draft-ietf-ippm-ipdv-03.txt | draft-ietf-ippm-ipdv-04.txt | |||
---|---|---|---|---|

Network Working Group C. Demichelis | Network Working Group C. Demichelis | |||

INTERNET-DRAFT CSELT | INTERNET-DRAFT CSELT | |||

Expiration Date: December 1999 P. Chimento | Expiration Date: December 1999 P. Chimento | |||

CTIT | CTIT | |||

June 1999 | October 1999 | |||

Instantaneous Packet Delay Variation Metric for IPPM | Instantaneous Packet Delay Variation Metric for IPPM | |||

<draft-ietf-ippm-ipdv-03.txt> | <draft-ietf-ippm-ipdv-04.txt> | |||

1. Status of this Memo | 1. Status of this Memo | |||

This document is an Internet-Draft and is in full conformance with | | This document is an Internet-Draft and is in full conformance with | | |||

all provisions of Section 10 of RFC2026. | all provisions of Section 10 of RFC2026. | |||

Internet-Drafts are working documents of the Internet Engineering | Internet-Drafts are working documents of the Internet Engineering | |||

Task Force (IETF), its areas, and its working groups. Note that | Task Force (IETF), its areas, and its working groups. Note that | |||

other groups may also distribute working documents as Internet- | other groups may also distribute working documents as Internet- | |||

Drafts. | Drafts. | |||

skipping to change at page 2, line 10 | skipping to change at page 2, line 10 | |||

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-way | 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. | |||

3. Introduction | 3. Introduction | |||

This memo takes as a reference the Draft-ietf "One-Way-Delay metric | | This memo is based on "A One-Way-Delay metric for IPPM", RFC 2679 | | |||

for IPPM" [1]. Part of the text in this memo is directly taken from | [2]. Part of the text in this memo is taken directly from that | |||

that Draft. | document. | |||

This memo defines a metric for variation in delay of packets that | ||||

flow from one host to another one through an IP path. Since the | ||||

metric is related to a variation, different definitions are possible | ||||

according to what the variation is measured against. | ||||

This memo defines a metric for variation in delay of packets that > | ||||

flow from one host to another one through an IP path. This quantity > | ||||

is sometimes called "jitter". This term, however, causes confusion > | ||||

because it is used in different ways by different groups of people. | | ||||

"Jitter" commonly has two meanings: The first meaning is the | | "Jitter" commonly has two meanings: The first meaning is the | | |||

variation of a signal with respect to some clock signal, where the | | variation of a signal with respect to some clock signal, where the | | |||

arrival time of the signal is expected to coincide with the arrival | | arrival time of the signal is expected to coincide with the arrival | | |||

of the clock signal. The second meaning has to do with the variation | | of the clock signal. The second meaning has to do with the variation | | |||

of a metric (e.g. delay) with respect to some reference metric (e.g. | | of a metric (e.g. delay) with respect to some reference metric (e.g. | | |||

average delay or minimum delay). The form of "jitter" that we talk | | average delay or minimum delay). The form of "jitter" that we talk | | |||

about here has to do almost exclusively with the second meaning, | | about here has to do almost exclusively with the second meaning, | | |||

rather than the first. See the section on the relationship with other | | rather than the first. For more information see the section on the | | |||

standards. | relationship with other standards. | |||

3.1. Definition | 3.1. Definition | |||

A definition of the Instantaneous Packet Delay Variation (ipdv) can | A definition of the Instantaneous Packet Delay Variation (ipdv) can | |||

be given for a pair of packets or for a packet inside a stream of | be given for a pair of packets or for a packet inside a stream of | |||

packets. | packets. | |||

For a pair of packets: | For a pair of packets: | |||

+ The ipdv of a pair of IP packets, that are transmitted from the | + The ipdv of a pair of IP packets, that are transmitted from the | |||

skipping to change at page 3, line 32 | skipping to change at page 3, line 31 | |||

measurement and corrections are possible. The related precision is | measurement and corrections are possible. The related precision is | |||

often comparable with the one that can be achieved with synchronized | often comparable with the one that can be achieved with synchronized | |||

clocks, being of the same order of magnitude of synchronization | clocks, being of the same order of magnitude of synchronization | |||

errors. This will be discussed below. | errors. This will be discussed below. | |||

3.3. General Issues Regarding Time | 3.3. General Issues Regarding Time | |||

Everything contained in the Section 2.2. of [2] applies also in this | | Everything contained in the Section 2.2. of [2] applies also in this | | |||

case. | case. | |||

In addition, we assume here that the reciprocal skew of the two | To summarize: As in [1] we define "skew" as the first derivative of > | |||

clocks can be decomposed into two parts: | the offset of a clock with respect to "true time" and define "drift" > | |||

as the second derivative of the offset of a clock with respect to > | ||||

"true time". > | ||||

+ A fixed one, called in this context "skew", given, for example, by | From there, we can construct "relative skew" and "relative drift" for > | |||

tolerances in physical dimensions of crystals. | two clocks C1 and C2 with respect to one another. These are natural > | |||

extensions of the basic framework definitions of these quantities: > | ||||

+ A variable one, called in this context "drift", given, for | + Relative offset = difference in clock times > | |||

example, by changes in temperature or other conditions of | ||||

operation. Both of these components are part of the term "skew" as | + Relative skew = first derivative of the difference in clock times > | |||

defined in the referenced Draft and in the Framework document. | ||||

+ Relative drift = second derivative of the difference in clock > | ||||

times > | ||||

NOTE: The drift of a clock, as it is above defined over a long period | NOTE: The drift of a clock, as it is above defined over a long period | |||

must have an average value that tends to zero while the period | must have an average value that tends to zero while the period | |||

becomes large since the frequency of the clock has a finite (and | becomes large since the frequency of the clock has a finite (and | |||

small) range. In order to underline the order of magnitude of this | small) range. In order to underline the order of magnitude of this | |||

effect,it is considered that the maximum range of drift for | effect,it is considered that the maximum range of drift for | |||

commercial crystals is about 50 part per million (ppm). Since it is | commercial crystals is about 50 part per million (ppm). Since it is | |||

mainly connected with variations in operating temperature (from 0 to | mainly connected with variations in operating temperature (from 0 to | |||

70 degrees Celsius), it is expected that a host will have a nearly | 70 degrees Celsius), it is expected that a host will have a nearly | |||

constant temperature during its operation period, and variations in | constant temperature during its operation period, and variations in | |||

skipping to change at page 4, line 26 | skipping to change at page 4, line 27 | |||

flow from a source host to a destination host (one-way ipdv). The | flow from a source host to a destination host (one-way ipdv). The | |||

initial assumption is that source and destination hosts have | initial assumption is that source and destination hosts have | |||

synchronized clocks. The definition of a singleton of one-way ipdv | synchronized clocks. The definition of a singleton of one-way ipdv | |||

metric is first considered, and then a definition of samples for ipdv | metric is first considered, and then a definition of samples for ipdv | |||

will be given. | will be given. | |||

Then the case of application to non-synchronized hosts will be | Then the case of application to non-synchronized hosts will be | |||

discussed, and the precision will be compared with the one of | discussed, and the precision will be compared with the one of | |||

synchronized clocks. | synchronized clocks. | |||

A bidirectional ipdv metric will be defined, as well as the | A bidirectional ipdv metric will be defined, as well as the > | |||

methodology for error corrections. This will not be a two-way metric, | methodology for error corrections. This will not be a two-way metric, > | |||

but a "paired" one-way in opposite directions. Some statistics | but a "paired" one-way in opposite directions. | |||

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 metric [2]. This section makes use of those parts of | One-Way-Delay metric [2]. This section makes use of those parts of | |||

the One-Way-Delay Draft that directly apply to the One-Way-ipdv | the One-Way-Delay Draft that directly apply to the One-Way-ipdv | |||

metric, or makes direct references to that Draft. | metric, or makes direct references to that Draft. | |||

5.1. Metric name | 5.1. Metric name | |||

skipping to change at page 5, line 32 | skipping to change at page 5, line 32 | |||

5.3. 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. | |||

5.4. 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 and the value of the type-P-One-Way-Delay | |||

One-Way-Delay from Src to Dst at T1 [via path]. T1 is the wire-time | from Src to Dst at T1. T1 is the wire-time at which Scr sent the | |||

at which Scr sent the first bit of the first packet, and T2 is the | first bit of the first packet, and T2 is the wire-time at which Src | |||

wire-time at which Src sent the first bit of the second packet. This | sent the first bit of the second packet. This metric is therefore | |||

metric is therefore ideally derived from the One-Way-Delay metric. | 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 times | measured value is anyway the difference in One-Way-Delay at the times | |||

T1 and T2, which is meaningful by itself, as long as the times T1 and | | T1 and T2, which is meaningful by itself, as long as the times T1 and | | |||

T2 denote the wire times of the packets sent from Src to Dst. | T2 denote the wire times of the packets sent from Src to Dst. | |||

Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to | Therefore, for a real number ddT "The type-P-one-way-ipdv from Src to | |||

Dst at T1, T2 [via path] is ddT" means that Src sent two consecutive | Dst at T1, T2 is ddT" means that Src sent two consecutive packets, | |||

packets, the first at wire-time T1 (first bit), and the second at | the first at wire-time T1 (first bit), and the second at wire-time T2 | |||

wire-time T2 (first bit) and the packets were received by Dst at | (first bit) and the packets were received by Dst at wire-time dT1+T1 | |||

wire-time dT1+T1 (last bit of the first packet), and at wire-time | (last bit of the first packet), and at wire-time dT2+T2 (last bit of | |||

dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT. | the second packet), and that dT2-dT1=ddT. | |||

"The type-P-one-way-ipdv from Src to Dst at T1,T2 [via path] is | "The type-P-one-way-ipdv from Src to Dst at T1,T2 is undefined" means | |||

undefined" means that Src sent the first bit of a packet at T1 and | that Src sent the first bit of a packet at T1 and the first bit of a | |||

the first bit of a second packet at T2 and that Dst did not receive | second packet at T2 and that Dst did not receive one or both packets. | |||

one or both packets. | ||||

5.5. Discussion | 5.5. Discussion | |||

Type-P-One-way-ipdv is a metric that makes use of the same | Type-P-One-way-ipdv is a metric that makes use of the same | |||

measurement 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 | + Being a differential measurement, this metric is less sensitive to | |||

clock synchronization problems. This issue will be more carefully | clock synchronization problems. This issue will be more carefully | |||

examined in section 7 of this memo. It is pointed out that, if the | examined in section 7 of this memo. It is pointed out that, if the | |||

reciprocal clock conditions change in time, the accuracy of the | relative clock conditions change in time, the accuracy of the | |||

measurement will depend on the time interval T2-T1 and the | measurement will depend on the time interval T2-T1 and the | |||

magnitude of possible errors will be discussed below. | magnitude of possible errors will be discussed below. | |||

+ A given methodology will have to include a way to determine | + A given methodology will have to include a way to determine | |||

whether a delay value is infinite or whether it is merely very | whether a delay value is infinite or whether it is merely very | |||

large (and the packet is yet to arrive at Dst). As noted by | large (and the packet is yet to arrive at Dst). As noted by | |||

Mahdavi and Paxson, simple upper bounds (such as the 255 seconds | Mahdavi and Paxson, simple upper bounds (such as the 255 seconds | |||

theoretical upper bound on the lifetimes of IP packets [Postel: | theoretical upper bound on the lifetimes of IP packets [Postel: | |||

RFC 791]) could be used, but good engineering, including an | RFC 791]) could be used, but good engineering, including an | |||

understanding of packet lifetimes, will be needed in practice. | understanding of packet lifetimes, will be needed in practice. | |||

skipping to change at page 7, line 26 | skipping to change at page 7, line 26 | |||

+ 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' portion | test packets of Type-P with these addresses. Any 'padding' portion | |||

of the packet needed only to make the test packet a given size | of the packet needed only to make the test packet a given size | |||

should be filled with randomized bits to avoid a situation in | should be filled with randomized bits to avoid a situation in | |||

which the measured delay is lower than it would otherwise be due | which the measured delay is lower than it would otherwise be due | |||

to compression techniques along the path. | to compression techniques along the path. | |||

+ At the Dst host, arrange to receive the packets. | + At the Dst host, arrange to receive the packets. | |||

+ At the Src host, place a timestamp in the first Type-P packet, | + At the Src host, place a timestamp in the first Type-P packet, | |||

and send it towards Dst [via path]. | and send it towards Dst. | |||

+ If the packet arrives within a reasonable period of time, take a | + If the packet arrives within a reasonable period of time, take a | |||

timestamp as soon as possible upon the receipt of the packet. By | timestamp as soon as possible upon the receipt of the packet. By | |||

subtracting the two timestamps, an estimate of One-Way-Delay can | subtracting the two timestamps, an estimate of One-Way-Delay can | |||

be computed. | be computed. | |||

+ Record this first delay value. | + Record this first delay value. | |||

+ At the Src host, place a timestamp in the second Type-P packet, | + At the Src host, place a timestamp in the second Type-P packet, | |||

and send it towards Dst [via path]. | and send it towards Dst. | |||

+ If the packet arrives within a reasonable period of time, take a | + If the packet arrives within a reasonable period of time, take a | |||

timestamp as soon as possible upon the receipt of the packet. By | timestamp as soon as possible upon the receipt of the packet. By | |||

subtracting the two timestamps, an estimate of One-Way-Delay can | subtracting the two timestamps, an estimate of One-Way-Delay can | |||

be computed. | be computed. | |||

+ By subtracting the second value of One-Way-Delay from the first | + By subtracting the second value of One-Way-Delay from the first | |||

value the ipdv value of the pair of packets is obtained. | 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 | |||

skipping to change at page 8, line 38 | skipping to change at page 8, line 38 | |||

ipdv. The residual error related to clocks is the difference of the | ipdv. The residual error related to clocks is the difference of the | |||

errors that are supposed to change from the time T1, at which the | errors that are supposed to change from the time T1, at which the | |||

first measurement is performed, to the time T2 at which the second | first measurement is performed, to the time T2 at which the second | |||

measure ment is performed. Synchronization, skew, accuracy and | measure ment is performed. Synchronization, skew, accuracy and | |||

resolution are here considered with the following notes: | 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 | + The effect of drift and skew errors on ipdv measurements can be > | |||

measurement is Tsync, and it is a linear function of time, through | quantified as follows: Suppose that the skew and drift functions > | |||

the skew value "sk", at time T1 the error will be Tsync1 and at | are known. Assume first that the skew function is linear in time. > | |||

time T2 the error will be Tsync2. The ipdv measurement will be | Clock offset if then also a function of time and the error evolves > | |||

affected by the error: Tsync2-Tsync1 = sk x (T2 - T1) depending on | as e(t) = K*t + O, where K is a constant and O is the offset at > | |||

skew and T2-T1. To minimize this error it is possible to reduce | time 0. In this case, the error added to the subtraction two > | |||

the time interval T2-T1, but this could limit the generality of | different time stamps (t2 > t1) is e(t2)-e(t1) = K*(t2 - t1) which > | |||

the metric. Methods for evaluating the synchronization error will | will be added to the time difference (t2 - t1). If the drift > | |||

be discussed below, since they come from a statistic over a | cannot be ignored, but we assume that the drift is a linear > | |||

significant sample. If the measurement conditions do not allow | function of time, then the skew is given by s(t) = M*(t**2) + N*t > | |||

neglecting the drift, assumed linear in the interval T2-T1, and | + S0, where M and N are constants and S0 is the skew at time 0. > | |||

having a value of "dr" expressed in ppm / sec., the ipdv error | The error added by the variable skew/drift process in this case > | |||

will become: Tsync2-Tsync1 = sk x (T2 - T1) + [dr x (T2-T1) x | becomes e(t) = O + s(t) and the error added to the difference in > | |||

(T2-T1)] / 2 Drift varies the skew value in the time. The limits | time stamps is e(t2)-e(t1) = N*(t2-t1) + M*{(t2-t1)**2}. > | |||

in which the skew can vary are anyway limited and small, so that a | It is the claim here (see remarks in section 3.3) that the effects > | |||

given drift cannot act indefinitely. Section 7 and Appendix A | of skew are rather small over the time scales that we are > | |||

provide more information on this point. | discussing here, since temperature variations in a system tend to > | |||

be slow relative to packet inter-transmission times and the range > | ||||

of drift is so small. | ||||

+ As far as accuracy and resolution are concerned, what is noted in | + As far as accuracy and resolution are concerned, what is noted in | |||

the Draft on One-Way-Delay [2] in section 3.7.1, applies also in | the one-way-delay document [2] in section 3.7.1, applies also in | |||

this case, with the further consideration, about resolution, that | this case, with the further consideration, about resolution, that | |||

in this case the uncertainty introduced is two times the one of a | in this case the uncertainty introduced is two times the one of a | |||

single delay measurement. Errors introduced by these effects are | single delay measurement. Errors introduced by these effects are | |||

often larger than the ones introduced by the drift. | often larger than the ones introduced by the drift. | |||

5.7.2. Errors/uncertainties related to Wire-time vs Host-time | 5.7.2. Errors/uncertainties related to Wire-time vs Host-time | |||

The content of sec. 3.7.2 of [2] applies also in this case, with the | The content of sec. 3.7.2 of [2] applies also in this case, with the | |||

following further consideration: The difference between Host-time and | following further consideration: The difference between Host-time and | |||

Wire-time can be in general decomposed into two components, of which | Wire-time can be in general decomposed into two components, of which | |||

one is constant and the other is variable. Only the variable | one is constant and the other is variable. Only the variable | |||

components will produce measurement errors, while the constant one | components will produce measurement errors, while the constant one | |||

will be canceled while calculating ipdv. | will be canceled while calculating ipdv. However, in most cases, the > | |||

fixed and variable components are not known exactly. | ||||

6. Definitions for Samples of One-way ipdv | 6. Definitions for Samples of One-way ipdv | |||

Starting from the definition of the singleton metric of one-way ipdv, | | Starting from the definition of the singleton metric of one-way ipdv, | | |||

we define a sample of such singletons. In the following, the two | | we define a sample of such singletons. In the following, the two | | |||

packets needed for a singleton measurement will be called a "pair". | | packets needed for a singleton measurement will be called a "pair". | | |||

A stream of test packets is generated where the second packet of a | | 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. | | pair is, at the same time, the first packet of the next pair. | | |||

skipping to change at page 12, line 7 | skipping to change at page 12, line 7 | |||

reception time Rx as "old values". | reception time Rx as "old values". | |||

+ On reception of the other packets Dst verifies the seuqence number | + On reception of the other packets Dst verifies the seuqence number | |||

and if it is correct, by using the "old values" and the newly | 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 | received ones, a value of ipdv is computed. Then Dst records the | |||

new sequence number, transmit and receive timestamps as "old | new sequence number, transmit and receive timestamps as "old | |||

values". | values". | |||

6.7. Errors and uncertainties | 6.7. Errors and uncertainties | |||

The same considerations apply that have been made about the singleton | The same considerations apply that have been made about the singleton > | |||

metric. An additional error can be introduced by the pseudo-random | metric. Additional error can be introduced by the pseudo-random > | |||

Poisson process as focused in [2]. Further considerations will be | Poisson process as discussed in [2]. Further considerations will be > | |||

made in section 7, and in Appendix A. | given in section 7. | | |||

6.8. Distribution of One-way-ipdv values | | 6.8. Distribution of One-way-ipdv values | | |||

The one-way-ipdv values are limited by virtue of the fact that there | | The one-way-ipdv values are limited by virtue of the fact that there | | |||

are upper and lower bounds on the one-way-delay values. Specifically, | | are upper and lower bounds on the one-way-delay values. Specifically, | | |||

one-way-delay is upper bounded by the value chosen as the maximum | | one-way-delay is upper bounded by the value chosen as the maximum | | |||

beyond which a packet is counted as lost. It is lower bounded by | | beyond which a packet is counted as lost. It is lower bounded by | | |||

propagation, transmission and nodal transit delays assuming that | | propagation, transmission and nodal transit delays assuming that | | |||

there are no queues or variable nodal delays in the path. Denote the | | 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 | | upper bound of one-way-delay by U and the lower bound by L and we see | | |||

skipping to change at page 13, line 14 | skipping to change at page 13, line 14 | |||

6.9.1. Type-P-One-way-ipdv-inverse-percentile | 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 | positive, or greater or equal to the threshold if the threshold is | |||

negative. | 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, these statistics provide the number of packets exceeding a | |||

beyond acceptable limits. | given limit. | |||

6.9.2. Type-P-One-way-ipdv-jitter | | 6.9.2. Type-P-One-way-ipdv-jitter | | |||

This metric was defined in [7] and is simply the absolute value of | | This metric is the same as the definition of "jitter" in [7], and is | | |||

the Type-P-One-way-ipdv. This can be used to derive a number of | | simply the absolute value of the Type-P-One-way-ipdv. | | |||

metrics. | | ||||

7. Discussion on clock synchronization | ||||

This section gives some considerations about the need of having | ||||

synchronized clocks at Src and Dst. These considerations are given as | ||||

a basis for discussion, they require further investigation. We start | ||||

from the analysis of the mean value of the ipdv distribution related | ||||

to a "continuous" sample. Some more detailed calculations are | ||||

presented in Appendix A. | ||||

7.1. Effects of synchronization errors | ||||

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 | ||||

clocks. It is first of all noted that the variable component "drift" | ||||

is physically limited and its effects can be interpreted by saying | ||||

that the total reciprocal skew of the two clocks can vary, ranging | ||||

from a min to a max. value in the time. This type of variation takes | ||||

place very slowly being mostly connected to variations in | ||||

temperature. | ||||

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, | ||||

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 | ||||

the same time T0. | ||||

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 In this conditions the measured ipdv should always be zero, and | ||||

what is actually measured is the error. | ||||

An ipdv value is measured at the beginning of time T with two packets | 6.9.3. The treatment of lost packets as having "infinite" or > | |||

having an interval of Ti(1).Another ipdv value is measured at the end | "undefined" delay complicates the derivation of statistics for ipdv. > | |||

of T with two packets having a time interval Ti(2). | Specifically, when packets in the measurement sequence are lost, > | |||

simple statistics such as sample mean cannot be computed. One > | ||||

possible approach to handling this problem is to reduce the event > | ||||

space by conditioning. That is, we consider conditional statistics; > | ||||

namely we estimate the mean ipdv (or jitter or other derivative > | ||||

statistic) conditioned on the event that successive packet pairs > | ||||

arrive at the destination (within the given timeout). While this > | ||||

itself is not without problems (what happens, for example, when every > | ||||

other packet is lost), it offers a way to make some (valid) > | ||||

statements about ipdv, at the same time avoiding events with > | ||||

undefined outcomes. We suggest that this be a topic for further > | ||||

study. | ||||

On our purposes other errors (like wire-time vs host-time) are not | 7. Discussion of clock synchronization | |||

considered since they are not relevant in this analysis, being common | ||||

to all the measurement methods. | ||||

It is then possible to calculate the values of the Tx and Rx | This section gives some considerations about the need of having | |||

timestamps as they are seen by the two clocks, and the related two | synchronized clocks at the source and destination. These | |||

ipdv values. | considerations are given as a basis for discussion and they require | |||

further investigation. > | ||||

The first ipdv value will be: ipdv1 = ts1*Ti(1) + ((ts2-ts1)/T)*Ti(1) | 7.1. Effects of synchronization errors > | |||

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 interval | Clock errors can be generated by two processes: the relative drift > | |||

Ti(i) between the two packets of the pair, and a second order term | and the relative skew of two given clocks. We should note that drift > | |||

due to the variation of that skew in the same interval. | is physically limited and so the total relative skew of two clocks > | |||

can vary between an upper and a lower bound. > | ||||

If, as in the most of practical cases, the drift can be considered | Suppose then that we have a measurement between two systems such that > | |||

close to zero, then ts1 = ts2, and the error is not depending on the | the clocks in the source and destination systems have at time 0 a > | |||

time at which the measurement is done. In addition, this type of | relative skew of s(0) and after a measurement interval T have skew > | |||

error can be corrected as it is indicated in the next paragraph and | s(T). We assume that the two clocks have an initial offset of O (that > | |||

discussed in Appendix A. | is letter O). > | |||

In any case the maximum error on an ipdv value will correspond to the | Now suppose that the packets travel from source to destination in > | |||

effect of the maximum reciprocal skew on the maximum interval between | constant time, in which case the ipdv is zero and the difference in > | |||

packets. | the timestamps of the two clocks is actually just the relative offset > | |||

of the clocks. Suppose further that at the beginning of the > | ||||

measurement interval the ipdv value is calculated from a packet pair > | ||||

and at the end of the measurement interval another ipdv value is > | ||||

calculated from another packet pair. Assume that the time interval > | ||||

covered by the first measurement is t1 and that covered by the second > | ||||

measurement is t2. Then > | ||||

7.2. Related precision | ipdv1 = s(0)*t1 + t1*(s(T)-s(0))/T > | |||

This means that: | ipdv2 = s(T)*t2 + t2*(s(T)-s(0))/T > | |||

+ If the skew is constant and is = ts all the ipdv(i) values are | assuming that the change is skew is linear in time. In most practical > | |||

increased by the quantity Ti(i)*ts with respect the actual value. | cases, it is claimed that the drift will be close to zero in which > | |||

The mean ipdv value will therefore increased of the quantity | case the second (correction) term in the above equations disappears. > | |||

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 | ||||

calculated. If together with ipdv(i), also the corresponding Ti(i) | ||||

are collected, for each ipdv(i) value a correcting term is | ||||

available, and a sample of "corrected" c-ipdv(i) values is | ||||

obtained, where c-ipdv(i) = ipdv(i) - Ti(i)*st. | ||||

+ Considering the total skew as subdivided into a fixed part and a | Note that in the above discussion, other errors, including the > | |||

variable part (skew and drift),respectively, ts and + or - td, | differences between host time and wire time, and externally-caused > | |||

from the mean ipdv value and the mean emission interval the | clock discontinuities (e.g. clock corrections) were ignored. Under > | |||

average skew can be derived in the period of interest (Appendix | these assumptions the maximum clock errors will be due to the maximum > | |||

A). The preceding correction can then be applied. The maximum | relative skew acting on the largest interval between packets. > | |||

residual error on an ipdv value is given by the difference between | ||||

the actual skew at the time in which the value has been measured | ||||

and the average skew, multiplied by the time interval between the | ||||

packets that have generated that ipdv value. Considerations on the | ||||

number of values in the sample affected by errors are reported in | ||||

Appendix A. | ||||

+ If the duration of the measurement is such that it is possible to | | 7.2. Estimating the skew of unsynchronized clocks > | |||

consider that the ipdv (without skew) is close to zero, the mean | ||||

value of the ipdv distribution will have the value of the average | ||||

skew multiplied by the mean value of the emission interval, as | ||||

supposed above. | ||||

+ We observe that the displacement due to the skew does not change | If the skew is linear (that is, if s(t) = S * t for constant S), the > | |||

the shape of the distribution, and, for example the Standard | error in ipdv values will depend on the time between the packets used > | |||

Deviation remains the same. What introduces a distortion is the | in calculating the value. If ti is the time between the ith and > | |||

effect of the drift, also when the mean value of this effect is | (i+1)st packet, then let Ti denote the sample mean time between > | |||

zero at the end of the measurement. The value of this distortion | packets and the average skew is s(Ti) = S * Ti. Note that E[Ti] > | |||

is limited to the effect of the total skew variation on the | should equal 1/lambda. In the event that the delays are constant, the > | |||

emission interval. | skew parameter S can be estimated from the estimate Ti of the time > | |||

between packets and the sample mean ipdv value. Under these > | ||||

assumptions, the ipdv values can be corrected by subtracting the > | ||||

estimated S * ti. > | ||||

+ In what has been said, skew and drift have been considered as | We observe that the displacement due to the skew does not change the > | |||

"reciprocal". In Appendix A it will be considered that each of the | shape of the distribution, and, for example the Standard Deviation > | |||

two clocks have a skew and a drift with respect a "true time", and | remains the same. What introduces a distortion is the effect of the > | |||

it will be observed that the difference is negligible with respect | drift, also when the mean value of this effect is zero at the end of > | |||

the situation in which one of the two clocks is taken as the "true | the measurement. The value of this distortion is limited to the > | |||

time". | effect of the total skew variation on the emission interval. > | |||

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 | It is therefore expected that in one direction that value is equal | |||

and 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 an | The reference duration of a bidirectional ipdv measurement between an | |||

host E and an host W is reached at time Tf such that for each time T | host E and an host W is reached at time Tf such that for each time T | |||

> Tf the expression ABS(E(ipdv E-W) - E(ipdv W-E))< epsilon, where | > 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 relative skew. | |||

At this point it is possible to evaluate the reciprocal skew. This | At this point it is possible to evaluate the relative skew. This | |||

will require the knowledge of the mean value of the intervals between | will require the knowledge of the mean value of the intervals between | |||

consecutive packets, that can be calculated over the transmitted | consecutive packets, that can be calculated over the transmitted | |||

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-way 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. | able to measure also the Round Trip Delay and its variations. | |||

Problems will anyway arise on the characterization of emission | Problems will anyway arise on the characterization of emission | |||

skipping to change at page 19, line 25 | skipping to change at page 19, line 9 | |||

In general, legitimate measurements must have their parameters | | In general, legitimate measurements must have their parameters | | |||

selected carefully in order to avoid interfering with normal traffic | | selected carefully in order to avoid interfering with normal traffic | | |||

in the network. Such measurements should also be authorized and | | in the network. Such measurements should also be authorized and | | |||

authenticated in some way so that attacks can be identified and | | authenticated in some way so that attacks can be identified and | | |||

intercepted. | | intercepted. | | |||

11. Acknowledgements | | 11. Acknowledgements | | |||

Thanks to Matt Zekauskas from Advanced and Ruediger Geib from | | Thanks to Matt Zekauskas from Advanced and Ruediger Geib from | | |||

Deutsche Telekom for discussions relating to the contents of this | | Deutsche Telekom for discussions relating to the contents of this | | |||

revised draft. | | revised draft. For this additional revision, discussions by e-mail > | |||

with Andy Scherrer were very helpful. | ||||

12. References | | 12. References | |||

[1] V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP | | [1] V.Paxon, G.Almes, J.Mahdavi, M.Mathis - "Framework for IP | |||

Performance Metrics", RFC 2330 Feb. 1998 | | Performance Metrics", RFC 2330 Feb. 1998 | |||

[2] G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", | | [2] G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", RFC | |||

Internet Draft <draft-ietf-ippm-delay-07.txt> May 1999 | | 2679, September 1999 | |||

[3] Draft New ITU-T Recommendation I.380 "Internet Protocol Data | | [3] ITU-T Recommendation I.380 "Internet Protocol Data | |||

Communication Service - IP Packet Transfer and Availability | | Communication Service - IP Packet Transfer and Availability | |||

Performance Parameters" | | Performance Parameters", February 1999 | |||

[4] Demichelis, Carlo - "Packet Delay Variation Comparison between | | [4] Demichelis, Carlo - "Packet Delay Variation Comparison between | |||

ITU-T and IETF Draft Definitions" March 1999 | | ITU-T and IETF Draft Definitions" March 1999 | |||

[5] ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer | | [5] ITU-T Recommendation I.356 "B-ISDN ATM Layer Cell Transfer | |||

Performance" | | Performance" | |||

[6] e-mail exchanges with Ruediger Geib | | [6] e-mail exchanges with Ruediger Geib | |||

[7] V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding | | [7] V. Jacobson, K. Nichols, K. Poduri - "An expedited forwarding | |||

PHB", Internet Draft, November 1998 <draft-ietf-diffserv-phb- | | PHB", RFC 2598, June 1999 | |||

ef-01.txt> | | ||||

13. Authors' Addresses | | 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 | |||

Philip Chimento <chimento@ctit.utwente.nl> | Philip Chimento <chimento@ctit.utwente.nl> | |||

CTIT - Centre for Telematics and Information Technology | CTIT - Centre for Telematics and Information Technology | |||

University of Twente | University of Twente | |||

Postbox 217 | Postbox 217 | |||

7500 AE Enschede | 7500 AE Enschede | |||

The Netherlands | The Netherlands | |||

Phone +31 53 489 4331 | Phone +31 53 489 4331 | |||

FAX +31 53 489 4524 | FAX +31 53 489 4524 | |||

APPENDIX A | Expiration date: April 2000 | |||

This Appendix considers the scenario in which two hosts have clocks | ||||

that are both not synchronized. Between the two hosts, in an | ||||

independent way and at the same time in both direction an ipdv | ||||

measurement is performed according the methodology that is described | ||||

in the main body of this Draft. This hypothetical scenario is only | ||||

supposed for discussing the theory and the characteristics of the | ||||

ipdv metric and its results, without considering implementation | ||||

issues. | ||||

14. Initial positions | ||||

The two hosts will be called West (W) and East (E). The two | ||||

measurements start at the same time, while the end of the measurement | ||||

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 | ||||

clock is T0w, the time declared by the East clock is T0e, while the | ||||

true time is T0t. | ||||

The W-clock is affected by an absolute skew of skw ppm and the E- | ||||

clock by an absolute skew of skw ppm. | ||||

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 | ||||

+dre ppm. | ||||

14.1. Evaluation of skew and drift effects | ||||

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 takes place. We consider the two extreme cases in which the | ||||

variation takes place uniformly from the beginning to the end of the | ||||

measurement and the variation takes place suddenly at a generic time | ||||

along the measurement. Let TM be the measurement time. | ||||

14.1.1. Mean ipdv value | ||||

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 | ||||

values, we consider what, in the two cases, is measured for first and | ||||

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. | ||||

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: | ||||

measured first Rx time - measured first Tx time OffsetEast + trueD*[1 | ||||

+ skEmin + (1/2)*drpsE] - OffsetWest | ||||

What is measured as last Delay is: | ||||

measured last Rx time - measured last Tx time OffsetEast + (TM + | ||||

trueD)*[1 + skEmin + (1/2)*2*dre] - | ||||

- OffsetWest - TM*[1 + skWmin + (1/2)*2*drw] | ||||

The difference between the last and first Delay is therefore: | ||||

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 | ||||

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). We | ||||

consider that, with very good approximation: | ||||

Mean emission interval (mti) = TM / number of ipdv values (N) | ||||

Therefore: | ||||

mean ipdv = (measured last Delay - measured first Delay) / N = | ||||

= mti*(skEmin - skWmin + dre - drw) | ||||

but we considered skEmin = ske - dre and skWmin = skw - drw and | ||||

therefore: | ||||

mean ipdv = (meas.lastD - meas.firstD) / mti*(reciprocal mean skew) | ||||

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 | ||||

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 | ||||

assumes skWmin and at time txE the East clock assumes skEmax. What | ||||

is measured as first Delay is now: | ||||

measured first Rx time - measured first Tx time OffsetEast + trueD*(1 | ||||

+ skEmin) - OffsetWest | ||||

What is measured as last Delay is: | ||||

measured last Rx time - measured last Tx time + OffsetEast + txE*(1 + | ||||

skEmin) + (TM - txE)*(1 + skEmax) + + trueD*(1 + skEmax) - - | ||||

OffsetWest - txW*(1 + skWmax) - (TM - txW)*(1 + skWmin) | ||||

but the mean skew values will be: | ||||

mskw = [skWmax*txW + skWmin*(TM - txW)] / TM mske = [skEmin*txE + | ||||

skEmax*(TM - txE)] / TM | ||||

the difference between the two delays therefore is: | ||||

TM*(mske - mskw) + 2*trueD*dre | ||||

and the mean ipdv value will be: | ||||

mean ipdv = mti*(mske - mskw) + 2*mti*trueD*dre/TM | ||||

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 mean ipdv value, and knowing the mean emission interval, the | ||||

relative skew of the clocks can be obtained. | ||||

More in general, independently on how the drift acts inside its | ||||

limits, we assert that always the mean ipdv value divided by the mean | ||||

emission interval produces the value of the mean reciprocal skew of | ||||

the two clocks, provided that the collected number of ipdv values is | ||||

significant for the statistics. | ||||

14.1.2. Errors and corrections | ||||

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 of them is associated to an emission interval ti between the two | ||||

packets that have produced the value itself. Then a better ipdv value | ||||

will be: corr.ipdv(i) = meas.ipdv(i) - ti * skew This is a better | ||||

value but not exactly the true one, since we supposed that both | ||||

clocks are not synchronized to the true time. Two errors are | ||||

affecting the corrective terms which are: | ||||

+ The reciprocal skew is measured as referred to 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 for the error affecting the ti value. | ||||

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 on the type of variation. Some cases are considered that | ||||

demonstrate that actually the proposed correction is not so much | ||||

effective in this case. Only the fixed part of the total clock | ||||

variation can be properly corrected. | ||||

14.1.3. Constant drift | ||||

The first case is the first one considered in the preceding | ||||

paragraph, where the drift is uniform. We suppose that a reciprocal | ||||

skew is measured and used for correction. | ||||

At the beginning of the measurement the actual reciprocal skew is: | ||||

init.skew = mean.skew - rel.max.drift | ||||

and at the end the actual reciprocal skew is: | ||||

final.skew = mean.skew + rel max.drift | ||||

The correction is effective only in the central part of the | ||||

measurement. At the beginning and at the end a residual error will | ||||

affect the ipdv values whose value will be: | ||||

ipdv(i).err = ti * rel.max.drift | ||||

We underline here that the error is larger for large intervals ti and | ||||

lower for short intervals ti. For intervals derived from a poissonian | ||||

arrival process, there are many short intervals and few large | ||||

intervals. We also note that a constant drift cannot last | ||||

indefinitely, since there is a minimum and a maximum for the skew. | ||||

14.1.4. Step of 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 | ||||

measurement, the calculated mean skew will be very close to the | ||||

actual skew of the largest part of the measurement. On that part the | ||||

correction will be effective, while over the remaining few values the | ||||

error will be twice with respect the preceding case. 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. | ||||

14.2. Comparison with a synchronized case | ||||

In this section we consider a case in which the two hosts have | ||||

synchronized clocks, and the synchronization is obtained by setting | ||||

the real time each second in each of the clocks. We optimistically | ||||

suppose that this is done exactly (without any imprecision). On the | ||||

clocks, anyway skew and drift continue to act. We refer to reciprocal | ||||

skew and drift, having already seen that this is significant. We | ||||

suppose to perform an ipdv measurement and we evaluate what is | ||||

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 over intervals falling completely between two | ||||

synchronization instants. In this case, the effect of | ||||

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 | ||||

synchronization instants) falls inside the interval. In this case the | ||||

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 to the synchronization period. The (few) large intervals will | ||||

produce a limited error while the (many) short intervals will | ||||

continue to produce errors of the same order of magnitude of the not | ||||

synchronized case. | ||||

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 zero. Therefore it is no more possible to correct the distortion | ||||

of the distribution. | ||||

Finally, it is necessary to add to these errors the unavoidable | ||||

imprecision of the synchronization process. We have to consider that | ||||

the magnitude of errors introduced by skew and drift is in the order | ||||

of tenth of microseconds. Not always the complete synchronization | ||||

process has a better precision. | ||||

14.3. Bidirectional measurement and components of ipdv | ||||

Three terms have been described that can displace the mean ipdv value | ||||

from zero. They are: | ||||

+ 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 effect of varying traffic that can increase or decrease along | ||||

limited periods, the average value of the One-Way-Delay. The | ||||

metric 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 | ||||

always present. This is not a distortion of the distribution, | ||||

since is part of the variation that is measured. This effect is | ||||

different, and usually concordant, on the two directions. | ||||

+ The difference between first and last instantaneous values of the | ||||

delay variation, that tends to zero when the number of collected | ||||

ipdv values becomes large. | ||||

In order to isolate the last two effects, we consider here a | ||||

measurement over a long period (e.g. 24 hours)where the drift is | ||||

negligible, and the effect of the skew has been corrected. | ||||

14.4. Slow variation in a given period | ||||

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 y-axis, by points localized by transmission and reception time of | ||||

each packet. Considering an arbitrary period of time Tper, which will | ||||

be a parameter of this procedure, it can be taken as a sliding window | ||||

over the sample and for each position of this window, established by | ||||

successive packets, the segment of straight line is calculated that | ||||

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 | ||||

has not changed, and different from one if that delay has increased | ||||

(>1) or decreased (<1). For each position of the window it is | ||||

therefore possible to find a value of "slow delay variation" with | ||||

Tper as a parameter. This will give an indication on variations | ||||

produced by different traffic conditions along the measurement | ||||

period. This item can be subject for further study. | ||||

At the same time this procedure offers a criterion for reducing the | ||||

error introduced in the calculation of the mean ipdv by the | ||||

instantaneous component of the difference between last and first | ||||

delay. Supposing that the timestamps, on which the metric is based, | ||||

are collected and then processed, if the method of the sliding window | ||||

is applied at the beginning and at the end of the collected sample, | ||||

it is possible to avoid starting and ending the measurement on values | ||||

possibly too different from the average (points too far away from the | ||||

calculated straight line). | | ||||

Expiration date: December, 1999 | ||||

End of changes. | ||||

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