference "RFCyyyy, section 5.1."
@@ 2272,22 +2305,22 @@
Metric for IP Performance Metrics (IPPM)", RFC 3393,
November 2002.
[RFC4148] Stephan, E., "IP Performance Metrics (IPPM) Metrics
Registry", BCP 108, RFC 4148, August 2005.
14.2. Informative References
[ID.ietfippmspatialcomposition]
Morton, A. and E. Stephan, "Spatial Composition of
 Metrics", draftietfippmspatialcomposition08 (work in
 progress), March 2009.
+ Metrics", draftietfippmspatialcomposition09 (work in
+ progress), June 2009.
[RFC2330] Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
"Framework for IP Performance Metrics", RFC 2330,
May 1998.
[RFC3432] Raisanen, V., Grotefeld, G., and A. Morton, "Network
performance measurement with periodic streams", RFC 3432,
November 2002.
Authors' Addresses