draft-ietf-ippm-ipdv-05.txt   draft-ietf-ippm-ipdv-06.txt 
Network Working Group C. Demichelis Network Working Group C. Demichelis
INTERNET-DRAFT CSELT INTERNET-DRAFT CSELT
Expiration Date: December 2000 P. Chimento Expiration Date: August 2001 P. Chimento
CTIT Ericsson IPI
July 2000 February 2001
Instantaneous Packet Delay Variation Metric for IPPM IP Packet Delay Variation Metric for IPPM
<draft-ietf-ippm-ipdv-05.txt> <draft-ietf-ippm-ipdv-06.txt>
1. Status of this Memo 1. Status of this Memo
This document is an Internet-Draft and is in full conformance with | This document is an Internet-Draft and is in full conformance with
all provisions of Section 10 of RFC2026. all provisions of Section 10 of RFC2026.
Internet-Drafts are working documents of the Internet Engineering Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF), its areas, and its working groups. Note that Task Force (IETF), its areas, and its working groups. Note that
other groups may also distribute working documents as Internet- other groups may also distribute working documents as Internet-
Drafts. Drafts.
Internet-Drafts are draft documents valid for a maximum of six months Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress." material or to cite them other than as "work in progress."
The list of current Internet-Drafts can be accessed at | The list of current Internet-Drafts can be accessed at
http://www.ietf.org/ietf/1id-abstracts.txt | http://www.ietf.org/ietf/1id-abstracts.txt
The list of Internet-Draft shadow directories can be accessed at | The list of Internet-Draft shadow directories can be accessed at
http://www.ietf.org/shadow.html http://www.ietf.org/shadow.html
This memo provides information for the Internet community. This memo This memo provides information for the Internet community. This memo
does not specify an Internet standard of any kind. Distribution of does not specify an Internet standard of any kind. Distribution of
this memo is unlimited. this memo is unlimited.
2. Abstract 2. Abstract
This memo refers to a metric for variation in delay of packets across This memo refers to a metric for variation in delay of packets across
Internet paths. The metric is based on statistics of the difference Internet paths. The metric is based on the difference in the One-Way-
in One-way-Delay of consecutive packets. This particular definition Delay of selected packets. This difference in delay is called "IP
of variation is called "Instantaneous Packet Delay Variation (ipdv)". Packet Delay variation."
The metric is valid for measurements between two hosts both in the The metric is valid for measurements between two hosts both in the
case that they have synchronized clocks and in the case that they are case that they have synchronized clocks and in the case that they are
not synchronized. In the second case it allows an evaluation of the not synchronized. We discuss both in this draft.
reciprocal skew. Measurements performed on both directions (Two-way
measurements) allow a better estimation of clock differences. The
precision that can be obtained is evaluated.
3. Introduction 3. Introduction
This memo is based on "A One-way-Delay metric for IPPM", RFC 2679 | This memo is based on "A One-Way-Delay metric for IPPM", RFC 2679
[2]. Part of the text in this memo is taken directly from that [2].
document.
This memo defines a metric for variation in delay of packets that > Part of the text in this memo is taken directly from that document.
flow from one host to another one through an IP path. This quantity >
is sometimes called "jitter". This term, however, causes confusion >
because it is used in different ways by different groups of people. |
"Jitter" commonly has two meanings: The first meaning is the |
variation of a signal with respect to some clock signal, where the |
arrival time of the signal is expected to coincide with the arrival |
of the clock signal. The second meaning has to do with the variation |
of a metric (e.g. delay) with respect to some reference metric (e.g. |
average delay or minimum delay). The form of "jitter" that we talk |
about here has to do almost exclusively with the second meaning, |
rather than the first. For more information see the section on the |
relationship with other standards.
3.1. Definition This memo defines a metric for variation in delay of packets that
flow from one host to another one through an IP path. This quantity
is sometimes called "jitter". This term, however, causes confusion
because it is used in different ways by different groups of people.
A definition of the Instantaneous Packet Delay Variation (ipdv) can "Jitter" commonly has two meanings: The first meaning is the
be given for a pair of packets or for a packet inside a stream of variation of a signal with respect to some clock signal, where the
packets. arrival time of the signal is expected to coincide with the arrival
of the clock signal. The second meaning has to do with the variation
of a metric (e.g. delay) with respect to some reference metric (e.g.
average delay or minimum delay).
For a pair of packets: The first meaning is used with reference to synchronous signals and
might be used to measure the quality of circuit emulation, for
example. There is also a metric called "wander" used in this context.
The second meaning is frequently used by computer scientists and
frequently (but not always) refers to variation in delay.
+ The ipdv of a pair of IP packets, that are transmitted from the In this document we will avoid the term "jitter" whenever possible
measurement point MP1 to the measurement point MP2, is the and stick to delay variation which is more precise.
difference between the One-way-Delay measured for the second
packet and the One-way-Delay measured for the first packet of the
pair.
For a stream of packets: 3.1. Definition
+ The Instantaneous Packet Delay Variation of an IP packet, inside a A definition of the IP Packet Delay Variation (ipdv) can be given for
stream of packets, going from the measurement point MP1 to the packets inside a stream of packets.
measurement point MP2, is the difference of the One-way-Delay of
that packet and the One-way-Delay of the preceding packet in the The IP Packet Delay Variation (ipdv) of a pair of packets within a
stream. stream of packets is defined for a selected pair of packets in the
stream going from measurement point MP1 to measurement point MP2 is
the difference between the one-way-delay of the first of the selected
packets and the one-way-delay of the second of the selected packets.
3.2. Motivation 3.2. Motivation
A number of services that can be supported by IP are sensitive to the One important use of delay variation is the sizing of playout buffers
regular delivery of packets and can be disturbed by instantaneous for applications requiring the regular delivery of packets (for
variations in delay, while they are not disturbed by slow variations, example, voice or video playout). What is normally important in this
that can last a relatively long time. A specific metric for quick case is the maximum delay variation, which is used to size playout
variations is therefore desirable. Metrics that can be derived from buffers for such applications [6]. Other uses of a delay variation
the analysis of statistics of ipdv can also be used, for example, for | metric are, for example, to determine the dynamics of queues within a
buffer dimensioning. The scope of this metric is to provide a way network (or router) where the changes in delay variation can be
for measurement of the quality delivered by a path. linked to changes in the queue length process at a given link or a
combination of links.
In addition, this type of metric is particularly robust with respect In addition, this type of metric is particularly robust with respect
differences and variations of the clocks of the two hosts. This differences and variations of the clocks of the two hosts. This
allows the use of the metric even if the two hosts that support the allows the use of the metric even if the two hosts that support the
measurement points are not synchronized. In the latter case measurement points are not synchronized. In the latter case
indications of reciprocal skew of the clocks can be derived from the indications of reciprocal skew of the clocks can be derived from the
measurement and corrections are possible. The related precision is measurement and corrections are possible. The related precision is
often comparable with the one that can be achieved with synchronized often comparable with the one that can be achieved with synchronized
clocks, being of the same order of magnitude of synchronization clocks, being of the same order of magnitude of synchronization
errors. This will be discussed below. errors. This will be discussed below.
The scope of this document is to provide a way to measure the ipdv
delivered on a path. Our goal is to provide a metric which can be
parameterized so that it can be used for various purposes. Any report
of the metric MUST include all the parameters associated with it so
that the conditions and meaning of the metric can be determined
exactly. We specifically do not specify particular values of the
metrics that IP networks must meet.
The flexibility of the metric can be viewed as a disadvantage but
there are some arguments for making it flexible. First, though there
are some uses of ipdv mentioned above, to some degree the uses of
ipdv are still a research topic and some room should be left for
experimentation. Secondly, there are different views in the community
of what precisely the definition should be (e.g. [7],[8],[9]). The
idea here is to parameterize the definition, rather than write a
different draft for each proposed definition. As long as all the
parameters are reported, it will be clear what is meant by a
particular use of ipdv. All the remarks in the draft hold, no matter
which parameters are chosen.
3.3. General Issues Regarding Time 3.3. General Issues Regarding Time
Everything contained in the Section 2.2. of [2] applies also in this | Everything contained in the Section 2.2. of [2] applies also in this
case. case.
To summarize: As in [1] we define "skew" as the first derivative of > To summarize: As in [1] we define "skew" as the first derivative of
the offset of a clock with respect to "true time" and define "drift" > the offset of a clock with respect to "true time" and define "drift"
as the second derivative of the offset of a clock with respect to > as the second derivative of the offset of a clock with respect to
"true time". > "true time".
From there, we can construct "relative skew" and "relative drift" for > From there, we can construct "relative skew" and "relative drift" for
two clocks C1 and C2 with respect to one another. These are natural > two clocks C1 and C2 with respect to one another. These are natural
extensions of the basic framework definitions of these quantities: > extensions of the basic framework definitions of these quantities:
+ Relative offset = difference in clock times > + Relative offset = difference in clock times
+ Relative skew = first derivative of the difference in clock times > + Relative skew = first derivative of the difference in clock times
+ Relative drift = second derivative of the difference in clock > + Relative drift = second derivative of the difference in clock
times > times
NOTE: The drift of a clock, as it is above defined over a long period NOTE: The drift of a clock, as it is above defined over a long period
must have an average value that tends to zero while the period must have an average value that tends to zero while the period
becomes large since the frequency of the clock has a finite (and becomes large since the frequency of the clock has a finite (and
small) range. In order to underline the order of magnitude of this small) range. In order to underline the order of magnitude of this
effect, it is considered that the maximum range of drift for effect, it is considered that the maximum range of drift for
commercial crystals is about 50 part per million (ppm). Since it is commercial crystals is about 50 part per million (ppm). Since it is
mainly connected with variations in operating temperature (from 0 to mainly connected with variations in operating temperature (from 0 to
70 degrees Celsius), it is expected that a host will have a nearly 70 degrees Celsius), it is expected that a host will have a nearly
constant temperature during its operation period, and variations in constant temperature during its operation period, and variations in
temperature, even if quick, could be less than one Celsius per temperature, even if quick, could be less than one Celsius per
second, and range in the order of few degrees. The total range of the second, and range in the order of few degrees. The total range of the
drift is usually related to variations from 0 to 70 Celsius. These drift is usually related to variations from 0 to 70 Celsius. These
are important points for evaluation of precision of ipdv are important points for evaluation of precision of ipdv
measurements, as will be seen below. measurements, as will be seen below.
4. Structure of this memo 4. A singleton definition of a One-way ipdv metric
The metric will be defined as applicable to a stream of packets that
flow from a source host to a destination host (one-way ipdv). The
initial assumption is that source and destination hosts have
synchronized clocks. The definition of a singleton of one-way ipdv
metric is first considered, and then a definition of samples for ipdv
will be given.
Then the case of application to non-synchronized hosts will be
discussed, and the precision will be compared with the one of
synchronized clocks.
A bidirectional ipdv metric will be defined, as well as the >
methodology for error corrections. This will not be a two-way metric, >
but a "paired" one-way in opposite directions.
5. A singleton definition of a One-way ipdv metric | The purpose of the singleton metric is to define what a single
instance of an ipdv measurement is. Note that it can only be
statistically significant in combination with other instances. It is
not intended to be meaningful as a singleton, in the sense of being
able to draw inferences from it.
This definition makes use of the corresponding definition of type-P- This definition makes use of the corresponding definition of type-P-
One-way-Delay metric [2]. This section makes use of those parts of One-Way-Delay metric [2]. This section makes use of those parts of
the One-way Delay Draft that directly apply to the One-way-ipdv the One-Way-Delay Draft that directly apply to the One-Way-ipdv
metric, or makes direct references to that Draft. metric, or makes direct references to that Draft.
5.1. Metric name 4.1. Metric name
Type-P-One-way-ipdv Type-P-One-way-ipdv
5.2. Metric parameters 4.2. Metric parameters
+ Src, the IP address of a host + Src, the IP address of a host
+ Dst, the IP address of a host + Dst, the IP address of a host
+ T1, a time + T1, a time
+ T2, a time. It is explicitly noted that also the difference T2-T1 + T2, a time
is a parameter of the measurement though this is already implicit,
since the times T1 and T2 exactly define the time conditions in
which the measurement takes place.
Note that the packet length is an implicit parameter of both the | + L, a packet length in bits. The packets of a Type P packet stream
Type-P-One-way-delay metric and the Type-P-One-way-ipdv metric, since | from which the singleton ipdv metric is taken MUST all be of the
this contributes to the overall one-way delay. We assume that the | same length.
packets sent for ipdv measurements are all of the same length.
5.3. Metric unit + F, a selection function defining unambiguously the two packets
from the stream selected for the metric.
+ I1,I2, times which mark that beginning and ending of the interval
in which the packet stream from which the singleton measurement is
taken occurs.
+ P, the specification of the packet type, over and above the source
and destination addresses
4.3. Metric unit
The value of a Type-P-One-way-ipdv is either a real number of seconds The value of a Type-P-One-way-ipdv is either a real number of seconds
(positive, zero or negative) or an undefined number of seconds. (positive, zero or negative) or an undefined number of seconds.
5.4. Definition 4.4. Definition
Type-P-One-way-ipdv is defined for two (consecutive) packets from Src We are given a Type P packet stream and I1 and I2 such that the first
to Dst, as the difference between the value of the Type-P-One-way- Type P packet to pass measurement point MP2 after I1 is given index 0
delay from Src to Dst at T2 and the value of the Type-P-One-way-Delay and the last Type P packet to pass measurement point MP2 before I2 is
from Src to Dst at T1. T1 is the wire-time at which Scr sent the given the highest index number.
first bit of the first packet, and T2 is the wire-time at which Src
sent the first bit of the second packet. This metric is therefore Type-P-One-way-ipdv is defined for two packets from Src to Dst
ideally derived from the One-way-Delay metric. selected by the selection function F, as the difference between the
value of the type-P-One-way- delay from Src to Dst at T2 and the
value of the type-P-One-Way-Delay from Src to Dst at T1. T1 is the
wire-time at which Scr sent the first bit of the first packet, and T2
is the wire-time at which Src sent the first bit of the second
packet. This metric is derived from the One-Way-Delay metric.
NOTE: The requirement of "consecutive" packets is not essential. The
measured value is anyway the difference in One-way-Delay at the times
T1 and T2, which is meaningful by itself, as long as the times T1 and |
T2 denote the wire times of the packets sent from Src to Dst. T2 denote the wire times of the packets sent from Src to Dst.
Therefore, for a real number ddT "The Type-P-one-way-ipdv from Src to Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to
Dst at T1, T2 is ddT" means that Src sent two consecutive packets, Dst at T1, T2 is ddT" means that Src sent two packets, the first at
the first at wire-time T1 (first bit), and the second at wire-time T2 wire-time T1 (first bit), and the second at wire-time T2 (first bit)
(first bit) and the packets were received by Dst at wire-time dT1+T1 and the packets were received by Dst at wire-time dT1+T1 (last bit of
(last bit of the first packet), and at wire-time dT2+T2 (last bit of the first packet), and at wire-time dT2+T2 (last bit of the second
the second packet), and that dT2-dT1=ddT. packet), and that dT2-dT1=ddT.
"The Type-P-one-way-ipdv from Src to Dst at T1,T2 is undefined" means "The type-P-one-way-ipdv from Src to Dst at T1,T2 is undefined" means
that Src sent the first bit of a packet at T1 and the first bit of a that Src sent the first bit of a packet at T1 and the first bit of a
second packet at T2 and that Dst did not receive one or both packets. second packet at T2 and that Dst did not receive one or both packets.
5.5. Discussion 4.5. Discussion
Type-P-One-way-ipdv is a metric that makes use of the same This metric definition depends on a stream of Type-P-One-Way-Delay
measurement methods provided for delay metrics. packets that have been measured. In general this can be a stream of
two or more packets, delimited by the interval endpoints I1 and I2.
There must be a stream of at least two packets in order for a
singleton ipdv measurement to take place. The purpose of the
selection function is to specify exactly which two packets from the
stream are to be used for the singleton measurement. Note that the
selection function may involve observing the one-way-delay of all the
Type P packets of the stream in the specified interval. Examples of a
selection function are:
+ Consecutive Type-P packets within the specified interval
+ Type-P packets with specified indices within the specified
interval
+ Type-P packets with the min and max one-way-delays within the
specified interval
+ Type-P packets with specified indices from the set of all defined
(i.e. non-infinite) one-way-delays Type-P packets within the
specified interval.
The following practical issues have to be considered: The following practical issues have to be considered:
+ Being a differential measurement, this metric is less sensitive to + Being a differential measurement, this metric is less sensitive to
clock synchronization problems. This issue will be more carefully clock synchronization problems. This issue will be more carefully
examined in section 7 of this memo. It is pointed out that, if the examined in section 7 of this memo. It is pointed out that, if the
relative clock conditions change in time, the accuracy of the relative clock conditions change in time, the accuracy of the
measurement will depend on the time interval T2-T1 and the measurement will depend on the time interval I2-I1 and the
magnitude of possible errors will be discussed below. magnitude of possible errors will be discussed below.
+ A given methodology will have to include a way to determine + A given methodology will have to include a way to determine
whether a delay value is infinite or whether it is merely very whether a delay value is infinite or whether it is merely very
large (and the packet is yet to arrive at Dst). As noted by large (and the packet is yet to arrive at Dst). As noted by
Mahdavi and Paxson, simple upper bounds (such as the 255 seconds Mahdavi and Paxson, simple upper bounds (such as the 255 seconds
theoretical upper bound on the lifetimes of IP packets [Postel: theoretical upper bound on the lifetimes of IP packets [Postel:
RFC 791]) could be used, but good engineering, including an RFC 791]) could be used, but good engineering, including an
understanding of packet lifetimes, will be needed in practice. understanding of packet lifetimes, will be needed in practice.
{Comment: Note that, for many applications of these metrics, the Comment: Note that, for many applications of these metrics, the
harm in treating a large delay as infinite might be zero or very harm in treating a large delay as infinite might be zero or very
small. A TCP data packet, for example, that arrives only after small. A TCP data packet, for example, that arrives only after
several multiples of the RTT may as well have been lost.} several multiples of the RTT may as well have been lost.
+ As with other 'type-P' metrics, the value of the metric may depend + As with other 'type-P' metrics, the value of the metric may depend
on such properties of the packet as protocol,(UDP or TCP) port on such properties of the packet as protocol,(UDP or TCP) port
number, size, and arrangement for special treatment (as with IP number, size, and arrangement for special treatment (as with IP
precedence or with RSVP). precedence or with RSVP).
+ If the packet is duplicated along the path (or paths!) so that + If the packet is duplicated along the path (or paths!) so that
multiple non-corrupt copies arrive at the destination, then the multiple non-corrupt copies arrive at the destination, then the
packet is counted as received, and the first copy to arrive packet is counted as received, and the first copy to arrive
determines the packet's One-way-Delay. determines the packet's One-Way-Delay.
+ If the packet is fragmented and if, for whatever reason, + If the packet is fragmented and if, for whatever reason,
reassembly does not occur, then the packet will be deemed lost. reassembly does not occur, then the packet will be deemed lost.
5.6. Methodologies It is assumed that the Type-P packet stream is generated according to
the Poisson sampling methodology described in [1].
4.6. Methodologies
As with other Type-P-* metrics, the detailed methodology will depend As with other Type-P-* metrics, the detailed methodology will depend
on the Type-P (e.g., protocol number, UDP/TCP port number, size, on the Type-P (e.g., protocol number, UDP/TCP port number, size,
precedence). Generally, for a given Type-P, the methodology would precedence).
proceed as follows:
The measurement methodology described in this section asssumes the
measurement and determination of ipdv in real-time as part of an
active measurement. Note that this can equally well be done a
posteriori, i.e. after the one-way-delay measurement is completed.
Generally, for a given Type-P, the methodology would proceed as
follows:
+ The need of synchronized clocks for Src and Dst will be discussed + The need of synchronized clocks for Src and Dst will be discussed
later. Here a methodology is presented that is based on later. Here a methodology is supposed that is based on
synchronized clocks. synchronized clocks.
+ At the Src host, select Src and Dst IP addresses, and form two + After time I1, start. At the Src host, select Src and Dst IP
test packets of Type-P with these addresses. Any 'padding' portion addresses, and form test packets of Type-P with these addresses
of the packet needed only to make the test packet a given size according to a given technique (e.g. the Poisson sampling
should be filled with randomized bits to avoid a situation in technique). Any 'padding' portion of the packet needed only to
which the measured delay is lower than it would otherwise be due make the test packet a given size should be filled with randomized
to compression techniques along the path. bits to avoid a situation in which the measured delay is lower
than it would otherwise be due to compression techniques along the
path.
+ At the Dst host, arrange to receive the packets. + At the Dst host, arrange to receive the packets.
+ At the Src host, place a timestamp in the first Type-P packet, + At the Src host, place a timestamp in the Type-P packet, and send
and send it towards Dst. it towards Dst.
+ If the packet arrives within a reasonable period of time, take a + If the packet arrives within a reasonable period of time, take a
timestamp as soon as possible upon the receipt of the packet. By timestamp as soon as possible upon the receipt of the packet. By
subtracting the two timestamps, an estimate of One-way-Delay can subtracting the two timestamps, an estimate of One-Way-Delay can
be computed. be computed.
+ Record this first delay value. + If the packet meets the selection function criterion for the first
packet, record this first delay value. Otherwise, continue
generating the Type-P packet stream as above until the criterion
is met or I2, whichever comes first.
+ At the Src host, place a timestamp in the second Type-P packet, + At the Src host, packets continue to be generated according to the
and send it towards Dst. given methodology. The Src host places a timestamp in the Type-P
packet, and send it towards Dst.
+ If the packet arrives within a reasonable period of time, take a + If the packet arrives within a reasonable period of time, take a
timestamp as soon as possible upon the receipt of the packet. By timestamp as soon as possible upon the receipt of the packet. By
subtracting the two timestamps, an estimate of One-way-Delay can subtracting the two timestamps, an estimate of One-Way-Delay can
be computed. be computed.
+ By subtracting the second value of One-way-Delay from the first + If the packet meets the criterion for the second packet for the
value the ipdv value of the pair of packets is obtained. second packet, then by subtracting the second value of One-Way-
Delay from the first value the ipdv value of the pair of packets
is obtained. Otherwise, packets continue to be generated until
the criterion for the second packet is fulfilled or I2, whichever
comes first.
+ If one or both packets fail to arrive within a reasonable period + If one or both packets fail to arrive within a reasonable period
of time, the ipdv is taken to be undefined. of time, the ipdv is taken to be undefined.
5.7. Errors and Uncertainties 4.7. Errors and Uncertainties
In the singleton metric of ipdv, factors that affect the measurement In the singleton metric of ipdv, factors that affect the measurement
are the same that can affect the One-way-Delay measurement, even if, are the same as those affecting the One-Way-Delay measurement, even
in this case, the influence is different. if, in this case, the influence is different.
The Framework document [1] provides general guidance on this point, The Framework document [1] provides general guidance on this point,
but we note here the following specifics related to delay metrics: but we note here the following specifics related to delay metrics:
+ Errors/uncertainties due to uncertainties in the clocks of the Src + Errors/uncertainties due to uncertainties in the clocks of the Src
and Dst hosts. and Dst hosts.
+ Errors/uncertainties due to the difference between 'wire time' and + Errors/uncertainties due to the difference between 'wire time' and
'host time'. 'host time'.
Each of these errors is discussed in more detail in the next Each of these errors is discussed in more detail in the following
paragraphs. paragraphs.
5.7.1. Errors/Uncertainties related to Clocks 4.7.1. Errors/Uncertainties related to Clocks
If, as a first approximation, the error that affects the first If, as a first approximation, the error that affects the first
measurement of One-way-Delay were the same of the one affecting the measurement of One-Way-Delay were the same as the one affecting the
second measurement, they will cancel each other when calculating second measurement, they will cancel each other when calculating
ipdv. The residual error related to clocks is the difference of the ipdv. The residual error related to clocks is the difference of the
errors that are supposed to change from the time T1, at which the errors that are supposed to change from time T1, at which the first
first measurement is performed, to the time T2 at which the second measurement is performed, to time T2 at which the second measurement
measure ment is performed. Synchronization, skew, accuracy and is performed. Synchronization, skew, accuracy and resolution are
resolution are here considered with the following notes: here considered with the following notes:
+ Errors in synchronization between source and destination clocks + Errors in synchronization between source and destination clocks
contribute to errors in both of the delay measurements required contribute to errors in both of the delay measurements required
for calculating ipdv. for calculating ipdv.
+ The effect of drift and skew errors on ipdv measurements can be > + The effect of drift and skew errors on ipdv measurements can be
quantified as follows: Suppose that the skew and drift functions > quantified as follows: Suppose that the skew and drift functions
are known. Assume first that the skew function is linear in time. > are known. Assume first that the skew function is linear in time.
Clock offset if then also a function of time and the error evolves > Clock offset if then also a function of time and the error evolves
as e(t) = K*t + O, where K is a constant and O is the offset at > as e(t) = K*t + O, where K is a constant and O is the offset at
time 0. In this case, the error added to the subtraction two > time 0. In this case, the error added to the subtraction two
different time stamps (t2 > t1) is e(t2)-e(t1) = K*(t2 - t1) which > different time stamps (t2 > t1) is e(t2)-e(t1) = K*(t2 - t1) which
will be added to the time difference (t2 - t1). If the drift > will be added to the time difference (t2 - t1). If the drift
cannot be ignored, but we assume that the drift is a linear > cannot be ignored, but we assume that the drift is a linear
function of time, then the skew is given by s(t) = M*(t**2) + N*t > function of time, then the skew is given by s(t) = M*(t**2) + N*t
+ S0, where M and N are constants and S0 is the skew at time 0. > + S0, where M and N are constants and S0 is the skew at time 0.
The error added by the variable skew/drift process in this case > The error added by the variable skew/drift process in this case
becomes e(t) = O + s(t) and the error added to the difference in > becomes e(t) = O + s(t) and the error added to the difference in
time stamps is e(t2)-e(t1) = N*(t2-t1) + M*{(t2-t1)**2}. > time stamps is e(t2)-e(t1) = N*(t2-t1) + M*{(t2-t1)**2}.
It is the claim here (see remarks in section 3.3) that the effects >
of skew are rather small over the time scales that we are > It is the claim here (see remarks in section 3.3) that the effects
discussing here, since temperature variations in a system tend to > of skew are rather small over the time scales that we are
be slow relative to packet inter-transmission times and the range > discussing here, since temperature variations in a system tend to
be slow relative to packet inter-transmission times and the range
of drift is so small. of drift is so small.
+ As far as accuracy and resolution are concerned, what is noted in + As far as accuracy and resolution are concerned, what is noted in
the one-way-delay document [2] in section 3.7.1, applies also in the one-way-delay document [2] in section 3.7.1, applies also in
this case, with the further consideration, about resolution, that this case, with the further consideration, about resolution, that
in this case the uncertainty introduced is two times the one of a in this case the uncertainty introduced is two times the one of a
single delay measurement. Errors introduced by these effects are single delay measurement. Errors introduced by these effects are
often larger than the ones introduced by the drift. often larger than the ones introduced by the drift.
5.7.2. Errors/uncertainties related to Wire-time vs Host-time 4.7.2. Errors/uncertainties related to Wire-time vs Host-time
The content of sec. 3.7.2 of [2] applies also in this case, with the The content of sec. 3.7.2 of [2] applies also in this case, with the
following further consideration: The difference between Host-time and following further consideration: The difference between Host-time and
Wire-time can be in general decomposed into two components, of which Wire-time can be in general decomposed into two components, of which
one is constant and the other is variable. Only the variable one is constant and the other is variable. Only the variable
components will produce measurement errors, while the constant one components will produce measurement errors, while the constant one
will be canceled while calculating ipdv. However, in most cases, the > will be canceled while calculating ipdv.
fixed and variable components are not known exactly.
6. Definitions for Samples of One-way ipdv However, in most cases, the fixed and variable components are not
known exactly.
Starting from the definition of the singleton metric of one-way ipdv, | 5. Definitions for Samples of One-way ipdv
we define a sample of such singletons. In the following, the two |
packets needed for a singleton measurement will be called a "pair". |
A stream of test packets is generated where the second packet of a | The goal of the sample definition is to make it possible to compute
pair is, at the same time, the first packet of the next pair. | the statistics of sequences of ipdv measurements. The singleton
definition is applied to a stream of test packets generated according
to a pseudo-random Poisson process with average arrival rate lambda.
If necessary, the interval in which the stream is generated can be
divided into sub-intervals on which the singleton definition of ipdv
can be applied. The result of this is a sequence of ipdv measurements
that can be analyzed by various statistical procedures.
+ Given particular binding of the parameters Src, Dst and Type-P, a | Starting from the definition of the singleton metric of one-way ipdv,
sample of values of parameter T1 is defined. To define the values | we define a sample of such singletons. In the following, the two
of T1, select a beginning time T0, a final time Tf, and an average | packets needed for a singleton measurement will be called a "pair".
rate lambda, then define a pseudo-random Poisson arrival process |
of rate lambda, whose values fall between T0 and Tf. The time |
interval between successive values of T1 will then average |
1/lambda. From the second value on, T1 value of the pair n |
coincides with T2 of the pair n-1, and the first packet of pair n |
coincides with the second packet of the pair n-1. |
6.1. Metric name 5.1. Metric name
Type-P-One-way-ipdv-stream Type-P-One-way-ipdv-stream
6.2. Parameters 5.2. Parameters
+ Src, the IP address of a host + Src, the IP address of a host
+ Dst, the IP address of a host + Dst, the IP address of a host
+ T0, a time + T0, a time
+ Tf, a time + Tf, a time
+ lambda, a rate in reciprocal seconds + lambda, a rate in reciprocal seconds
6.3. Metric Units: + L, a packet length in bits. The packets of a Type P packet stream
from which the sample ipdv metric is taken MUST all be of the same
length.
A sequence of triads whose elements are: + F, a selection function defining unambiguously the packets from
the stream selected for the metric.
+ T, a time + I(i),I(i+1), i >=0, pairs of times which mark the beginning and
ending of the intervals in which the packet stream from which the
measurement is taken occurs. I(0) >= T0 and assuming that n is the
largest index, I(n) <= Tf.
+ Ti, a time interval. + P, the specification of the packet type, over and above the source
and destination addresses
5.3. Metric Units:
A sequence of triples whose elements are:
+ T1, T2,times
+ dT a real number or an undefined number of seconds + dT a real number or an undefined number of seconds
6.4. Definition 5.4. Definition
A pseudo-random Poisson process is defined such that it begins at or A pseudo-random Poisson process is defined such that it begins at or
before T0, with average arrival rate lambda, and ends at or after Tf. before T0, with average arrival rate lambda, and ends at or after Tf.
Those time values T(i) greater than or equal to T0 and less than or Those time values T(i) greater than or equal to T0 and less than or
equal to Tf are then selected. Starting from time T0, at each pair of equal to Tf are then selected for packet generation times.
times T(i), T(i+1) of this process a value of Type-P-One-way-ipdv is
obtained. The value of the sample is the sequence made up of the
resulting <time, time interval, ipdv> triple, where the time interval
is given by T(i+1)-T(i). Each time T(i), excluding the first and the
last, is therefore at the same time the the second time of pair i and
the first time of pair i+1. The result is shown in figure 3
|T(i-2) |T(i-1) |T(i) |T(i+1) Each packet falling within one of the sub-intervals I(i), I(i+1) is
_____|__________|___________________|__________|________ tested to determine whether it meets the criteria of the selection
pair i-1 pair i pair i+1 function F as the first or second of a packet pair needed to compute
ipdv. The sub-intervals can be defined such that a sufficient number
of singleton samples for valid statistical estimates can be obtained.
Figure 3 The triples defined above consist of the transmission times of the
first and second packets of each singleton included in the sample,
and the ipdv in seconds.
6.5. Discussion 5.5. Discussion
Note first that, since a pseudo-random number sequence is employed, Note first that, since a pseudo-random number sequence is employed,
the sequence of times, and hence the value of the sample, is not the sequence of times, and hence the value of the sample, is not
fully specified. Pseudo-random number generators of good quality will fully specified. Pseudo-random number generators of good quality will
be needed to achieve the desired qualities. be needed to achieve the desired qualities.
The sample is defined in terms of a Poisson process both to avoid the The sample is defined in terms of a Poisson process both to avoid the
effects of self-synchronization and also capture a sample that is effects of self-synchronization and also capture a sample that is
statistically as unbiased as possible. {Comment: there is, of course, statistically as unbiased as possible. There is, of course, no claim
no claim that real Internet traffic arrives according to a Poisson that real Internet traffic arrives according to a Poisson arrival
arrival process.} process.
6.6. Methodology The sample metric can best be explained with a couple of examples:
For the first example, assume that the selection function specifies
the "non-infinite" max and min one-way-delays over each sub-interval.
We can define contiguous sub-intervals of fixed specifiec length and
produce a sequence each of whose elements is the triple <transmission
time of the max delay packet, transmission time of the min delay
packet, D(max)-D(min)> which is collected for each sub-interval. A
second example is the selection function that specifies packets whose
indices (sequence numbers) are just the integers below a certain
bound. In this case, the sub-intervals are defined by the
transmission times of the generated packets and the sequence produced
is just <T(i), T(i+1), D(i)-D(i+1)> where D(i) denotes the one-way
delay of the ith packet of a stream.
This definition of the sample metric encompasses both the definition
proposed in [9] and the one proposed in [9].
5.6. Methodology
Since packets can be lost or duplicated or can arrive in a different Since packets can be lost or duplicated or can arrive in a different
order than the order sent, in order to recognize the pairs of test order than the order sent, in order to recognize the pairs of test
packets, they should be marked with a sequence number. For duplicated packets, they should be marked with a sequence number. For duplicated
packets only the first received copy should be considered. If a packets only the first received copy should be considered.
packet is lost, two values of ipdv will be undefined, since each
packet is common to two pairs.
Steps for measurement can be the following: Otherwise, the methodology is the same as for the singleton
measurement, with the exception that the singleton measurement is
repeated a number of times.
+ Starting from a given time T, Src generates a test packet as for a 5.7. Errors and uncertainties
singleton metrics, inserts in the packet a sequence number and the
transmission time stamp Tx, then sorts the time Ti at which the
next packet has to be sent.
+ At time Ti, Src repeats the previous step, unless T(i) > Tf. The same considerations apply that have been made about the singleton
metric. Additional error can be introduced by the pseudo-random
Poisson process as discussed in [2]. Further considerations will be
given in section 7.
+ On reception of the first packet, or the first packet after a 6. Statistics for One-way-ipdv
sequence number error, Dst records sequence number and
transmission timestamp that are contained in the packet and the
reception time Rx as "old values".
+ On reception of the other packets Dst verifies the seuqence number Some statistics are suggested which can provide useful information in
and if it is correct, by using the "old values" and the newly analyzing the behavior of the packets flowing from Src to Dst. The
received ones, a value of ipdv is computed. Then Dst records the statistics are assumed to be computed from an ipdv sample of
new sequence number, transmit and receive timestamps as "old reasonable size.
values".
6.7. Errors and uncertainties The purpose is not to define every possible statistic for ipdv, but
ones which have been proposed or used.
The same considerations apply that have been made about the singleton > 6.1. Lost Packets and ipdv statistics
metric. Additional error can be introduced by the pseudo-random >
Poisson process as discussed in [2]. Further considerations will be >
given in section 7. |
6.8. Distribution of One-way-ipdv values | The treatment of lost packets as having "infinite" or "undefined"
delay complicates the derivation of statistics for ipdv.
Specifically, when packets in the measurement sequence are lost,
simple statistics such as sample mean cannot be computed. One
possible approach to handling this problem is to reduce the event
space by conditioning. That is, we consider conditional statistics;
namely we estimate the mean ipdv (or other derivative statistic)
conditioned on the event that selected packet pairs arrive at the
destination (within the given timeout). While this itself is not
without problems (what happens, for example, when every other packet
is lost), it offers a way to make some (valid) statements about ipdv,
at the same time avoiding events with undefined outcomes.
The one-way-ipdv values are limited by virtue of the fact that there | In practical terms, what this means is throwing out the samples where
are upper and lower bounds on the one-way-delay values. Specifically, | one or both of the selected packets has an undefined delay. The
one-way-delay is upper bounded by the value chosen as the maximum | sample space is reduced (conditioned) and we can compute the usual
beyond which a packet is counted as lost. It is lower bounded by | statistics, understanding that formally they are conditional.
propagation, transmission and nodal transit delays assuming that |
there are no queues or variable nodal delays in the path. Denote the |
upper bound of one-way-delay by U and the lower bound by L and we see |
that one-way-ipdv can only take on values in the (open) interval (L- |
U, U-L). |
In any finite interval, the one-way-delay can vary monotonically | 6.2. Distribution of One-way-ipdv values
(non-increasing or non-decreasing) or of course it can vary in both |
directions in the interval, within the limits of the half-open |
interval [L,U). Accordingly, within that interval, the one-way-ipdv |
values can be positive, negative, or a mixture (including 0). |
Since the range of values is limited, the one-way-ipdv cannot | The one-way-ipdv values are limited by virtue of the fact that there
increase or decrease indefinitely. Suppose, for example, that the | are upper and lower bounds on the one-way-delay values. Specifically,
ipdv has a positive 'run' (i.e. a long sequence of positive values). | one-way-delay is upper bounded by the value chosen as the maximum
At some point in this 'run', the positive values must approach 0 (or | beyond which a packet is counted as lost. It is lower bounded by
become negative) if the one-way-delay remains finite. Otherwise, the | propagation, transmission and nodal transit delays assuming that
one-way-delay bounds would be violated. If such a run were to | there are no queues or variable nodal delays in the path. Denote the
continue infinitely long, the sample mean (assuming no packets are | upper bound of one-way-delay by U and the lower bound by L and we see
lost) would approach 0 (because the one-way-ipdv values must approach | that one-way-ipdv can only take on values in the (open) interval (L-
0). Note, however, that this says nothing about the shape of the | U, U-L).
distribution, or whether it is symmetric. Note further that over |
significant intervals, depending on the width of the interval [L,U), | In any finite interval, the one-way-delay can vary monotonically
(non-increasing or non-decreasing) or of course it can vary in both
directions in the interval, within the limits of the half-open
interval [L,U). Accordingly, within that interval, the one-way-ipdv
values can be positive, negative, or a mixture (including 0).
Since the range of values is limited, the one-way-ipdv cannot
increase or decrease indefinitely. Suppose, for example, that the
ipdv has a positive 'run' (i.e. a long sequence of positive values).
At some point in this 'run', the positive values must approach 0 (or
become negative) if the one-way-delay remains finite. Otherwise, the
one-way-delay bounds would be violated. If such a run were to
continue infinitely long, the sample mean (assuming no packets are
lost) would approach 0 (because the one-way-ipdv values must approach
0). Note, however, that this says nothing about the shape of the
distribution, or whether it is symmetric. Note further that over
significant intervals, depending on the width of the interval [L,U),
that the sample mean one-way-ipdv could be positive, negative or 0. that the sample mean one-way-ipdv could be positive, negative or 0.
6.9. Some statistics for One-way-ipdv There are basically two ways to represent the distribution of values
of an ipdv sample: an empirical pdf and an empirical cdf. The
empirical pdf is most often represented as a histogram where the
range of values of an ipdv sample is divided into bins of a given
length and each bin contains the proportion of values falling between
the two limits of the bin. (Sometimes instead the number of values
falling between the two limits is used). The empirical cdf is simply
the proportion of ipdv sample values less than a given value, for a
sequence of values selected from the range of ipdv values.
Some statistics are suggested which can provide useful information in | 6.3. Type-P-One-way-ipdv-percentile
analyzing the behavior of the packets flowing from Src to Dst. The |
focus is on the instantaneous behavior of the connection. Other |
statistics can be defined if needed.
6.9.1. Type-P-One-way-ipdv-inverse-percentile Given a Type-P One-Way-ipdv sample and a percent X between 0% and
100%, the Xth percentile of all ipdv values in the sample. The 50th
percentile is the median.
Given a Type-P-One-way-ipdv-Stream and a time threshold, that can be 6.4. Type-P-One-way-ipdv-inverse-percentile
either positive or negative, the fraction of all the ipdv values in
the Stream less than or equal to the threshold, if the threshold is
positive, or greater or equal to the threshold if the threshold is
negative.
For many real-time services that require a regular delivery of the Given a Type-P-One-way-ipdv sample and a given value Y, the percent
packets, these statistics provide the number of packets exceeding a of ipdv sample values less than or equal to Y.
given limit.
6.9.2. Type-P-One-way-ipdv-jitter | 6.5. Type-P-One-way-ipdv-jitter
This metric is the same as the definition of "jitter" in [7], and is | Although the use of the term "jitter" is deprecated, we use it here
simply the absolute value of the Type-P-One-way-ipdv. | following the authors in [7]. In that document, the selection
function specifies that consecutive packets of the Type-P stream are
to be selected for the packet pairs used in ipdv computation. They
then take the absolute value of the ipdv values in the sample. The
authors in [7] use the resulting sample to compare the behavior of
two different scheduling algorithms.
6.9.3. The treatment of lost packets as having "infinite" or > 6.6. Type-P-One-way-peak-to-peak-ipdv
"undefined" delay complicates the derivation of statistics for ipdv. >
Specifically, when packets in the measurement sequence are lost, > In this case, the selection function used in collecting the Type-P-
simple statistics such as sample mean cannot be computed. One > One-Way-ipdv sample specifies that the first packet of each pair to
possible approach to handling this problem is to reduce the event > be the packet with the maximum Type-P-One-Way-Delay in each sub-
space by conditioning. That is, we consider conditional statistics; > interval and the second packet of each pair to be the packet with the
namely we estimate the mean ipdv (or jitter or other derivative > minimum Type-P-One-Way-Delay in each sub-interval. The resulting
statistic) conditioned on the event that successive packet pairs > sequence of values is the peak-to-peak delay variation in each sub-
arrive at the destination (within the given timeout). While this > interval of the measurement interval.
itself is not without problems (what happens, for example, when every >
other packet is lost), it offers a way to make some (valid) >
statements about ipdv, at the same time avoiding events with >
undefined outcomes. We suggest that this be a topic for further >
study.
7. Discussion of clock synchronization 7. Discussion of clock synchronization
This section gives some considerations about the need of having This section gives some considerations about the need of having
synchronized clocks at the source and destination. These synchronized clocks at the source and destination. These
considerations are given as a basis for discussion and they require considerations are given as a basis for discussion and they require
further investigation. > further investigation.
7.1. Effects of synchronization errors >
Clock errors can be generated by two processes: the relative drift >
and the relative skew of two given clocks. We should note that drift >
is physically limited and so the total relative skew of two clocks >
can vary between an upper and a lower bound. >
Suppose then that we have a measurement between two systems such that >
the clocks in the source and destination systems have at time 0 a >
relative skew of s(0) and after a measurement interval T have skew >
s(T). We assume that the two clocks have an initial offset of O (that >
is letter O). >
Now suppose that the packets travel from source to destination in >
constant time, in which case the ipdv is zero and the difference in >
the timestamps of the two clocks is actually just the relative offset >
of the clocks. Suppose further that at the beginning of the >
measurement interval the ipdv value is calculated from a packet pair >
and at the end of the measurement interval another ipdv value is >
calculated from another packet pair. Assume that the time interval >
covered by the first measurement is t1 and that covered by the second >
measurement is t2. Then >
ipdv1 = s(0)*t1 + t1*(s(T)-s(0))/T >
ipdv2 = s(T)*t2 + t2*(s(T)-s(0))/T >
assuming that the change is skew is linear in time. In most practical >
cases, it is claimed that the drift will be close to zero in which >
case the second (correction) term in the above equations disappears. >
Note that in the above discussion, other errors, including the >
differences between host time and wire time, and externally-caused >
clock discontinuities (e.g. clock corrections) were ignored. Under >
these assumptions the maximum clock errors will be due to the maximum >
relative skew acting on the largest interval between packets. >
7.2. Estimating the skew of unsynchronized clocks >
If the skew is linear (that is, if s(t) = S * t for constant S), the >
error in ipdv values will depend on the time between the packets used >
in calculating the value. If ti is the time between the ith and >
(i+1)st packet, then let Ti denote the sample mean time between >
packets and the average skew is s(Ti) = S * Ti. Note that E[Ti] >
should equal 1/lambda. In the event that the delays are constant, the >
skew parameter S can be estimated from the estimate Ti of the time >
between packets and the sample mean ipdv value. Under these >
assumptions, the ipdv values can be corrected by subtracting the >
estimated S * ti. >
We observe that the displacement due to the skew does not change the >
shape of the distribution, and, for example the Standard Deviation >
remains the same. What introduces a distortion is the effect of the >
drift, also when the mean value of this effect is zero at the end of >
the measurement. The value of this distortion is limited to the >
effect of the total skew variation on the emission interval. >
8. Definition for a bidirectional ipdv metric
We now consider that the action of the skew on one direction is the
same, with opposite sign, of the action on the other direction. The
idea of performing at the same time two independent measurements in
the two directions is suggested by this fact.
If, after a long measurement, the variable conditions of the system
under test have reached the situation of a contribution close to zero
to the mean value of the ipdv distribution, it is expected that only
the action of the average skew has modified the measured mean value.
It is therefore expected that in one direction that value is equal
and opposite to the one measured in the other direction.
This fact offers the possibility of defining a theoretical reference
measurement duration in the following way:
The reference duration of a bidirectional ipdv measurement between an
host E and an host W is reached at time Tf such that for each time
T > Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where
epsilon is what we can consider as zero, is always verified. This is
one, but not the only method for verifying that the mean ipdv value
has reached the value of the average relative skew.
At this point it is possible to evaluate the relative skew. This
will require the knowledge of the mean value of the intervals between
consecutive packets, that can be calculated over the transmitted
stream, by using the collected time stamps.
A bidirectional measurement can be defined not only as twin one-way
independent metrics that take place (nearly) at the same time, but
also as a two-way metric making use of packets looped back at one
end. This metric, that can be object of further study, would be
able to measure also the Round Trip Delay and its variations.
Problems will anyway arise on the characterization of emission
intervals in the backward direction. They would be produced by the
combination of the original Poisson arrival process and the effect of
ipdv on the forward direction. It has to be studied if this sequence
of intervals is still suitable for the measurement. also other
possibilities can be envisaged for obtaining a proper backward
sequence and still maintain the loopback concept.
9. Relationship to other standards |
The ITU definitions are based on delay variation as defined for ATM |
cells [5]. We will discuss these briefly first and then discuss the |
ITU's definition for IP packets [3]. |
9.1. 1-Point Cell Delay Variation |
The ITU looks at cell delay variation from two different points of |
view. The first, called 1-point cell delay variation, is essentially |
a measure of how a cell stream varies from a stated cell rate (e.g. |
the peak cell rate). The basic idea behind the measurement is as |
follows: The observer at the measurement point notes cell arrival |
times and clock ticks. The clock ticks at a constant rate, based on |
the peak cell rate for the cell stream. The difference between the |
cell arrival times and the clock ticks is the 1-point cell delay |
variation. If a cell arrives later than the clock tick, the clock |
"restarts" at the actual cell arrival time, and continues to tick at |
a constant rate from that point. |
The purpose of this measure is to identify what is called "cell |
clumping" and non-conforming cells. That is, to idenify cells that |
violate the leaky bucket parameters defined for that cell stream. |
That is why the clock skips when a cell is later than the normal |
inter-cell time defined by the peak cell rate. It is of much less |
interest when cells are late than when they arrive too close |
together. |
9.2. 2-Point Delay Variation, Cells and Packets |
2-Point cell delay variation, as defined in [5] is closer to what is |
defined here. The basic idea behind this metric is that two |
measurement points, whose clocks are synchronized, observe a cell |
stream and timestamp when each cell passes. The difference in the |
timestamps for a cell is essentially the one-way delay. There is also |
assumed to be a one-way cell delay for a reference cell which we will |
denote d0. The cell delay variation for the ith cell is then di-d0. |
Note that this is not an absolute value, but that the cell delay |
variation can be either positive or negative. [5] does not specify |
how to choose the reference cell delay. |
In [3] there is an informative appendix describing packet delay |
variation, which means that the material is not binding as a |
standard. The definitions are very similar to [5] with "packet" |
subsituting for "cell" in most places. One difference is that [3] |
offers two ways to define the reference packet (with the default |
being the first): |
+ Take the delay of the first packet of the sequence as the |
reference time. |
+ Take the average one-way packet delay as the reference time. | 7.1. Effects of synchronization errors
9.3. Discussion | Clock errors can be generated by two processes: the relative drift
and the relative skew of two given clocks. We should note that drift
is physically limited and so the total relative skew of two clocks
can vary between an upper and a lower bound.
9.3.1. Differences | Suppose then that we have a measurement between two systems such that
the clocks in the source and destination systems have at time 0 a
relative skew of s(0) and after a measurement interval T have skew
s(T). We assume that the two clocks have an initial offset of O (that
is letter O).
Demichelis [4] points out a number of problems with the 2-point PDV | Now suppose that the packets travel from source to destination in
definition in [3]. First of all is the issue of choosing the | constant time, in which case the ipdv is zero and the difference in
reference delay time. If this is chosen arbitrarily, it becomes | the timestamps of the two clocks is actually just the relative offset
uncertain how to compare the measurements taken from two non- | of the clocks. Suppose further that at the beginning of the
overlapping periods. If it is chosen as an average, that can also be | measurement interval the ipdv value is calculated from a packet pair
a problem, because over long periods of time in a network, the | and at the end of the measurement interval another ipdv value is
average one-way delay can vary widely. A twenty-four hour average as | calculated from another packet pair. Assume that the time interval
the reference time can seriously overestimate the actual delay | covered by the first measurement is t1 and that covered by the second
variation at a given time of day because the night-time hours, when | measurement is t2. Then
the delay can be expected to approach the propagation and node time, |
is included in the average. On the other hand, there is no clear way |
to partition the time in order to find averages for certain periods |
of time and compute the delay variation with reference to these |
averages. |
Another problem pointed out in [4] is the fact that 2-point PDV | ipdv1 = s(0)*t1 + t1*(s(T)-s(0))/T
requires synchronized clocks, whereas in this document Demichelis |
shows that synchronized clocks are not absolutely necessary for ipdv. |
9.3.2. Relationship between the metrics | ipdv2 = s(T)*t2 + t2*(s(T)-s(0))/T
The ipdv metric described here and the 1-point cell delay variation | assuming that the change is skew is linear in time. In most practical
metric described in [5] do not really have much in common (see also | cases, it is claimed that the drift will be close to zero in which
[4]). 1-point delay variation is really intended to talk about the | case the second (correction) term in the above equations disappears.
relationship of cell arrival times to a given periodic event, and |
consequently is more closely related to the first definition of |
"jitter" given in Section 3 above. |
2-point delay variation (actually, the packet variant described in | Note that in the above discussion, other errors, including the
[3]) is related to ipdv, and this relationship can be made precise as | differences between host time and wire time, and externally-caused
follows: Suppose that an arbitrarily chosen packet is designated as | clock discontinuities (e.g. clock corrections) were ignored. Under
the reference packet for the 2-point measurement and also as the | these assumptions the maximum clock errors will be due to the maximum
start packet of the ipdv measurement. Denote this packet by p(0). | relative skew acting on the largest interval between packets.
Then given ipdv measurements for a series of packets, the 2-point |
delay variation for packet i is p(0) + the sum from k=1 to i of |
ipdv(k). |
Similarly, given a sequence of 2-point delay variation measurements | 7.2. Estimating the skew of unsynchronized clocks
we can derive the ipdv measurement as follows: Denote the 2-point |
delay variation measurement for packet i as v(i). Then the ipdv value |
for the pair of packets p(k-1), p(k) is simply v(k)-v(k-1) [6]. |
9.3.3. Summary | If the skew is linear (that is, if s(t) = S * t for constant S), the
error in ipdv values will depend on the time between the packets used
in calculating the value. If ti is the time between the packet pair,
then let Ti denote the sample mean time between packets and the
average skew is s(Ti) = S * Ti. In the event that the delays are
constant, the skew parameter S can be estimated from the estimate Ti
of the time between packets and the sample mean ipdv value. Under
these assumptions, the ipdv values can be corrected by subtracting
the estimated S * ti.
As described above, there are a number of disadvantages of the | We observe that the displacement due to the skew does not change the
2-point packet delay variation approach. Further, the ipdv approach | shape of the distribution, and, for example the Standard Deviation
described here is general enough to provide the same information as | remains the same. What introduces a distortion is the effect of the
the 2-point packet delay variation measurements. Because of this, and | drift, also when the mean value of this effect is zero at the end of
because of the (possibly) looser clock synchronization requirements | the measurement. The value of this distortion is limited to the
of ipdv, we recommend the one-way-ipdv approach for the delay | effect of the total skew variation on the emission interval.
variation measurement. |
10. Security Considerations | 8. Security Considerations
The one-way-ipdv metric has the same security properties as the one- | The one-way-ipdv metric has the same security properties as the one-
way-delay metric [2]. The packets contain no user information, and so | way-delay metric [2]. The packets contain no user information, and so
privacy of user data is not a concern. It is still possible that | privacy of user data is not a concern. It is still possible that
there could be an attempt at a denial of service attack by sending | there could be an attempt at a denial of service attack by sending
many measurement packets into the network; there could also be | many measurement packets into the network; there could also be
attempts to disrupt measurements by diverting packets or corrupting | attempts to disrupt measurements by diverting packets or corrupting
them. | them.
In general, legitimate measurements must have their parameters | In general, legitimate measurements must have their parameters
selected carefully in order to avoid interfering with normal traffic | selected carefully in order to avoid interfering with normal traffic
in the network. Such measurements should also be authorized and | in the network. Such measurements should also be authorized and
authenticated in some way so that attacks can be identified and | authenticated in some way so that attacks can be identified and
intercepted. | intercepted.
11. Acknowledgements | 9. Acknowledgements
Thanks to Matt Zekauskas from Advanced and Ruediger Geib from | This major revision of the draft resulted from e-mail discussions
Deutsche Telekom for discussions relating to the contents of this | with and suggestions from Mike Pierce, Ruediger Geib, Glenn
revised draft. For this additional revision, discussions by e-mail > Grotefeld, and Al Morton. For previous revisions of this document,
with Andy Scherrer were very helpful. discussions with Ruediger Geib, Matt Zekaukas and Andy Scherer were
very helpful.
12. References 10. References
[1] V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP [1] V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP
Performance Metrics", RFC 2330 Feb. 1998 Performance Metrics", RFC 2330 Feb. 1998
[2] G.Almes, S.Kalidindi - "A One-way-Delay Metric for IPPM", RFC [2] G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", RFC
2679, September 1999 2679, September 1999
[3] ITU-T Recommendation I.380 "Internet Protocol Data [3] ITU-T Recommendation Y.1540 (formerly numbered I.380)
Communication Service - IP Packet Transfer and Availability "Internet Protocol Data Communication Service - IP Packet
Performance Parameters", February 1999 Transfer and Availability Performance Parameters", February 1999
[4] Demichelis, Carlo - "Packet Delay Variation Comparison between [4] Demichelis, Carlo - "Packet Delay Variation Comparison between
ITU-T and IETF Draft Definitions" March 1999 ITU-T and IETF Draft Definitions" November 2000 (in the IPPM
mail archives)
[5] ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer [5] ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer
Performance" Performance"
[6] e-mail exchanges with Ruediger Geib [6] S. Keshav - "An Engineering Approach to Computer Networking",
Addison-Wesley 1997, ISBN 0-201-63442-2
[7] V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding [7] V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding
PHB", RFC 2598, June 1999 PHB", RFC 2598, June 1999
13. Authors' Addresses [8] ITU-T Draft Recommendation Y.1541 - "Internet Protocol
Communication Service - IP Performance and Availability
Objectives and Allocations", April 2000
[9] Demichelis, Carlo - "Improvement of the Instantaneous Packet
Delay Variation (IPDV) Concept and Applications", World
Telecommunications Congress 2000, 7-12 May 2000
11. Authors' Addresses
Carlo Demichelis <carlo.demichelis@cselt.it> Carlo Demichelis <carlo.demichelis@cselt.it>
CSELT - Centro Studi E Laboratori Telecomunicazioni S.p.A CSELT - Centro Studi E Laboratori Telecomunicazioni S.p.A
Via G. Reiss Romoli 274 Via G. Reiss Romoli 274
10148 - TORINO 10148 - TORINO
Italy Italy
Phone +39 11 228 5057 Phone +39 11 228 5057
Fax. +39 11 228 5069 Fax. +39 11 228 5069
Philip Chimento <chimento@ctit.utwente.nl> Philip Chimento <chimento@torrentnet.com>
CTIT - Centre for Telematics and Information Technology Ericsson IPI
University of Twente 7301 Calhoun Place
Postbox 217 Rockville, Maryland
7500 AE Enschede 20855
The Netherlands USA
Phone +31 53 489 4331 Phone +1-240-314-3597
FAX +31 53 489 4524
Expiration date: December 2000 Expiration date: August 2001
 End of changes. 

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