draft-ietf-ippm-ipdv-02.txt   draft-ietf-ippm-ipdv-03.txt 
Network Working Group C. Demichelis
Network Working Group C.Demichelis CSELT INTERNET-DRAFT CSELT
Expiration Date: December 1999 P. Chimento
expires May 1999 CTIT
June 1999
Instantaneous Packet Delay Variation Metric for IPPM Instantaneous Packet Delay Variation Metric for IPPM
<draft-ietf-ippm-ipdv-02.txt> <draft-ietf-ippm-ipdv-03.txt>
1. Status of this Memo 1. Status of this Memo
This document is an Internet Draft. Internet Drafts are working doc- This document is an Internet-Draft and is in full conformance with |
uments of the Internet Engineering Task Force (IETF), its areas, and all provisions of Section 10 of RFC2026.
its working groups. Note that other groups may also distribute work-
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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 statistics of the difference
in One-Way-Delay of consecutive packets. This particular definition in One-Way-Delay of consecutive packets. This particular definition
of variation is called "Instantaneous Packet Delay Variation (ipdv)". of variation is called "Instantaneous Packet Delay Variation (ipdv)".
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. In the second case it allows an evaluation of the
reciprocal skew. Measurements performed on both directions (Two-ways reciprocal skew. Measurements performed on both directions (Two-way
measurements) allow a better estimation of clock differences. The measurements) allow a better estimation of clock differences. The
precision that can be obtained is evaluated. precision that can be obtained is evaluated.
I-D Ipdv Metric November 1998
3. Introduction 3. Introduction
This memo takes as a reference the Draft-ietf "One-Way-Delay metric for This memo takes as a reference the Draft-ietf "One-Way-Delay metric |
IPPM" that it is supposed to be known. Part of the text in this memo is for IPPM" [1]. Part of the text in this memo is directly taken from
directly taken from that Draft. that Draft.
This memo defines a metric for variation in delay of packets that flow This memo defines a metric for variation in delay of packets that
from one host to another one through an IP path. Since the metric is flow from one host to another one through an IP path. Since the
related to a variation, different definitions are possible according metric is related to a variation, different definitions are possible
to what the variation is measured against. according to what the variation is measured against.
NOTE: The terminology used in this Draft will be re-visited as soon as "Jitter" commonly has two meanings: The first meaning is the |
a terminology document will be available. variation of a signal with respect to some clock signal, where the |
So far the following is considered: arrival time of the signal is expected to coincide with the arrival |
- The term Jitter is derived from the well known definition given for of the clock signal. The second meaning has to do with the variation |
transmission of electrical pulses associated to a clock, and it seems of a metric (e.g. delay) with respect to some reference metric (e.g. |
to be able to describe variations with respect to an expected arrival average delay or minimum delay). The form of "jitter" that we talk |
time. about here has to do almost exclusively with the second meaning, |
- Each entity adopted as a reference for variation measurements defines rather than the first. See the section on the relationship with other |
a specific metric. Each metric describes a specific aspect or effect standards.
of the behavior of the System Under Test (SUT).
- Among entities that can be adopted, as an example, it is possible to
consider a reference delay for the path, a reference delay for the Src
Dst pair, the Mean One-Way-Delay over a period of interest, the Delay
variation that can be derived considering the difference between the
actual and the expected arrival time, the difference between the
delay of a packet and the last measured similar delay.
3.1. Definition 3.1. Definition
A definition of the Instantaneous Packet Delay Variation (ipdv) can be A definition of the Instantaneous Packet Delay Variation (ipdv) can
given for a pair of packets or for a packet inside a stream of packets. be given for a pair of packets or for a packet inside a stream of
packets.
For a pair of packets: For a pair of packets:
- The ipdv of a pair of IP packets, that are transmitted from the measu-
rement point MP1 to the measurement point MP2, is the difference + The ipdv of a pair of IP packets, that are transmitted from the
between the One-Way-Delay measured for the second packet and the One- measurement point MP1 to the measurement point MP2, is the
Way-Delay measured for the first packet of the pair. 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: For a stream of packets:
- The Instantaneous Packet Delay Variation of an IP packet, inside a
stream of packets, going from the measurement point MP1 to the measu-
rement point MP2, is the difference of the One-Way-Delay of that
packet and the One-Way-Delay of the preceding packet in the stream.
I-D Ipdv Metric November 1998 + The Instantaneous Packet Delay Variation of an IP packet, inside a
stream of packets, going from the measurement point MP1 to the
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
stream.
3.2. Motivation 3.2. Motivation
A number of services that can be supported by IP are sensitive to the A number of services that can be supported by IP are sensitive to the
regular delivery of packets and can be disturbed by instantaneous va- regular delivery of packets and can be disturbed by instantaneous
riations in delay, while they are not disturbed by slow variations, variations in delay, while they are not disturbed by slow variations,
that can last a relatively long time. A specific metric for quick va- that can last a relatively long time. A specific metric for quick
riations is therefore desirable. Metrics that can be derived from the variations is therefore desirable. Metrics that can be derived from
analysis of statistics of ipdv can also be used, for example, for the analysis of statistics of ipdv can also be used, for example, for |
buffer dimensioning, but this memo is not intended in that sense. buffer dimensioning. The scope of this metric is to provide a way
The scope of this metric is to provide a way for measurement of the for measurement of the quality delivered by a path.
quality delivered by a path.
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 allow differences and variations of the clocks of the two hosts. This
the use of the metric even if the two hosts that support the measure- allows the use of the metric even if the two hosts that support the
-ment points are not synchronized. In the latter case indications on measurement points are not synchronized. In the latter case
reciprocal skew of the clocks can be derived from the measurement and indications of reciprocal skew of the clocks can be derived from the
corrections are possible. The related precision is often comparable measurement and corrections are possible. The related precision is
with the one that can be achieved with synchronized clocks, being of often comparable with the one that can be achieved with synchronized
the same order of magnitude of synchronization errors. This will clocks, being of the same order of magnitude of synchronization
be discussed below. errors. This will be discussed below.
3.3. General Issues Regarding Time 3.3. General Issues Regarding Time
All what is contained in the paragraph 2.2. of the Draft ippm on One- Everything contained in the Section 2.2. of [2] applies also in this |
Way Delay metric (2.2. General Issues Regarding Time) applies also in case.
this case.
In addition, it is here considered that the reciprocal skew of the two In addition, we assume here that the reciprocal skew of the two
clocks can be decomposed into two parts: clocks can be decomposed into two parts:
* A fixed one, called in this context "skew", given, for example, by
tolerances in physical dimensions of crystals.
* A variable one, called in this context "drift", given, for example,
by changes in temperature or other conditions of operation.
Both of this components are part of the term "skew" as defined in the
referenced Draft and in the Framework document.
NOTE: The drift of a clock, as it is above defined over a long period + A fixed one, called in this context "skew", given, for example, by
must have an average value that tends to zero while the period becomes tolerances in physical dimensions of crystals.
large since the frequency of the clock has a finite (and little)
range. In order to underline the order of magnitude of this effect,it
is considered that the maximum range of drift for commercial crystals
is about 50 part per million (ppm). Since it is mainly connected with
variations in operating temperature (from 0 to 70 degrees Celsius), it
is expected that a host will have a nearly constant temperature during
its operation period, and variations in temperature, even if quick,
could be less than one Celsius per second, and range in the order of
I-D Ipdv Metric November 1998 + A variable one, called in this context "drift", given, for
example, by changes in temperature or other conditions of
operation. Both of these components are part of the term "skew" as
defined in the referenced Draft and in the Framework document.
few degrees. The total range of the drift is usually related to varia- NOTE: The drift of a clock, as it is above defined over a long period
-tions from 0 to 70 Celsius. These are important points for evaluation must have an average value that tends to zero while the period
of precision of ipdv measurements, as it will see below. becomes large since the frequency of the clock has a finite (and
small) range. In order to underline the order of magnitude of this
effect,it is considered that the maximum range of drift for
commercial crystals is about 50 part per million (ppm). Since it is
mainly connected with variations in operating temperature (from 0 to
70 degrees Celsius), it is expected that a host will have a nearly
constant temperature during its operation period, and variations in
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
drift is usually related to variations from 0 to 70 Celsius. These
are important points for evaluation of precision of ipdv
measurements, as will be seen below.
4. Structure of this memo 4. Structure of this memo
The metric will be defined as applicable to a stream of packets that 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 ini- flow from a source host to a destination host (one-way ipdv). The
tial assumption is that source and destination hosts have synchronized initial assumption is that source and destination hosts have
clocks. synchronized clocks. The definition of a singleton of one-way ipdv
The definition of a singleton of one-way ipdv metric is first consi- metric is first considered, and then a definition of samples for ipdv
-dered, and then a definition of samples for ipdv will be given. will be given.
Then the case of application to not synchronized hosts will be dis-
cussed, and the precision will be compared with the one of the previous
case.
A bidirectional ipdv metric will be defined, as well as the methodology Then the case of application to non-synchronized hosts will be
for error corrections. This will not be a two-ways metric, but a discussed, and the precision will be compared with the one of
"paired" one-way in opposite directions. Some statistics describing the synchronized clocks.
IP path's behavior will be proposed.
In the Appendix A a more detailed analysis is reported of the ipdv A bidirectional ipdv metric will be defined, as well as the
theory and of the characteristics of ipdv distribution. methodology for error corrections. This will not be a two-way metric,
but a "paired" one-way in opposite directions. Some statistics
describing the IP path's behavior will be proposed.
5. A singleton definition of a One-way ipdv metric 5. A singleton definition of a One-way ipdv metric |
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, that is supposed to be known. This section makes use One-Way-Delay metric [2]. This section makes use of those parts of
of those parts of the One-Way-Delay Draft that directly apply to the the One-Way-Delay Draft that directly apply to the One-Way-ipdv
One-Way-ipdv metric, or makes direct references to that Draft. metric, or makes direct references to that Draft.
5.1. Metric name 5.1. Metric name
Type-P-One-way-ipdv Type-P-One-way-ipdv
5.2. Metric parameters 5.2. Metric parameters
+ Scr, 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. It is explicitly noted that also the difference T2-T1
is a parameter of the measurement though this is already implicit, is a parameter of the measurement though this is already implicit,
since the times T1 and T2 exactly define the time conditions in which since the times T1 and T2 exactly define the time conditions in
the measurement takes place. which the measurement takes place.
I-D Ipdv Metric November 1998
+ Path, the path from Src to Dst; in cases where there is only one Note that the packet length is an implicit parameter of both the |
path from Src to Dst, this optional parameter can be omitted. Type-P-One-way-delay metric and the Type-P-One-way-ipdv metric, since |
{Comment: the presence of path is motivated by cases such as with this contributes to the overall one-way delay. We assume that the |
Merit's NetNow setup, in which a Src on one NAP can reach a Dst on packets sent for ipdv measurements are all of the same length.
another NAP by either of several different backbone networks.
Generally, this optional parameter is useful only when several dif-
-ferent routes are possible from Src to Dst. Using the loose source
route IP option is avoided since it would often artificially worsen
the performance observed, and since it might not be supported along
some paths.}
5.2. Metric unit 5.3. 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.
5.3. Definition 5.4. Definition
Type-P-One-way-ipdv is defined for two (consecutive) packets from Src Type-P-One-way-ipdv is defined for two (consecutive) packets from Src
to Dst, as the difference between the value of the type-P-One-way- to Dst, as the difference between the value of the type-P-One-way-
delay from Src to Dst at T2 [via path] and the value of the type-P- delay from Src to Dst at T2 [via path] and the value of the type-P-
One-Way-Delay from Src to Dst at T1 [via path]. T1 is the wire-time One-Way-Delay from Src to Dst at T1 [via path]. T1 is the wire-time
at which Scr sent the first bit of the first packet, and T2 is the 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 wire-time at which Src sent the first bit of the second packet. This
metric is therefore ideally derived from the One-Way-Delay metric. metric is therefore ideally derived from the One-Way-Delay metric.
NOTE: The requirement of "consecutive" packets is not essential. The NOTE: The requirement of "consecutive" packets is not essential. The
measured value is anyway the difference in One-Way-Delay at the measured value is anyway the difference in One-Way-Delay at the times
times T1 and T2, which is meaningful by itself, as long as the T1 and T2, which is meaningful by itself, as long as the times T1 and |
times T1 and T2 are such to describe the investigated charac- T2 denote the wire times of the packets sent from Src to Dst.
-teristics. These times will be better defined later.
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 [via path] is ddT" means that Src sent two consecutive Dst at T1, T2 [via path] is ddT" means that Src sent two consecutive
packets whose the first at wire-time T1 (first bit), and the second packets, the first at wire-time T1 (first bit), and the second at
wire-time T2 (first bit) and the packets were received by Dst at wire wire-time T2 (first bit) and the packets were received by Dst at
-time dT1+T1 (last bit of the first packet), and, respectively, at wire-time dT1+T1 (last bit of the first packet), and at wire-time
wire-time dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT. dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT.
"The type-P-one-way-ipdv from Src to Dst at T1,T2 [via path] is unde-
fined" means 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.
I-D Ipdv Metric November 1998 "The type-P-one-way-ipdv from Src to Dst at T1,T2 [via path] is
undefined" means 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.
5.4. Discussion 5.5. Discussion
Type-P-One-way-ipdv is a metric that makes use of the same measurement Type-P-One-way-ipdv is a metric that makes use of the same
methods provided for delay metrics. measurement methods provided for delay metrics.
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 clock synchronization problems. This issue will be more + Being a differential measurement, this metric is less sensitive to
carefully examined in section 6. of this memo. It is pointed clock synchronization problems. This issue will be more carefully
out that, if the reciprocal clock conditions change in time, examined in section 7 of this memo. It is pointed out that, if the
the accuracy of the measurement will depend on the time inter- reciprocal clock conditions change in time, the accuracy of the
-val T2-T1 and the amount of possible errors will be discussed measurement will depend on the time interval T2-T1 and the
below. magnitude of possible errors will be discussed below.
+ A given methodology will have to include a way to determine whether a
delay value is infinite or whether it is merely very large (and + A given methodology will have to include a way to determine
the packet is yet to arrive at Dst). whether a delay value is infinite or whether it is merely very
As noted by Mahdavi and Paxson, simple upper bounds (such as the large (and the packet is yet to arrive at Dst). As noted by
255 seconds theoretical upper bound on the lifetimes of IP Mahdavi and Paxson, simple upper bounds (such as the 255 seconds
packets [Postel: RFC 791]) could be used, but good engineering, theoretical upper bound on the lifetimes of IP packets [Postel:
including an understanding of packet lifetimes, will be nee- RFC 791]) could be used, but good engineering, including an
-ded in practice. {Comment: Note that, for many applications of understanding of packet lifetimes, will be needed in practice.
these metrics, the harm in treating a large delay as infinite {Comment: Note that, for many applications of these metrics, the
might be zero or very small. A TCP data packet, for example, harm in treating a large delay as infinite might be zero or very
that arrives only after several multiples of the RTT may as well small. A TCP data packet, for example, that arrives only after
have been lost.} several multiples of the RTT may as well have been lost.}
+ Usually a path is such that if the first packet is largely delayed,
it can "stop" the second packet of the pair and vary its delay. + As with other 'type-P' metrics, the value of the metric may depend
This is not a problem for the definition since is, in any case, on such properties of the packet as protocol,(UDP or TCP) port
part of the description of the path's behavior. number, size, and arrangement for special treatment (as with IP
+ As with other 'type-P' metrics, the value of the metric may de- precedence or with RSVP).
-pend on such properties of the packet as protocol,(UDP or TCP)
port number, size, and arrangement for special treatment (as
with IP 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, reas-
-sembly does not occur, then the packet will be deemed lost.
5.5. Methodologies + If the packet is fragmented and if, for whatever reason,
reassembly does not occur, then the packet will be deemed lost.
5.6. 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). precedence). Generally, for a given Type-P, the methodology would
proceed as follows:
I-D Ipdv Metric November 1998
Generally, for a given Type-P, the methodology would proceed as fol-
lows:
+ The need of synchronized clocks for Src and Dst will be discus- + The need of synchronized clocks for Src and Dst will be discussed
-sed later. Here a methodology is supposed 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 + At the Src host, select Src and Dst IP addresses, and form two
test packets of Type-P with these addresses. Any 'padding' por- test packets of Type-P with these addresses. Any 'padding' portion
-tion of the packet needed only to make the test packet a given of the packet needed only to make the test packet a given size
size should be filled with randomized bits to avoid a situation should be filled with randomized bits to avoid a situation in
in which the measured delay is lower than it would otherwise which the measured delay is lower than it would otherwise be due
be due to compression techniques along the path. to compression techniques along the path.
+ Optionally, select a specific path and arrange for Src to send
the packets to that path. {Comment: This could be done, for
example, by installing a temporary host-route for Dst in Src's
routing table.}
+ 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 prepared first
Type-P packet, and send it towards Dst [via path]. + At the Src host, place a timestamp in the first Type-P packet,
and send it towards Dst [via path].
+ 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. + Record this first delay value.
+ At the Src host, place a timestamp in the prepared second
Type-P packet, and send it towards Dst [via path]. + At the Src host, place a timestamp in the second Type-P packet,
and send it towards Dst [via path].
+ 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 value
the ipdv value of the pair of packets is obtained. + By subtracting the second value of One-Way-Delay from the first
value the ipdv value of the pair of packets is obtained.
+ 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.
5.6. Errors and Uncertainties 5.7. 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 that can affect the One-Way-Delay measurement, even if,
in this case, the influence is different. in this case, the influence is different.
The Framework document provides general guidance on this point, but The Framework document [1] provides general guidance on this point,
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 and Dst hosts.
+ Errors/uncertainties due to the difference between 'wire time'
and 'host time'.
I-D Ipdv Metric November 1998 + Errors/uncertainties due to uncertainties in the clocks of the Src
and Dst hosts.
Each of these type of errors are discussed in more detail in the next + Errors/uncertainties due to the difference between 'wire time' and
'host time'.
Each of these errors is discussed in more detail in the next
paragraphs. paragraphs.
5.6.1. Errors/Uncertainties related to Clocks 5.7.1. Errors/Uncertainties related to Clocks
If, as a first approximation, the error that affects the first measu- If, as a first approximation, the error that affects the first
rement of One-Way-Delay were the same of the one affecting the second measurement of One-Way-Delay were the same of the one affecting the
measurement, they will cancel each other when calculating ipdv. The second measurement, they will cancel each other when calculating
residual error related to clocks is the difference of the said errors ipdv. The residual error related to clocks is the difference of the
that are supposed to change from the time T1, at which the first errors that are supposed to change from the time T1, at which the
measurement is performed, to the time T2 at which the second measure- first measurement is performed, to the time T2 at which the second
measure ment is performed. Synchronization, skew, accuracy and
resolution are here considered with the following notes:
ment is performed. Synchronization, skew, accuracy and resolution are
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.
+ If the synchronization error affecting the One-Way-Delay measurement
is Tsync, and it is a linear function of time, through the skew
value "sk", at time T1 the error will be Tsync1 and at time T2
the error will be Tsync2. The ipdv measurement will be affected
by the error:
Tsync2-Tsync1 = sk x (T2 - T1)
depending on skew and T2-T1. To minimize this error it is pos-
sible to reduce the time interval T2-T1, but this could limit
the generality of the metric.
Methods for evaluating the synchronization error will be discus-
sed below, since they come from a statistic over a significant
sample.
If the measurement conditions do not allow to neglect the drift,
supposed as linear in the interval T2-T1, and having a value of
"dr" expressed in ppm / sec., the ipdv error will become:
Tsync2-Tsync1 = sk x (T2 - T1) + [dr x (T2-T1) x (T2-T1)] / 2
It has to be noted that the presence of drift varies the skew
value in the time. The limits in which the skew can vary are
anyway limited and little, so that a given drift cannot act
indefinitely. Section 7 and Appendix A provide more information
on this point.
+ As far as accuracy and resolution are concerned, what is noted
in the above referenced Draft on One-Way-Delay at section 3.7.1,
applies also in this case, with the further consideration, about
resolution, that in this case the uncertainty introduced is two
times the one of a single delay measurement. Errors introduced
by these effects are often larger than the ones introduced by
the drift.
I-D Ipdv Metric November 1998
5.6.2. Errors/uncertainties related to Wire-time vs Host-time + If the synchronization error affecting the One-Way-Delay
measurement is Tsync, and it is a linear function of time, through
The content of sec. 3.7.2 of the above referenced Draft applies also the skew value "sk", at time T1 the error will be Tsync1 and at
in this case, with the following further consideration: time T2 the error will be Tsync2. The ipdv measurement will be
The difference between Host-time and Wire-time can be in general de- affected by the error: Tsync2-Tsync1 = sk x (T2 - T1) depending on
composed into two components, whose one is constant and the other is skew and T2-T1. To minimize this error it is possible to reduce
variable around zero. Only the variable components will produce measu- the time interval T2-T1, but this could limit the generality of
rement errors, while the constant one will be canceled while calcu- the metric. Methods for evaluating the synchronization error will
lating ipdv. be discussed below, since they come from a statistic over a
significant sample. If the measurement conditions do not allow
6. Definitions for Samples of One-way ipdv neglecting the drift, assumed linear in the interval T2-T1, and
having a value of "dr" expressed in ppm / sec., the ipdv error
Starting from the definition of the singleton metric of one-way ipdv, will become: Tsync2-Tsync1 = sk x (T2 - T1) + [dr x (T2-T1) x
(T2-T1)] / 2 Drift varies the skew value in the time. The limits
some ways of building a sample of such singletons are here described. in which the skew can vary are anyway limited and small, so that a
In particular two "discontinuous" samples and one "continuous" sample given drift cannot act indefinitely. Section 7 and Appendix A
are defined, and the last one is proposed, being the most suitable for provide more information on this point.
describing the aspect of the path's behavior underlined in the motiva-
tion.
In the following, the two packets needed for a singleton measurement
will be called a "pair".
6.1. "Discontinuous" definitions
A general definition can be the following:
Given particular binding of the parameters Src, Dst, path, and
Type-P, a sample of values of parameters T1 and T2 is defined.
The means for defining the values of T1 is to select a beginning
time T0, a final time Tf, and an average 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. Another si-
milar, but independent, pseudo-random Poisson arrival process
based on T0', Tf' and lambda', will produce a series of t'
values. The time interval between successive t' values will then
average 1/lambda'. For each T1 value that has been obtained
by the first process, it is then possible to calculate the
successive T2 values as the successive T1 values plus the
successive intervals of t'.
The result is shown in figure 1.
This general definition is likely go give problems, if no limits are
considered for the obtained values. For example, the emission
time of the first packet of a pair, could fall before the emission
time of the second packet of the preceding pair. Probably this could
be acceptable (provided that there are means to recognize pairs -e.g.
I-D Ipdv Metric November 1998
use of sequence numbers-), but the concept itself of ipdv would be,at
least, slightly changed. A way for avoiding this type of philosophical
problems can be to give some rules on the values T0, Tf, lambda,
T0', Tf', lambda', without changing the meaning of the metric.
|<- average interval 1/lambda ->|
| |
|<- av.int. | |<- av.int. |
|1/lambda'->| | 1/lambda'->|
_____|___________|___________________|_____________|________
pair i pair i+1
Figure 1
As an example, it could be defined that the process of sorting the
interval between pairs starts after the interval between packets in a
pair is expired, obtaining the result of figure 2:
|<--- av. int.......| + As far as accuracy and resolution are concerned, what is noted in
..........................| 1/lambda --->| the Draft on One-Way-Delay [2] in section 3.7.1, applies also in
| | this case, with the further consideration, about resolution, that
|<- av.int. | |<- av.int. | in this case the uncertainty introduced is two times the one of a
|1/lambda'->| | 1/lambda'->| single delay measurement. Errors introduced by these effects are
_____|___________|___________________|_____________|________ often larger than the ones introduced by the drift.
pair i pair i+1
Figure 2
Still other problems can be envisaged with these two definitions which 5.7.2. Errors/uncertainties related to Wire-time vs Host-time
are described in some more detail in Appendix A.
6.2. A "continuous" definition 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
Wire-time can be in general decomposed into two components, of which
one is constant and the other is variable. Only the variable
components will produce measurement errors, while the constant one
will be canceled while calculating ipdv.
A way for naturally avoiding the previous problems and producing a 6. Definitions for Samples of One-way ipdv
testing environment closer to actual scenarios is to adopt the follo-
wing "continuous" definition.
A continuous stream of test packets can be supposed, where the second
packet of a pair is, at the same time, the first packet of the next
pair. Therefore the preceding definitions become:
+ Given particular binding of the parameters Src, Dst, path, and Starting from the definition of the singleton metric of one-way ipdv, |
Type-P, a sample of values of parameter T1 is defined. we define a sample of such singletons. In the following, the two |
The means for defining the values of T1 is to select a beginning packets needed for a singleton measurement will be called a "pair". |
time T0, a final time Tf, and an average rate lambda, then
define a pseudo-random Poisson arrival process of rate lambda,
I-D Ipdv Metric November 1998 A stream of test packets is generated where the second packet of a |
pair is, at the same time, the first packet of the next pair. |
whose values fall between T0 and Tf. The time interval between + Given particular binding of the parameters Src, Dst and Type-P, a |
successive values of T1 will then average 1/lambda. From the sample of values of parameter T1 is defined. To define the values |
second value on, T1 value of the pair n coincides with T2 of of T1, select a beginning time T0, a final time Tf, and an average |
the pair n-1, and the first packet of pair n coincides with the rate lambda, then define a pseudo-random Poisson arrival process |
second packet of the pair n-1. of rate lambda, whose values fall between T0 and Tf. The time |
For the moment, in the following, this last definition will be con- interval between successive values of T1 will then average |
sidered. Further refinement is required and is for further discussion. 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. |
6.3. Metric name 6.1. Metric name
Type-P-One-way-ipdv-stream Type-P-One-way-ipdv-stream
6.4. Parameters 6.2. 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
+ Path, the path* from Src to Dst; in cases where there is only
one path from Src to Dst, this optional parameter can be omitted
+ T0, a time + T0, a time
+ Tf, a time + Tf, a time
+ lambda, a rate in reciprocal seconds + lambda, a rate in reciprocal seconds
6.5. Metric Units: 6.3. Metric Units:
A sequence of triads whose elements are: A sequence of triads whose elements are:
+ T, a time + T, a time
+ Ti, a time interval. + Ti, a time interval.
+ dT a real number or an undefined number of seconds + dT a real number or an undefined number of seconds
6.6. Definition 6.4. 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 Ti 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 T, at each pair of equal to Tf are then selected. Starting from time T0, at each pair of
times T(i), T(i+1)of this process a value of Type-P-One-way-ipdv is 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 obtained. The value of the sample is the sequence made up of the
resulting <time, time interval, ipdv> triad, where the time interval resulting <time, time interval, ipdv> triple, where the time interval
is given by T(i+1)-T(i). Each obtained time T(i), excluding the first is given by T(i+1)-T(i). Each time T(i), excluding the first and the
and the last, is therefore at the same time the the second time of last, is therefore at the same time the the second time of pair i and
pair i and the first time of pair i+1. The result is shown in figure 3 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) |T(i-2) |T(i-1) |T(i) |T(i+1)
_____|__________|___________________|__________|________ _____|__________|___________________|__________|________
pair i-1 pair i pair i+1 pair i-1 pair i pair i+1
Figure 3 Figure 3
I-D Ipdv Metric November 1998
6.7. Discussion 6.5. 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 fully specified. Pseudo-random number generators of good quality will
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 statistically as unbiased as possible. {Comment: there is, of course,
course, no claim that real Internet traffic arrives according to a no claim that real Internet traffic arrives according to a Poisson
Poisson arrival process.} arrival process.}
6.8. Methodology 6.6. 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 with respect the one of emission, in order to recognize the order than the order sent, in order to recognize the pairs of test
pairs of test packets, they should be marked with a Sequence Number packets, they should be marked with a sequence number. For duplicated
or make use of any other tool suitable to the scope. For duplicated packets only the first received copy should be considered. If a
packets only the first received copy should be considered. If a pac- packet is lost, two values of ipdv will be undefined, since each
ket is lost, two values of ipdv will be undefined, since each packet, packet is common to two pairs.
in the supposed "continuous" definition, is common to two pairs.
Steps for measurement can be the following: Steps for measurement can be the following:
+ Starting from a given time T, Src generates a test packet as for
a singleton metrics, inserts in the packet a Sequence Number + Starting from a given time T, Src generates a test packet as for a
and the transmission Time Stamp Tx,then sorts the time Ti at singleton metrics, inserts in the packet a sequence number and the
which the next packet has to be sent. 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. + At time Ti, Src repeats the previous step, unless T(i) > Tf.
+ On reception of the first packet, or the first packet after a SN
error, Dst records SN and Tx timestamp that are contained in
the packet and the reception time Rx as "old values".
+ On reception of the other packets Dst verifies the SN and if it is
correct, by using the "old values" and the newly received ones,
a value of ipdv is computed. Then Dst records the new SN, Tx
and Rx timestamps as "old values".
6.9. Errors and uncertainties + On reception of the first packet, or the first packet after a
sequence number error, Dst records sequence number and
transmission timestamp that are contained in the packet and the
reception time Rx as "old values".
The same considerations apply that have been made about the single- + On reception of the other packets Dst verifies the seuqence number
ton metric. An additional error can be introduced by the pseudo-ran- and if it is correct, by using the "old values" and the newly
dom Poisson process as focused in the above referenced Draft. received ones, a value of ipdv is computed. Then Dst records the
Further considerations will be made in section 7, and in Appendix A. new sequence number, transmit and receive timestamps as "old
values".
6.10 Some statistics for One-way-ipdv 6.7. Errors and uncertainties
Some statistics are here considered, that can provide useful informa- The same considerations apply that have been made about the singleton
-tion in analyzing the behavior of the packets flowing from Src to Dst metric. An additional error can be introduced by the pseudo-random
Poisson process as focused in [2]. Further considerations will be
made in section 7, and in Appendix A.
I-D Ipdv Metric November 1998 6.8. Distribution of One-way-ipdv values |
These statistics are given having in mind a practical use of them. The The one-way-ipdv values are limited by virtue of the fact that there |
focus is on the instantaneous behavior of the connection, while buffer are upper and lower bounds on the one-way-delay values. Specifically, |
dimensioning is not in the scope of this document. one-way-delay is upper bounded by the value chosen as the maximum |
Other statistics can be defined if needed. beyond which a packet is counted as lost. It is lower bounded by |
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). |
6.10.1. Type-P-One-way-ipdv-inverse-percentile 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.
6.9. Some statistics for One-way-ipdv
Some statistics are suggested which can provide useful information in |
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-Stream and a time threshold, that can be Given a Type-P-One-way-ipdv-Stream and a time threshold, that can be
either positive or negative, the fraction of all the ipdv values in 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 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 ne- positive, or greater or equal to the threshold if the threshold is
gative. negative.
For many real-time services that require a regular delivery of the For many real-time services that require a regular delivery of the
packets, this statistics can give the amount of packets received packets, this statistics can give the amount of packets received
beyond acceptable limits. beyond acceptable limits.
6.10.2 Type-P-One-way-ipdv-standard-deviation 6.9.2. Type-P-One-way-ipdv-jitter |
Given a Type-P-One-way-ipdv-Stream, the distribution of ipdv values
is considered and the Standard Deviation can be calculated as an
indication of regularity of delivery. For practical purposes it can be
useful to define a total standard deviation, computed over the com-
plete set of value, and a standard deviation computed over the sub-
set of those values that do not exceed given positive and negative
thresholds. This allows a more accurate description of the performan-
ce experienced by packets. Details on the shape of the ipdv distribu-
tion are given in Appendix A.
6.10.3 Type-P-One-way-ipdv-average
This statistic should tend to a value of ZERO for a number of ipdv This metric was defined in [7] and is simply the absolute value of |
values that tend to infinite. The behavior of Type-P-One-way-ipdv- the Type-P-One-way-ipdv. This can be used to derive a number of |
average, and its meaning, are issues for the next section 7. metrics. |
7. Discussion on clock synchronization 7. Discussion on clock synchronization
This section gives some considerations about the need of having syn- This section gives some considerations about the need of having
chronized clocks at Src and Dst. These considerations are given as a synchronized clocks at Src and Dst. These considerations are given as
basis for discussion, they require further investigation. We start a basis for discussion, they require further investigation. We start
from the analysis of the mean value of the ipdv distribution related from the analysis of the mean value of the ipdv distribution related
to a "continuous" sample. Some more detailed calculations are presented to a "continuous" sample. Some more detailed calculations are
in Appendix A. presented in Appendix A.
I-D Ipdv Metric November 1998
7.1. Mean value of ipdv distribution.
If D(i) is the delay of packet "i", and ipdv(i) is the i-th value of
ipdv in the distribution of a sample of "n" values, collected with
the described methodology, we can write:
ipdv(1) = D1 - D0
..........
ipdv(i) = D(i) - D(i-1)
..........
ipdv(n) = D(n) - D(n-1)
The mean value of ipdv distribution will result in
E(ipdv) = (D(n) - D(0))/n
If an actual measurement is performed, that lasts a period of time
long enough to contain a number "n" sufficiently large and, supposing
synchronized clocks, such that the network conditions (traffic) allow
to find a D(n) not too different from D(0), e.g. a time of n x 24
hours, E(ipdv) will tend to zero, since the difference D(n) - D(0) will
remain finite and little.
7.2. Effects of a varying traffic
If the mean values of delay D are changing inside a given period of
time, for example they are increasing due to an increment of traffic,
we can consider, as a first approximation, the ipdv values as decom-
posed into two components, one being instantaneous and another one
as having a constant rate dD and corresponding to the increment "per
interval" of the mean value of D. The mean value of the distribution
will be shifted of the value dD corresponding to the mean value of
the interval between test packets. This will happen only during the
monotonic variation, and is not a distortion, since it is the record
of the instantaneous behavior. When the conditions will come back
to the initial ones, the distribution will resume a mean value around
zero. As for the case of drift, also in this case a monotonic varia-
-tion cannot take place indefinitely. In Appendix A a method is given
for subdividing the variation into these two components over short
periods, in order to have indications on variations of traffic condi-
-tions.
7.3. Effects of synchronization errors 7.1. Effects of synchronization errors
We refer here to the two components that can generate this type of We refer here to the two components that can generate this type of
errors that are the reciprocal "skew" and "drift" of the Src and Dst errors that are the reciprocal "skew" and "drift" of the Src and Dst
clocks. It is first of all noted that the variable component "drift" clocks. It is first of all noted that the variable component "drift"
I-D Ipdv Metric November 1998
is physically limited and its effects can be interpreted by saying is physically limited and its effects can be interpreted by saying
that the total reciprocal skew of the two clocks can vary, ranging from that the total reciprocal skew of the two clocks can vary, ranging
a min to a max. value in the time. This type of variation takes place from a min to a max. value in the time. This type of variation takes
very slowly being mostly connected to variations in temperature. place very slowly being mostly connected to variations in
temperature.
We suppose to perform a measurement between a Src and a Dst that have We suppose to perform a measurement between a Src and a Dst that have
a reciprocal, initial skew of "ts1" and a reciprocal drift such that, a reciprocal, initial skew of "ts1" and a reciprocal drift such that,
after the time T the total skew is "ts2". It is not here a limitation after the time T the total skew is "ts2". It is not here a limitation
to consider that at the beginning of time T the two clocks indicate to consider that at the beginning of time T the two clocks indicate
the same time T0. the same time T0.
In order to analyze the effects produced by this situation we suppose In order to analyze the effects produced by this situation we suppose
that packets are transferred, from Src to Dst, with a constant delay D that packets are transferred, from Src to Dst, with a constant delay
In this conditions the measured ipdv should always be zero, and what D In this conditions the measured ipdv should always be zero, and
is actually measured is the error. what is actually measured is the error.
An ipdv value is measured at the beginning of time T with two packets An ipdv value is measured at the beginning of time T with two packets
having an interval of Ti(1).Another ipdv value is measured at the end having an interval of Ti(1).Another ipdv value is measured at the end
of T with two packets having a time interval Ti(2). of T with two packets having a time interval Ti(2).
On our purposes other errors (like wire-time vs host-time) are not On our purposes other errors (like wire-time vs host-time) are not
considered since they are not relevant in this analysis, being common considered since they are not relevant in this analysis, being common
to all the measurement methods. to all the measurement methods.
It is then possible to calculate the values of the Tx and Rx time- It is then possible to calculate the values of the Tx and Rx
stamps as they are seen by the two clocks, and the related two ipdv timestamps as they are seen by the two clocks, and the related two
values. ipdv values.
The first ipdv value will be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1) The first ipdv value will be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1)
The second ipdv value will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2) The second ipdv value will be: ipdv2 = ts2*Ti(2) +((ts2-ts1)/T)*Ti(2)
The error is given by the effect of the skew during the time inter- The error is given by the effect of the skew during the time interval
val Ti(i) between the two packets of the pair, and a second order Ti(i) between the two packets of the pair, and a second order term
term due to the variation of that skew in the same interval. due to the variation of that skew in the same interval.
If, as in the most of practical cases, the drift can be considered If, as in the most of practical cases, the drift can be considered
close to zero, then ts1 = ts2, and the error is not depending on the close to zero, then ts1 = ts2, and the error is not depending on the
time at which the measurement is done. In addition, this type of time at which the measurement is done. In addition, this type of
error can be corrected as it is indicated in the next paragraph and error can be corrected as it is indicated in the next paragraph and
discussed in Appendix A. discussed in Appendix A.
In any case the maximum error on an ipdv value will correspond to the In any case the maximum error on an ipdv value will correspond to the
effect of the maximum reciprocal skew on the maximum interval between effect of the maximum reciprocal skew on the maximum interval between
packets. packets.
I-D Ipdv Metric November 1998 7.2. Related precision
7.4. Related precision
This means that: This means that:
1) + If the skew is constant and is = ts all the ipdv(i) values are
+ If the skew is constant and is = ts all the ipdv(i) values are
increased by the quantity Ti(i)*ts with respect the actual value. increased by the quantity Ti(i)*ts with respect the actual value.
The mean ipdv value will therefore increased of the quantity The mean ipdv value will therefore increased of the quantity
E[Ti(i)]*ts, which is measured. Also E[Ti(i)] can be measured, and E[Ti(i)]*ts, which is measured. Also E[Ti(i)] can be measured, and
should be related to lambda. That means that the skew ts can be should be related to lambda. That means that the skew ts can be
calculated. If together with ipdv(i), also the corresponding Ti(i) calculated. If together with ipdv(i), also the corresponding Ti(i)
are collected, for each ipdv(i) value a correcting term is avai- are collected, for each ipdv(i) value a correcting term is
-lable, and a sample of "corrected" c-ipdv(i) values is obtained, available, and a sample of "corrected" c-ipdv(i) values is
where c-ipdv(i) = ipdv(i) - Ti(i)*st. obtained, where c-ipdv(i) = ipdv(i) - Ti(i)*st.
2) + Considering the total skew as subdivided into a fixed part and a
+ Considering the total skew as subdivided into a fixed part and a
variable part (skew and drift),respectively, ts and + or - td, variable part (skew and drift),respectively, ts and + or - td,
from the mean ipdv value and the mean emission interval the average from the mean ipdv value and the mean emission interval the
skew can be derived in the period of interest (Appendix A). The average skew can be derived in the period of interest (Appendix
preceding correction can then be applied. The maximum residual er- A). The preceding correction can then be applied. The maximum
-ror on an ipdv value is given by the difference between the actual residual error on an ipdv value is given by the difference between
skew at the time in which the value has been measured and the ave- the actual skew at the time in which the value has been measured
-rage skew, multiplied by the time interval between the packets and the average skew, multiplied by the time interval between the
that have generated that ipdv value. Considerations on the number packets that have generated that ipdv value. Considerations on the
of values in the sample affected by errors are reported in number of values in the sample affected by errors are reported in
Appendix A. Appendix A.
3) + If the duration of the measurement is such that it is possible
to consider that the effect of the items at points 7.1 and 7.2, + If the duration of the measurement is such that it is possible to |
are close to zero, the mean value of the ipdv distribution will consider that the ipdv (without skew) is close to zero, the mean
have the value of the average skew multiplied by the mean value of value of the ipdv distribution will have the value of the average
the emission interval, as supposed above. skew multiplied by the mean value of the emission interval, as
4) + We observe that the displacement due to the skew does not change supposed above.
the shape of the distribution, and, for example the Standard Devi-
ation remains the same. What introduces a distortion is the effect + We observe that the displacement due to the skew does not change
of the drift, also when the mean value of this effect is zero at the shape of the distribution, and, for example the Standard
the end of the measurement. The value of this distortion is limited Deviation remains the same. What introduces a distortion is the
to the effect of the total skew variation on the emission interval. effect of the drift, also when the mean value of this effect is
5) + In what has been said, skew and drift have been considered as zero at the end of the measurement. The value of this distortion
reciprocal". In Appendix A it will be considered that each of the is limited to the effect of the total skew variation on the
emission interval.
+ In what has been said, skew and drift have been considered as
"reciprocal". In Appendix A it will be considered that each of the
two clocks have a skew and a drift with respect a "true time", and two clocks have a skew and a drift with respect a "true time", and
it will be observed that the difference is negligible with respect it will be observed that the difference is negligible with respect
the situation in which one of the two clocks is taken as the "true the situation in which one of the two clocks is taken as the "true
time". time".
I-D Ipdv Metric November 1998
8. Definition for a bidirectional ipdv metric 8. Definition for a bidirectional ipdv metric
We now consider that the action of the skew on one direction is the 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 same, with opposite sign, of the action on the other direction. The
idea of performing at the same time two independent measurements in idea of performing at the same time two independent measurements in
the two directions is suggested by this fact. the two directions is suggested by this fact.
If, after a long measurement, the variable conditions of the system If, after a long measurement, the variable conditions of the system
under test have reached the situation of a contribution close to zero 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 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. the action of the average skew has modified the measured mean value.
It is therefore expected that on one direction that value is equal and It is therefore expected that on one direction that value is equal
opposite to the one measured in the other direction. and opposite to the one measured in the other direction.
This fact offers the possibility of defining a theoretical reference This fact offers the possibility of defining a theoretical reference
measurement duration in the following way: measurement duration in the following way:
The reference duration of a bidirectional ipdv measurement between The reference duration of a bidirectional ipdv measurement between an
an host E and an host W is reached at time Tf such that for each time host E and an host W is reached at time Tf such that for each time T
T > Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where > 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 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 one, but not the only method for verifying that the mean ipdv value
has reached the value of the average reciprocal skew. has reached the value of the average reciprocal skew.
At this point it is possible to evaluate the reciprocal skew. At this point it is possible to evaluate the reciprocal skew. This
This will require the knowledge of the mean value of the intervals will require the knowledge of the mean value of the intervals between
between consecutive packets, that can be calculated over the trans- consecutive packets, that can be calculated over the transmitted
-mitted stream, by using the collected time stamps. stream, by using the collected time stamps.
A bidirectional measurement can be defined not only as twin one-way A bidirectional measurement can be defined not only as twin one-way
independent metrics that take place (nearly) at the same time, but independent metrics that take place (nearly) at the same time, but
also as a two-ways metric making use of packets looped back at one also as a two-way metric making use of packets looped back at one
end. This metric, that can be object of further study/Draft, would be end. This metric, that can be object of further study/Draft, would be
able to measure also the Round Trip Delay and its variations. Problems able to measure also the Round Trip Delay and its variations.
will anyway arise on the characterization of emission intervals in the Problems will anyway arise on the characterization of emission
backward direction. They would be produced by the combination of the intervals in the backward direction. They would be produced by the
original Poisson arrival process and the effect of ipdv on the forward combination of the original Poisson arrival process and the effect of
direction. It has to be studied if this sequence of intervals is still ipdv on the forward direction. It has to be studied if this sequence
suitable for the measurement. also other possibilities can be of intervals is still suitable for the measurement. also other
envisaged for obtaining a proper backward sequence and still maintain possibilities can be envisaged for obtaining a proper backward
the loopback concept. sequence and still maintain the loopback concept.
I-D Ipdv Metric November 1998 9. Relationship to other standards |
9. References 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]. |
V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP Performance 9.1. 1-Point Cell Delay Variation |
Metrics", Internet Draft <draft-ietf-ippm-framework-01.txt> Feb. 1998
G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", Internet The ITU looks at cell delay variation from two different points of |
Draft <draft-ietf-ippm-delay-01.txt> Nov. 1997 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. |
10. Author's Address 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. |
9.3. Discussion |
9.3.1. Differences |
Demichelis [4] points out a number of problems with the 2-point PDV |
definition in [3]. First of all is the issue of choosing the |
reference delay time. If this is chosen arbitrarily, it becomes |
uncertain how to compare the measurements taken from two non- |
overlapping periods. If it is chosen as an average, that can also be |
a problem, because over long periods of time in a network, the |
average one-way delay can vary widely. A twenty-four hour average as |
the reference time can seriously overestimate the actual delay |
variation at a given time of day because the night-time hours, when |
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 |
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 |
The ipdv metric described here and the 1-point cell delay variation |
metric described in [5] do not really have much in common (see also |
[4]). 1-point delay variation is really intended to talk about the |
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 |
[3]) is related to ipdv, and this relationship can be made precise as |
follows: Suppose that an arbitrarily chosen packet is designated as |
the reference packet for the 2-point measurement and also as the |
start packet of the ipdv measurement. Denote this packet by p(0). |
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 |
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 |
As described above, there are a number of disadvantages of the |
2-point packet delay variation approach. Further, the ipdv approach |
described here is general enough to provide the same information as |
the 2-point packet delay variation measurements. Because of this, and |
because of the (possibly) looser clock synchronization requirements |
of ipdv, we recommend the one-way-ipdv approach for the delay |
variation measurement. |
10. Security Considerations |
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 |
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 |
many measurement packets into the network; there could also be |
attempts to disrupt measurements by diverting packets or corrupting |
them. |
In general, legitimate measurements must have their parameters |
selected carefully in order to avoid interfering with normal traffic |
in the network. Such measurements should also be authorized and |
authenticated in some way so that attacks can be identified and |
intercepted. |
11. Acknowledgements |
Thanks to Matt Zekauskas from Advanced and Ruediger Geib from |
Deutsche Telekom for discussions relating to the contents of this |
revised draft. |
12. References |
[1] V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP |
Performance Metrics", RFC 2330 Feb. 1998 |
[2] G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", |
Internet Draft <draft-ietf-ippm-delay-07.txt> May 1999 |
[3] Draft New ITU-T Recommendation I.380 "Internet Protocol Data |
Communication Service - IP Packet Transfer and Availability |
Performance Parameters" |
[4] Demichelis, Carlo - "Packet Delay Variation Comparison between |
ITU-T and IETF Draft Definitions" March 1999 |
[5] ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer |
Performance" |
[6] e-mail exchanges with Ruediger Geib |
[7] V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding |
PHB", Internet Draft, November 1998 <draft-ietf-diffserv-phb- |
ef-01.txt> |
13. 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
I-D Ipdv Metric November 1998 Philip Chimento <chimento@ctit.utwente.nl>
CTIT - Centre for Telematics and Information Technology
University of Twente
Postbox 217
7500 AE Enschede
The Netherlands
Phone +31 53 489 4331
FAX +31 53 489 4524
APPENDIX A APPENDIX A
This Appendix considers the scenario in which two hosts have clocks This Appendix considers the scenario in which two hosts have clocks
that are both not synchronized. Between the two hosts, in an inde- that are both not synchronized. Between the two hosts, in an
-pendent way and at the same time in both direction an ipdv measure- independent way and at the same time in both direction an ipdv
-ment is performed according the methodology that is described in the measurement is performed according the methodology that is described
main body of this Draft. in the main body of this Draft. This hypothetical scenario is only
This hypothetical scenario is only supposed for discussing the theory supposed for discussing the theory and the characteristics of the
and the characteristics of the ipdv metric and its results, without ipdv metric and its results, without considering implementation
considering implementation issues. issues.
A.1 - Initial positions 14. Initial positions
The two hosts will be called West (W) and East (E). The two measure- The two hosts will be called West (W) and East (E). The two
-ments start at the same time, while the end of the measurement it is measurements start at the same time, while the end of the measurement
supposed to be decided by the results of the measurement itself. it is supposed to be decided by the results of the measurement
itself.
At the beginning of the measurement the time declared by the West At the beginning of the measurement the time declared by the West
clock is T0w, the time declared by the East clock is T0e, while the clock is T0w, the time declared by the East clock is T0e, while the
true time is T0t. true time is T0t.
The W-clock is affected by an absolute skew of skw ppm and the E-clock The W-clock is affected by an absolute skew of skw ppm and the E-
by an absolute skew of skw ppm. clock by an absolute skew of skw ppm.
The W-clock is affected by an absolute drift ranging from -drw ppm to The W-clock is affected by an absolute drift ranging from -drw ppm to
+drw ppm, the E-clock by an absolute drift ranging from -dre ppm to +drw ppm, the E-clock by an absolute drift ranging from -dre ppm to
+dre ppm. +dre ppm.
A.2 - Evaluation of skew and drift effects 14.1. Evaluation of skew and drift effects
In order to evaluate the effect of the drift on this type of metric, In order to evaluate the effect of the drift on this type of metric,
it is necessary to consider the time in which the variation of the skew it is necessary to consider the time in which the variation of the
takes place. We consider the two extreme cases in which the variation skew takes place. We consider the two extreme cases in which the
takes place uniformly from the beginning to the end of the measurement variation takes place uniformly from the beginning to the end of the
and the variation takes place suddenly at a generic time along the measurement and the variation takes place suddenly at a generic time
measurement. Let TM be the measurement time. along the measurement. Let TM be the measurement time.
A.2.1 - Mean ipdv value 14.1.1. Mean ipdv value
Since the mean ipdv value, as it has been seen, is the difference of Since the mean ipdv value, as it has been seen, is the difference of
the last delay minus the first, divided by the number of considered the last delay minus the first, divided by the number of considered
values, we consider what, in the two cases, is measured for first and values, we consider what, in the two cases, is measured for first and
last delay. last delay.
We call trueDf the true first Delay and trueDl the true last Delay. We call trueDf the true first Delay and trueDl the true last Delay.
For the evaluation that we want to do, it is not a limitation to
consider that they are equal and have a value of trueD. We also
consider as time 0 the true time at which the transmission of the
first packet starts from West toward East.
I-D Ipdv Metric November 1998 In case of continuous drift we define a "drift per second" as: drpsW
= 2*drw / TM and drpsE = 2*dre / TM along the measurement this
For the evaluation that we want to do, it is not a limitation to con- will bring the skew from a value of: skWmin = skw - drw ;
-sider that they are equal and have a value of trueD. We also consider skEmin = ske - dre to a value of skWmax = skw + drw ; skEmax =
as time 0 the true time at which the transmission of the first packet ske + dre
starts from West toward East.
In case of continuous drift we define a "drift per second" as:
drpsW = 2*drw / TM and drpsE = 2*dre / TM
along the measurement this will bring the skew from a value of:
skWmin = skw - drw ; skEmin = ske - dre
to a value of
skWmax = skw + drw ; skEmax = ske + dre
What is measured as first Delay is: What is measured as first Delay is:
measured first Rx time - measured first Tx time measured first Rx time - measured first Tx time OffsetEast + trueD*[1
OffsetEast + trueD*[1 + skEmin + (1/2)*drpsE] - OffsetWest + skEmin + (1/2)*drpsE] - OffsetWest
What is measured as last Delay is: What is measured as last Delay is:
measured last Rx time - measured last Tx time measured last Rx time - measured last Tx time OffsetEast + (TM +
OffsetEast + (TM + trueD)*[1 + skEmin + (1/2)*2*dre] - trueD)*[1 + skEmin + (1/2)*2*dre] -
- OffsetWest - TM*[1 + skWmin + (1/2)*2*drw] - OffsetWest - TM*[1 + skWmin + (1/2)*2*drw]
The difference between the last and first Delay is therefore: The difference between the last and first Delay is therefore:
TM*(skEmin - skWmin + dre - drw) - trueD*drpsE/(2*TM) TM*(skEmin - skWmin + dre - drw) - trueD*drpsE/(2*TM)
if TM = 10 hours drpsE is in the order of 50*10E-6 / 36000 that is if TM = 10 hours drpsE is in the order of 50*10E-6 / 36000 that is
about 10E-9 and the second term of the expression is in the order of about 10E-9 and the second term of the expression is in the order of
10E-14 for true delays in the order of 1 sec (negligible term). 10E-14 for true delays in the order of 1 sec (negligible term). We
We consider that, with very good approximation: consider that, with very good approximation:
Mean emission interval (mti) = TM / number of ipdv values (N) Mean emission interval (mti) = TM / number of ipdv values (N)
Therefore: Therefore:
mean ipdv = (measured last Delay - measured first Delay) / N = mean ipdv = (measured last Delay - measured first Delay) / N =
= mti*(skEmin - skWmin + dre - drw) = mti*(skEmin - skWmin + dre - drw)
but we considered skEmin = ske - dre and skWmin = skw - drw but we considered skEmin = ske - dre and skWmin = skw - drw and
and therefore: therefore:
mean ipdv = (meas.lastD - meas.firstD) / mti*(reciprocal mean skew) mean ipdv = (meas.lastD - meas.firstD) / mti*(reciprocal mean skew)
The previous procedure is now applied to the case in which the total The previous procedure is now applied to the case in which the total
drift takes place in a very short time. Some cases are possible, and drift takes place in a very short time. Some cases are possible, and
we consider the one in which at the beginning the West clock has we consider the one in which at the beginning the West clock has
skWmax and the East clock has skEmin, at time txW the West clock skWmax and the East clock has skEmin, at time txW the West clock
assumes skWmin and at time txE the East clock assumes skEmax. assumes skWmin and at time txE the East clock assumes skEmax. What
is measured as first Delay is now:
I-D Ipdv Metric November 1998
What is measured as first Delay is now:
measured first Rx time - measured first Tx time measured first Rx time - measured first Tx time OffsetEast + trueD*(1
OffsetEast + trueD*(1 + skEmin) - OffsetWest + skEmin) - OffsetWest
What is measured as last Delay is: What is measured as last Delay is:
measured last Rx time - measured last Tx time measured last Rx time - measured last Tx time + OffsetEast + txE*(1 +
+ OffsetEast + txE*(1 + skEmin) + (TM - txE)*(1 + skEmax) + skEmin) + (TM - txE)*(1 + skEmax) + + trueD*(1 + skEmax) - -
+ trueD*(1 + skEmax) - OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin)
- OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin)
but the mean skew values will be: but the mean skew values will be:
mskw = [skWmax*txW + skWmin*(TM - txW)] / TM mskw = [skWmax*txW + skWmin*(TM - txW)] / TM mske = [skEmin*txE +
mske = [skEmin*txE + skEmax*(TM - txE)] / TM skEmax*(TM - txE)] / TM
the difference between the two delays therefore is: the difference between the two delays therefore is:
TM*(mske - mskw) + 2*trueD*dre TM*(mske - mskw) + 2*trueD*dre
and the mean ipdv value will be: and the mean ipdv value will be:
mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM
the second term of the second member in the previous hypotheses is in the second term of the second member in the previous hypotheses is in
the order of the nanosecond, and we neglect it. Also in this case, from the order of the nanosecond, and we neglect it. Also in this case,
the mean ipdv value, and knowing the mean emission interval, the rela- from the mean ipdv value, and knowing the mean emission interval, the
-tive skew of the clocks can be obtained. relative skew of the clocks can be obtained.
More in general, independently on how the drift acts inside its limits, More in general, independently on how the drift acts inside its
we assert that always the mean ipdv value divided by the mean emission limits, we assert that always the mean ipdv value divided by the mean
interval produces the value of the mean reciprocal skew of the two emission interval produces the value of the mean reciprocal skew of
clocks, provided that the collected number of ipdv values is signi- the two clocks, provided that the collected number of ipdv values is
-ficant for the statistics. significant for the statistics.
A.2.2 - Errors and corrections 14.1.2. Errors and corrections
If the drift is always close to zero, it is possible to obtain the If the drift is always close to zero, it is possible to obtain the
true value of the reciprocal skew and correct all the ipdv values. Each true value of the reciprocal skew and correct all the ipdv values.
of them is associated to an emission interval ti between the two Each of them is associated to an emission interval ti between the two
packets that have produced the value itself. Then a better ipdv value packets that have produced the value itself. Then a better ipdv value
will be: will be: corr.ipdv(i) = meas.ipdv(i) - ti * skew This is a better
corr.ipdv(i) = meas.ipdv(i) - ti * skew value but not exactly the true one, since we supposed that both
This is a better value but not exactly the true one, since we supposed clocks are not synchronized to the true time. Two errors are
that both clocks are not synchronized to the true time. Two errors are
affecting the corrective terms which are: affecting the corrective terms which are:
I-D Ipdv Metric November 1998
+ The reciprocal skew is measured as referred to the Src clock + The reciprocal skew is measured as referred to the Src clock
+ The interval ti is measured by the Src clock. + The interval ti is measured by the Src clock.
These are second order errors since the measured skew will be affected
by a "relative" error in the order of the Src skew, an the same is These are second order errors since the measured skew will be
for the error affecting the ti value. affected by a "relative" error in the order of the Src skew, an the
same is for the error affecting the ti value.
If the drift is significant and it can range from the lower to the If the drift is significant and it can range from the lower to the
upper limit of its field, the measured average of the skew will depend upper limit of its field, the measured average of the skew will
on the type of variation. Some cases are considered that demonstrate depend on the type of variation. Some cases are considered that
that actually the proposed correction is not so much effective in this demonstrate that actually the proposed correction is not so much
case. Only the fixed part of the total clock variation can be properly effective in this case. Only the fixed part of the total clock
corrected. variation can be properly corrected.
A.2.2.1 - Constant drift 14.1.3. Constant drift
The first case is the first one considered in the preceding paragraph, The first case is the first one considered in the preceding
where the drift is uniform. We suppose that a reciprocal skew is measu- paragraph, where the drift is uniform. We suppose that a reciprocal
-red and used for correction. skew is measured and used for correction.
At the beginning of the measurement the actual reciprocal skew is: At the beginning of the measurement the actual reciprocal skew is:
init.skew = mean.skew - rel.max.drift init.skew = mean.skew - rel.max.drift
and at the end the actual reciprocal skew is: and at the end the actual reciprocal skew is:
final.skew = mean.skew + rel max.drift final.skew = mean.skew + rel max.drift
The correction is effective only in the central part of the measurement. The correction is effective only in the central part of the
At the beginning and at the end a residual error will affect the ipdv measurement. At the beginning and at the end a residual error will
values whose value will be: affect the ipdv values whose value will be:
ipdv(i).err = ti * rel.max.drift ipdv(i).err = ti * rel.max.drift
We underline here that the error is larger for large intervals ti and We underline here that the error is larger for large intervals ti and
lower for short intervals ti. For intervals derived from a poissonian lower for short intervals ti. For intervals derived from a poissonian
arrival process, there are many short intervals and few large intervals. arrival process, there are many short intervals and few large
We also note that a constant drift cannot last indefinitely, since there intervals. We also note that a constant drift cannot last
is a minimum and a maximum for the skew. indefinitely, since there is a minimum and a maximum for the skew.
A.2.2.2 - Step of drift 14.1.4. Step of drift
In this case the error profile depends on the time at which the drift In this case the error profile depends on the time at which the drift
changes. If the change is near the beginning or near the end of the changes. If the change is near the beginning or near the end of the
measurement, the calculated mean skew will be very close to the actual measurement, the calculated mean skew will be very close to the
skew of the largest part of the measurement. On that part the correc- actual skew of the largest part of the measurement. On that part the
-tion will be effective, while over the remaining few values the error correction will be effective, while over the remaining few values the
will be twice with respect the preceding case. error will be twice with respect the preceding case. The worse
condition is produced by a change in drift in the middle of the
I-D Ipdv Metric November 1998 measurement. In this case the correction would be useful only if the
drift was significantly less than the skew.
The worse condition is produced by a change in drift in the middle of
the measurement. In this case the correction would be useful only if
the drift was significantly less than the skew.
A.3 - Comparison with a synchronized case 14.2. Comparison with a synchronized case
In this section we consider a case in which the two hosts have synchro- In this section we consider a case in which the two hosts have
-nized clocks, and the synchronization is obtained by setting the real synchronized clocks, and the synchronization is obtained by setting
time each second in each of the clocks. We optimistically suppose that the real time each second in each of the clocks. We optimistically
this is done exactly (without any imprecision). On the clocks, anyway suppose that this is done exactly (without any imprecision). On the
skew and drift continue to act. We refer to reciprocal skew and drift, clocks, anyway skew and drift continue to act. We refer to reciprocal
having already seen that this is significant. We suppose to perform an skew and drift, having already seen that this is significant. We
ipdv measurement and we evaluate what is measured by the mean ipdv suppose to perform an ipdv measurement and we evaluate what is
value and what is the error on the measured ipdv values. measured by the mean ipdv value and what is the error on the measured
ipdv values.
We notice, first of all, that nothing changes for ipdv values measured We notice, first of all, that nothing changes for ipdv values
over intervals falling completely between two synchronization instants. measured over intervals falling completely between two
In this case, the effect of synchronization is only to put to zero the synchronization instants. In this case, the effect of
offset, that does not appear in the calculation of ipdv values. synchronization is only to put to zero the offset, that does not
appear in the calculation of ipdv values.
Something different happens if the synchronization instant (or more Something different happens if the synchronization instant (or more
synchronization instants) falls inside the interval. In this case the synchronization instants) falls inside the interval. In this case the
error can range from + to - the error related to one second interval, error can range from + to - the error related to one second interval,
or, more in general, from + to - the error related to an interval equal or, more in general, from + to - the error related to an interval
to the synchronization period. The (few) large intervals will produce equal to the synchronization period. The (few) large intervals will
a limited error while the (many) short intervals will continue to produce a limited error while the (many) short intervals will
produce errors of the same order of magnitude of the not synchronized continue to produce errors of the same order of magnitude of the not
case. synchronized case.
Besides, even if the drift is negligible, the mean ipdv value is no Besides, even if the drift is negligible, the mean ipdv value is no
more suitable to calculate the skew, and it will be much more close to more suitable to calculate the skew, and it will be much more close
zero. Therefore it is no more possible to correct the distortion of the to zero. Therefore it is no more possible to correct the distortion
distribution. of the distribution.
Finally, it is necessary to add to these errors the unavoidable impre- Finally, it is necessary to add to these errors the unavoidable
cision of the synchronization process. We have to consider that the imprecision of the synchronization process. We have to consider that
magnitude of errors introduced by skew and drift is in the order of the magnitude of errors introduced by skew and drift is in the order
tenth of microseconds. Not always the complete synchronization process of tenth of microseconds. Not always the complete synchronization
has a better precision. process has a better precision.
A.4 - Bidirectional measurement and components of ipdv 14.3. Bidirectional measurement and components of ipdv
Three terms have been described that can displace the mean ipdv value Three terms have been described that can displace the mean ipdv value
from zero. They are: from zero. They are:
I-D Ipdv Metric November 1998 + The total skew, already discussed above, that always acts in an
equal way and opposite direction over the two directions between
West and East hosts.
- The total skew, already discussed above, that always acts in an equal + The effect of varying traffic that can increase or decrease along
way and opposite direction over the two directions between West and limited periods, the average value of the One-Way-Delay. The
East hosts. metric above presented supposes that the measurement period is
- The effect of varying traffic that can increase or decrease along large enough for considering this effect as tending to zero. It
limited periods, the average value of the One-Way-Delay. The metric is explicitly noted that the effect will produce a zero effect
above presented supposes that the measurement period is large enough
for considering this effect as tending to zero.
It is explicitly noted that the effect will produce a zero effect
only on the mean ipdv value, while the effect on values ipdv(i) is only on the mean ipdv value, while the effect on values ipdv(i) is
always present. This is not a distortion of the distribution, since always present. This is not a distortion of the distribution,
is part of the variation that is measured. This effect is different, since is part of the variation that is measured. This effect is
and usually concordant, on the two directions. different, and usually concordant, on the two directions.
- The difference between first and last instantaneous values of the
+ The difference between first and last instantaneous values of the
delay variation, that tends to zero when the number of collected delay variation, that tends to zero when the number of collected
ipdv values becomes large. ipdv values becomes large.
In order to isolate the last two effects, we consider here a measurement In order to isolate the last two effects, we consider here a
over a long period (e.g. 24 hours)where the drift is negligible, and measurement over a long period (e.g. 24 hours)where the drift is
the effect of the skew has been corrected. negligible, and the effect of the skew has been corrected.
A.4.1 - Slow variation in a given period 14.4. Slow variation in a given period
The packets of the stream can be represented on a system of cartesian The packets of the stream can be represented on a system of cartesian
orthogonal axes with transmission time on x-axis and reception time on orthogonal axes with transmission time on x-axis and reception time
y-axis, by points localized by transmission and reception time of each on y-axis, by points localized by transmission and reception time of
packet. Considering an arbitrary period of time Tper, which will be a each packet. Considering an arbitrary period of time Tper, which will
parameter of this procedure, it can be taken as a sliding window over be a parameter of this procedure, it can be taken as a sliding window
the sample and for each position of this window, established by suc- over the sample and for each position of this window, established by
-cessive packets, the segment of straight line is calculated that best successive packets, the segment of straight line is calculated that
approximate the points, by means of a linear regression method. best approximate the points, by means of a linear regression method.
The slope of this segment will be one if along the period the delay The slope of this segment will be one if along the period the delay
has not changed, and different from one if that delay has increased (>1) has not changed, and different from one if that delay has increased
or decreased (<1). For each position of the window it is therefore (>1) or decreased (<1). For each position of the window it is
possible to find a value of "slow delay variation" with Tper as a therefore possible to find a value of "slow delay variation" with
parameter. This will give an indication on variations produced by Tper as a parameter. This will give an indication on variations
different traffic conditions along the measurement period. This item produced by different traffic conditions along the measurement
can be subject for further study. period. This item can be subject for further study.
At the same time this procedure offers a criterion for reducing the At the same time this procedure offers a criterion for reducing the
error introduced in the calculation of the mean ipdv by the instanta- error introduced in the calculation of the mean ipdv by the
-neous component of the difference between last and first delay. instantaneous component of the difference between last and first
Supposing that the timestamps, on which the metric is based, are delay. Supposing that the timestamps, on which the metric is based,
collected and then processed, if the method of the sliding window is are collected and then processed, if the method of the sliding window
applied at the beginning and at the end of the collected sample, it is applied at the beginning and at the end of the collected sample,
is possible to avoid starting and ending the measurement on values it is possible to avoid starting and ending the measurement on values
possibly too different from the average (points too far away from the possibly too different from the average (points too far away from the
calculated straight line). calculated straight line). |
I-D Ipdv Metric November 1998
A.5 - Symmetry of an ipdv distribution and emission intervals
It is demonstrated that, if the packets of the test sequence are pro-
pagated in an independent way, in the sense that none of them is
influenced by the preceding packets (large emission intervals), the ipdv
distribution will be perfectly symmetrical. If the variation of the
delay is such that some packets is delayed by the preceding one (ideal-
-ly queued to it in a buffer), the related ipdv value generated will
have a lower limit, that will be the negative value of the emission
interval minus the time required for transmitting the packet from the
buffer. If the intervals were constant, this would correspond to a well
defined value, that would allow to measure the bandwidth of the bottle-
-neck provided by the output of that buffer. Since the intervals are
derived from a poissonian arrival process, this limit is not a fixed
one, and is not immediately evident of the ipdv distribution.
Another effect of this interference among packets is that also the
packet following the queued one will produce a lower ipdv value since
it will "gain" the time of latency in the buffer of the previous one.
The total effect is that the ipdv values will tend to concentrate on
the negative side of the distribution, with some limitation on the
negative maximum values. In other words, the negative side of the
distribution will be shorter than the positive one, but containing more
values. Nothing changes for the meaning of the mean ipdv value.
This asymmetry is not a distortion, since represents the actual propa-
-gation characteristics. For the supposed type of intervals, the dis-
-tribution is always asymmetrical, since always are present intervals
lower than the delay variability, and the degree of asymmetry will
change with the level of interference.
The relationship between asymmetry and the combination of average emis- Expiration date: December, 1999
-sion interval and available bandwidth can be investigated and could
provide information about the level of congestion of the network
 End of changes. 

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