draft-ietf-ippm-ipdv-01.txt | draft-ietf-ippm-ipdv-02.txt | |||
---|---|---|---|---|

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

expires 16 January 1999 | expires May 1999 | |||

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

<draft-ietf-ippm-ipdv-01.txt> | <draft-ietf-ippm-ipdv-02.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. Internet Drafts are working doc- | |||

uments of the Internet Engineering Task Force (IETF), its areas, and | uments of the Internet Engineering Task Force (IETF), its areas, and | |||

its working groups. Note that other groups may also distribute work- | its working groups. Note that other groups may also distribute work- | |||

ing documents as Internet Drafts. | ing documents as Internet Drafts. | |||

Internet Drafts are draft documents valid for a maximum of six | Internet Drafts are draft documents valid for a maximum of six | |||

months, and may be updated, replaced, or obsoleted by other documents | months, and may be updated, replaced, or obsoleted by other documents | |||

at any time. It is inappropriate to use Internet Drafts as reference | at any time. It is inappropriate to use Internet Drafts as reference | |||

material or to cite them other than as ``work in progress''. | material or to cite them other than as ``work in progress''. | |||

To learn the current status of any Internet Draft, please check the | To learn the current status of any Internet Draft, please check the | |||

``1id-abstracts.txt'' listing contained in the Internet Drafts shadow | ``1id-abstracts.txt'' listing contained in the Internet Drafts shadow | |||

directories on ftp.is.co.za (Africa), nic.nordu.net (Europe), | directories on ftp.is.co.za (Africa), nic.nordu.net (Europe), | |||

munnari.oz.au (Pacific Rim), ftp.ietf.org (US East Coast), or | munnari.oz.au (Pacific Rim), ds.internic.net (US East Coast), or | |||

ftp.isi.edu (US West Coast). | ftp.isi.edu (US West Coast). | |||

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 | |||

relative skew. Measurements performed on both directions (Two-ways | reciprocal skew. Measurements performed on both directions (Two-ways | |||

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. | |||

This memo is intended to have, as much as possible, the structure of | I-D Ipdv Metric November 1998 | |||

the ippm draft on one-way delay metric. | ||||

I-D Ipdv Metric July 1998 | ||||

3. Introduction | 3. Introduction | |||

This memo refers to the Draft-ietf "One-way-delay metric for IPPM" that | This memo takes as a reference the Draft-ietf "One-Way-Delay metric for | |||

supposes as known. Part of the text in this memo is directly taken from | IPPM" that it is supposed to be known. Part of the text in this memo is | |||

that Draft. | directly taken from 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 flow | |||

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

related to a variation, different definitions are possible according | related to a variation, different definitions are possible according | |||

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

NOTE: The terminology used in this Draft will be re-visited as soon as | ||||

a terminology document will be available. | ||||

So far the following is considered: | ||||

- The term Jitter is derived from the well known definition given for | ||||

transmission of electrical pulses associated to a clock, and it seems | ||||

to be able to describe variations with respect to an expected arrival | ||||

time. | ||||

- Each entity adopted as a reference for variation measurements defines | ||||

a specific metric. Each metric describes a specific aspect or effect | ||||

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 | |||

The Instantaneous Packet Delay Variation of an IP packet, inside a | 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 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 | ||||

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: | ||||

- The Instantaneous Packet Delay Variation of an IP packet, inside a | ||||

stream of packets, going from the measurement point MP1 to the measu- | 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 | rement point MP2, is the difference of the One-Way-Delay of that | |||

and the One-Way Delay of preceding packet in the stream. | packet and the One-Way-Delay of the preceding packet in the stream. | |||

I-D Ipdv Metric November 1998 | ||||

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 va- | |||

riations in delay, while they are not disturbed by slow variations, | riations 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 va- | |||

riations is therefore desirable. Metrics that can be derived from the | riations is therefore desirable. Metrics that can be derived from the | |||

analysis of statistics of ipdv can also be used for buffer | analysis of statistics of ipdv can also be used, for example, for | |||

dimensioning, but this memo is not intended in that sense. The scope | buffer dimensioning, but this memo is not intended in that sense. | |||

is to provide a way for measurement of the quality delivered by a | The scope of this metric is to provide a way for measurement of the | |||

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 allow | |||

the use of the metric even if the two hosts that support the measure- | the use of the metric even if the two hosts that support the measure- | |||

ment points are not synchronized. The related precision is comparable | -ment points are not synchronized. In the latter case indications on | |||

with the one that can be achieved with synchronized clocks. This will | reciprocal skew of the clocks can be derived from the measurement and | |||

corrections are possible. The related precision is often comparable | ||||

with the one that can be achieved with synchronized clocks, being of | ||||

the same order of magnitude of synchronization errors. This will | ||||

be discussed below. | 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- | All what is contained in the paragraph 2.2. of the Draft ippm on One- | |||

way delay metric (2.2. General Issues Regarding Time) applies also in | Way Delay metric (2.2. General Issues Regarding Time) applies also in | |||

this case. | this case. | |||

In addition, it is here considered that the relative skew of the two | In addition, it is here considered 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 | * A fixed one, called in this context "skew", given, for example, by | |||

tolerances in physical dimension of crystals. | tolerances in physical dimensions of crystals. | |||

I-D Ipdv Metric July 1998 | ||||

* A variable one, called in this context "drift", given, for example, | * A variable one, called in this context "drift", given, for example, | |||

by changes in temperature or other conditions of operation. | by changes in temperature or other conditions of operation. | |||

Both of this components are part of the term "skew" as defined in the | Both of this components are part of the term "skew" as defined in the | |||

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

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 becomes | ||||

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 | ||||

few degrees. The total range of the drift is usually related to varia- | ||||

-tions from 0 to 70 Celsius. These are important points for evaluation | ||||

of precision of ipdv measurements, as it will see 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 ini- | |||

-tial assumption is that source and destination hosts have synchronized | tial assumption is that source and destination hosts have synchronized | |||

clocks. | clocks. | |||

The definition of a singleton of one-way ipdv metric is first consi- | The definition of a singleton of one-way ipdv metric is first consi- | |||

dered, and then a definition of samples for ipdv will be given. | -dered, and then a definition of samples for ipdv will be given. | |||

Then the case of application to not synchronized hosts will be dis- | 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 | cussed, and the precision will be compared with the one of the previous | |||

case. | case. | |||

A bidirectional ipdv metric will be defined, and the methodology for | A bidirectional ipdv metric will be defined, as well as the methodology | |||

error corrections. This will not be a two-ways metric, but a "paired" | for error corrections. This will not be a two-ways metric, but a | |||

one-way in opposite directions. Some statistics describing the IP | "paired" one-way in opposite directions. Some statistics describing the | |||

path's behavior will be proposed. | IP path's behavior will be proposed. | |||

In the Appendix A a more detailed analysis is reported of the ipdv | ||||

theory and of the characteristics of ipdv distribution. | ||||

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, that is supposed to be known. This section makes use | |||

of those parts of the One-way-delay Draft that directly apply to the | of those parts of the One-Way-Delay Draft that directly apply to the | |||

One-way-ipdv metric, or makes direct references to that Draft. | One-Way-ipdv 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 | + Scr, 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 which | |||

the measurement takes place. | the measurement takes place. | |||

+ Path, the path from Src to Dst; in cases where there is only one | ||||

I-D Ipdv Metric July 1998 | I-D Ipdv Metric November 1998 | |||

+ 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. | path from Src to Dst, this optional parameter can be omitted. | |||

{Comment: the presence of path is motivated by cases such as with | {Comment: the presence of path is motivated by cases such as with | |||

Merit's NetNow setup, in which a Src on one NAP can reach a Dst on | Merit's NetNow setup, in which a Src on one NAP can reach a Dst on | |||

another NAP by either of several different backbone networks. Gener- | another NAP by either of several different backbone networks. | |||

ally, this optional parameter is useful only when several different | Generally, this optional parameter is useful only when several dif- | |||

routes are possible from Src to Dst. Using the loose source route IP | -ferent routes are possible from Src to Dst. Using the loose source | |||

option is avoided since it would often artificially worsen the per- | route IP option is avoided since it would often artificially worsen | |||

formance observed, and since it might not be supported along some | the performance observed, and since it might not be supported along | |||

paths.} | some paths.} | |||

5.2. Metric unit | 5.2. 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 | 5.3. 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 times | measured value is anyway the difference in One-Way-Delay at the | |||

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

T2 are such to describe the investigated characteristics. These times | times T1 and T2 are such to describe the investigated charac- | |||

will be better defined later. | -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 whose the first at wire-time T1 (first bit), and the second | |||

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 wire | |||

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

wire-time dT2+T2 (last bit of the second packet), and that dT2-dT1=ddT. | wire-time 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- | "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 | 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 | first bit of a second packet at T2 and that Dst did not receive one | |||

or both packets. | or both packets. | |||

I-D Ipdv Metric November 1998 | ||||

5.4. Discussion | 5.4. 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 measurement | |||

methods provided for delay metrics. | methods provided for delay metrics. | |||

I-D Ipdv Metric July 1998 | ||||

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

to clock synchronization problems. This issue will be more care- | to clock synchronization problems. This issue will be more | |||

fully examined in section 6. of this memo. It is pointed out | carefully examined in section 6. of this memo. It is pointed | |||

that, if the reciprocal clock conditions change in time, the ac- | out that, if the reciprocal clock conditions change in time, | |||

curacy of the measurement will depend on the time interval T2-T1 | the accuracy of the measurement will depend on the time inter- | |||

and the amount of possible errors will be discussed below. | -val T2-T1 and the amount of possible errors will be discussed | |||

+ A given methodology will have to include a way to deter- | below. | |||

mine whether a delay value is infinite or whether it is mere- | + A given methodology will have to include a way to determine whether a | |||

ly very large (and the packet is yet to arrive at Dst). | delay value is infinite or whether it is merely very large (and | |||

the packet is yet to arrive at Dst). | ||||

As noted by Mahdavi and Paxson, simple upper bounds (such as the | As noted by Mahdavi and Paxson, simple upper bounds (such as the | |||

255 seconds theoretical upper bound on the lifetimes of IP | 255 seconds theoretical upper bound on the lifetimes of IP | |||

packets [Postel: RFC 791]) could be used, but good engineering, | packets [Postel: RFC 791]) could be used, but good engineering, | |||

including an understanding of packet lifetimes, will be nee- | including an understanding of packet lifetimes, will be nee- | |||

ded in practice. {Comment: Note that, for many applications of | -ded in practice. {Comment: Note that, for many applications of | |||

these metrics, the harm in treating a large delay as infinite | these metrics, the harm in treating a large delay as infinite | |||

might be zero or very small. A TCP data packet, for example, | might be zero or very small. A TCP data packet, for example, | |||

that arrives only after several multiples of the RTT may as well | that arrives only after several multiples of the RTT may as well | |||

have been lost.} | have been lost.} | |||

+ Usually a path is such that if the first packet is largely delayed, | + 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. | it can "stop" the second packet of the pair and vary its delay. | |||

This is not a problem for the definition since is, in any case, | This is not a problem for the definition since is, in any case, | |||

part of the description of the path's behavior. | part of the description of the path's behavior. | |||

+ As with other 'type-P' metrics, the value of the metric may de- | + As with other 'type-P' metrics, the value of the metric may de- | |||

pend on such properties of the packet as protocol,(UDP or TCP) | -pend on such properties of the packet as protocol,(UDP or TCP) | |||

port number, size, and arrangement for special treatment (as | port number, size, and arrangement for special treatment (as | |||

with IP precedence or with RSVP). | 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- | + If the packet is fragmented and if, for whatever reason, reas- | |||

sembly does not occur, then the packet will be deemed lost. | -sembly does not occur, then the packet will be deemed lost. | |||

5.5. Methodologies | 5.5. 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). | |||

I-D Ipdv Metric November 1998 | ||||

Generally, for a given Type-P, the methodology would proceed as fol- | Generally, for a given Type-P, the methodology would proceed as fol- | |||

lows: | lows: | |||

+ The need of synchronized clocks for Src and Dst will be discus- | + The need of synchronized clocks for Src and Dst will be discus- | |||

sed later. Here a methodology is supposed that is based on | -sed later. Here a methodology is supposed that is based on | |||

synchronized clocks. | synchronized clocks. | |||

I-D Ipdv Metric July 1998 | ||||

+ 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' por- | |||

tion of the packet needed only to make the test packet a given | -tion of the packet needed only to make the test packet a given | |||

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

in which the measured delay is lower than it would otherwise | in which the measured delay is lower than it would otherwise | |||

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

+ Optionally, select a specific path and arrange for Src to send | + Optionally, select a specific path and arrange for Src to send | |||

the packets to that path. {Comment: This could be done, for | the packets to that path. {Comment: This could be done, for | |||

example, by installing a temporary host-route for Dst in Src's | example, by installing a temporary host-route for Dst in Src's | |||

routing table.} | 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 | + At the Src host, place a timestamp in the prepared first | |||

Type-P packet, and send it towards Dst [via path]. | 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 | + At the Src host, place a timestamp in the prepared second | |||

Type-P packet, and send it towards Dst [via path]. | 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 | + By subtracting the second value of One-Way-Delay from the first value | |||

the ipdv value of the pair of packets is obtained. | 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 | 5.6. 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 provides general guidance on this point, but | |||

we note here the following specifics related to delay metrics: | we note here the following specifics related to delay metrics: | |||

+ Errors/uncertainties due to uncertainties in the clocks of the | + Errors/uncertainties due to uncertainties in the clocks of the | |||

Src and Dst hosts. | Src and Dst hosts. | |||

+ Errors/uncertainties due to the difference between 'wire time' | + Errors/uncertainties due to the difference between 'wire time' | |||

and 'host time'. | and 'host time'. | |||

Each of these are discussed in more detail below. | ||||

5.6.1. Errors/Uncertainties related to Clocks | I-D Ipdv Metric November 1998 | |||

If, as a first approximation, the error that affects the first measu- | Each of these type of errors are discussed in more detail in the next | |||

rement of one-way delay were the same of the one affecting the second | paragraphs. | |||

I-D Ipdv Metric July 1998 | 5.6.1. Errors/Uncertainties related to Clocks | |||

If, as a first approximation, the error that affects the first measu- | ||||

rement of One-Way-Delay were the same of the one affecting the second | ||||

measurement, they will cancel each other when calculating ipdv. The | measurement, they will cancel each other when calculating ipdv. The | |||

residual error related to clocks is the difference of the said errors | residual error related to clocks is the difference of the said errors | |||

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

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

ment is performed. Synchronization, skew, accuracy and resolution are | ment is performed. Synchronization, skew, accuracy and resolution are | |||

here considered with the following notes: | here considered with the following notes: | |||

+ Errors in synchronization between source and destination clocks | + Errors in synchronization between source and destination clocks | |||

contribute to errors in both of the delay measurements required | contribute to errors in both of the delay measurements required | |||

for calculating ipdv. | for calculating ipdv. | |||

+ If the synchronization error is Tsync, and it is a linear func- | + If the synchronization error affecting the One-Way-Delay measurement | |||

tion of time, through the skew value, at time T1 the error will | is Tsync, and it is a linear function of time, through the skew | |||

be Tsync1 and at time T2 the error will be Tsync2. The ipdv mea- | value "sk", at time T1 the error will be Tsync1 and at time T2 | |||

surement will be affected by the error Tsync2-Tsync1, depending | the error will be Tsync2. The ipdv measurement will be affected | |||

from skew and T2-T1. To minimize this error it is possible to | by the error: | |||

reduce the time interval T2-T1, but this could limit the genera- | Tsync2-Tsync1 = sk x (T2 - T1) | |||

lity of the metric. Methods for evaluating the synchronization | depending on skew and T2-T1. To minimize this error it is pos- | |||

error will be discussed below, since they come from a statistic | sible to reduce the time interval T2-T1, but this could limit | |||

over a significant sample. | 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 | + 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, | in the above referenced Draft on One-Way-Delay at section 3.7.1, | |||

applies also in this case, with the further consideration, about | applies also in this case, with the further consideration, about | |||

resolution, that in this case the uncertainty introduced is two | resolution, that in this case the uncertainty introduced is two | |||

times the one of a single delay measurement. | 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 | 5.6.2. Errors/uncertainties related to Wire-time vs Host-time | |||

The content of sec. 3.7.2 of the above referenced Draft applies also | The content of sec. 3.7.2 of the above referenced Draft applies also | |||

in this case, with the following further consideration: | in this case, with the following further consideration: | |||

The difference between Host-time and Wire-time can be in general de- | The difference between Host-time and Wire-time can be in general de- | |||

composed into two components, whose one is constant and the other is | composed into two components, whose one is constant and the other is | |||

variable around zero. Only the variable components will produce measu- | variable around zero. Only the variable components will produce measu- | |||

rement errors, while the constant one will be canceled while calcu- | rement errors, while the constant one will be canceled while calcu- | |||

lating ipdv. | lating ipdv. | |||

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, | |||

some ways of building a sample of such singletons are here described | ||||

that have to be further analyzed in order to find the best way of con- | ||||

sidering all the related problems. In the following, the two packets | ||||

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

I-D Ipdv Metric July 1998 | some ways of building a sample of such singletons are here described. | |||

In particular two "discontinuous" samples and one "continuous" sample | ||||

are defined, and the last one is proposed, being the most suitable for | ||||

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. A "discontinuous" definition | 6.1. "Discontinuous" definitions | |||

A general definition can be the following: | A general definition can be the following: | |||

Given particular binding of the parameters Src, Dst, path, and | Given particular binding of the parameters Src, Dst, path, and | |||

Type-P, a sample of values of parameters T1 and T2 is defined. | 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 | 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 | time T0, a final time Tf, and an average rate lambda, then | |||

define a pseudo-random Poisson arrival process of rate lambda, | define a pseudo-random Poisson arrival process of rate lambda, | |||

whose values fall between T0 and Tf. The time interval between | whose values fall between T0 and Tf. The time interval between | |||

successive values of T1 will then average 1/lambda. Another si- | successive values of T1 will then average 1/lambda. Another si- | |||

milar, but independent, pseudo-random Poisson arrival process | milar, but independent, pseudo-random Poisson arrival process | |||

based on T0', Tf' and lambda', will produce a series of t' | based on T0', Tf' and lambda', will produce a series of t' | |||

values. The time interval between successive t' values will then | values. The time interval between successive t' values will then | |||

average 1/lambda'. For each T1 value that has been obtained | average 1/lambda'. For each T1 value that has been obtained | |||

by the first process, it is then possible to calculate the | by the first process, it is then possible to calculate the | |||

successive T2 values as the successive T1 values plus the | successive T2 values as the successive T1 values plus the | |||

successive intervals of t'. | successive intervals of t'. | |||

The result is shown in figure 1. | The result is shown in figure 1. | |||

|<- average interval 1/lambda ->| | ||||

| | | ||||

|<- av.int. | |<- av.int. | | ||||

|1/lambda'->| | 1/lambda'->| | ||||

_____|___________|___________________|_____________|________ | ||||

pair i pair i+1 | ||||

Figure 1 | ||||

This general definition is likely go give problems, if no limits are | This general definition is likely go give problems, if no limits are | |||

considered for the obtained values. For example, the emission | 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 first packet of a pair, could fall before the emission | |||

time of the second packet of the preceding pair. Probably this could | time of the second packet of the preceding pair. Probably this could | |||

be acceptable (provided that there are means to recognize pairs -e.g. | 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 | use of sequence numbers-), but the concept itself of ipdv would be,at | |||

least, slightly changed. A way for avoiding this type of philosophical | least, slightly changed. A way for avoiding this type of philosophical | |||

problems can be to give some rules on the values T0, Tf, lambda, | problems can be to give some rules on the values T0, Tf, lambda, | |||

T0', Tf', lambda', without changing the meaning of the metric. | 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.......| | ||||

..........................| 1/lambda --->| | ||||

| | | ||||

|<- av.int. | |<- av.int. | | ||||

|1/lambda'->| | 1/lambda'->| | ||||

_____|___________|___________________|_____________|________ | ||||

pair i pair i+1 | ||||

Figure 2 | ||||

Still other problems can be envisaged with these two definitions which | ||||

are described in some more detail in Appendix A. | ||||

6.2. A "continuous" definition | 6.2. A "continuous" definition | |||

A way to naturally avoid the previous problem is to adopt the following | A way for naturally avoiding the previous problems and producing a | |||

definition. | 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 | 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 | packet of a pair is, at the same time, the first packet of the next | |||

pair. Therefore the preceding definition becomes: | pair. Therefore the preceding definitions become: | |||

I-D Ipdv Metric July 1998 | ||||

+ Given particular binding of the parameters Src, Dst, path, and | + Given particular binding of the parameters Src, Dst, path, and | |||

Type-P, a sample of values of parameter T1 is defined. | Type-P, a sample of values of parameter T1 is defined. | |||

The means for defining the values of T1 is to select a beginning | 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 | time T0, a final time Tf, and an average rate lambda, then | |||

define a pseudo-random Poisson arrival process of rate lambda, | define a pseudo-random Poisson arrival process of rate lambda, | |||

I-D Ipdv Metric November 1998 | ||||

whose values fall between T0 and Tf. The time interval between | whose values fall between T0 and Tf. The time interval between | |||

successive values of T1 will then average 1/lambda. From the | successive values of T1 will then average 1/lambda. From the | |||

second value on, T1 value of the pair n coincides with T2 of the | second value on, T1 value of the pair n coincides with T2 of | |||

pair n-1, and the first packet of pair n coincides with the se- | the pair n-1, and the first packet of pair n coincides with the | |||

cond packet of the pair n-1. | second packet of the pair n-1. | |||

For the moment, in the following, this second definition will be con- | For the moment, in the following, this last definition will be con- | |||

sidered. Further refinement is required and is for further discussion. | sidered. Further refinement is required and is for further discussion. | |||

6.3. Metric name | 6.3. Metric name | |||

Type-P-One-way-ipdv-stream | Type-P-One-way-ipdv-stream | |||

6.4. Parameters | 6.4. 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 | + 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 | 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: | 6.5. Metric Units: | |||

A sequence of triads whose elements are: | A sequence of triads whose elements are: | |||

+ T, a time | + T, a time | |||

skipping to change at page 9, line 51 | skipping to change at page 11, line 47 | |||

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 Ti 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 T, 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> triad, 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 obtained time T(i), excluding the first | |||

and the last, is therefore at the same time the the second time of | and the last, is therefore at the same time the the second time of | |||

pair i and the first time of pair i+1. The result is shown in figure 2 | pair i and the first time of pair i+1. The result is shown in figure 3 | |||

|T(i-2) |T(i-1) |T(i) |T(i+1) | |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 2 | ||||

I-D Ipdv Metric July 1998 | Figure 3 | |||

I-D Ipdv Metric November 1998 | ||||

6.7. Discussion | 6.7. 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 be needed to achieve the desired qualities. | will 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 | |||

skipping to change at page 10, line 49 | skipping to change at page 12, line 48 | |||

+ On reception of the other packets Dst verifies the SN and if it is | + 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, | correct, by using the "old values" and the newly received ones, | |||

a value of ipdv is computed. Then Dst records the new SN, Tx | a value of ipdv is computed. Then Dst records the new SN, Tx | |||

and Rx timestamps as "old values". | and Rx timestamps as "old values". | |||

6.9. Errors and uncertainties | 6.9. Errors and uncertainties | |||

The same considerations apply that have been made about the single- | The same considerations apply that have been made about the single- | |||

ton metric. An additional error can be introduced by the pseudo-ran- | ton metric. An additional error can be introduced by the pseudo-ran- | |||

dom Poisson process as focused in the above referenced Draft. | dom Poisson process as focused in the above referenced Draft. | |||

Further considerations will be made in section 7. | Further considerations will be made in section 7, and in Appendix A. | |||

I-D Ipdv Metric July 1998 | ||||

6.10 Some statistics for One-way-ipdv | 6.10 Some statistics for One-way-ipdv | |||

Some statistics are here considered, that can provide useful informa- | Some statistics are here considered, that can provide useful informa- | |||

tion in analyzing the behavior of the packets flowing from Src to Dst | -tion in analyzing the behavior of the packets flowing from Src to Dst | |||

I-D Ipdv Metric November 1998 | ||||

These statistics are given having in mind a practical use of them. The | These statistics are given having in mind a practical use of them. The | |||

focus is on the instantaneous behavior of the connection, while buffer | focus is on the instantaneous behavior of the connection, while buffer | |||

dimensioning is not in the scope of this document. | dimensioning is not in the scope of this document. | |||

Other statistics can be defined if needed. | Other statistics can be defined if needed. | |||

6.10.1. Type-P-One-way-ipdv-inverse-percentile | 6.10.1. 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 | |||

skipping to change at page 11, line 32 | skipping to change at page 13, line 28 | |||

gative. | gative. | |||

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 | 6.10.2 Type-P-One-way-ipdv-standard-deviation | |||

Given a Type-P-One-way-ipdv-Stream, the distribution of ipdv values | Given a Type-P-One-way-ipdv-Stream, the distribution of ipdv values | |||

is considered and the Standard Deviation can be calculated as an | is considered and the Standard Deviation can be calculated as an | |||

indication of regularity of delivery. For practical purposes it can | indication of regularity of delivery. For practical purposes it can be | |||

useful to define a total standard deviation, computed over the com- | useful to define a total standard deviation, computed over the com- | |||

plete set of value, and a standard deviation computed over the sub- | plete set of value, and a standard deviation computed over the sub- | |||

set of those values that do not exceed given positive and negative | set of those values that do not exceed given positive and negative | |||

thresholds. This allows a more accurate description of the performan- | thresholds. This allows a more accurate description of the performan- | |||

ce experienced by packets. | 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 | 6.10.3 Type-P-One-way-ipdv-average | |||

This statistic should tend to a value of ZERO for a number of ipdv | This statistic should tend to a value of ZERO for a number of ipdv | |||

values that tend to infinite. The behavior of Type-P-One-way-ipdv- | values that tend to infinite. The behavior of Type-P-One-way-ipdv- | |||

average, and its meaning, are issues for the next section 7. | average, and its meaning, are issues for the next section 7. | |||

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 syn- | |||

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

basis for discussion, they require further investigation. We start | 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. | to a "continuous" sample. Some more detailed calculations are presented | |||

in Appendix A. | ||||

I-D Ipdv Metric July 1998 | I-D Ipdv Metric November 1998 | |||

7.1. Mean value of ipdv distribution. | 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 | 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 | ipdv in the distribution of a sample of "n" values, collected with | |||

the described methodology, we can write: | the described methodology, we can write: | |||

ipdv(1) = D1 - D0 | ipdv(1) = D1 - D0 | |||

.......... | .......... | |||

ipdv(i) = D(i) - D(i-1) | ipdv(i) = D(i) - D(i-1) | |||

.......... | .......... | |||

ipdv(n) = D(n) - D(n-1) | ipdv(n) = D(n) - D(n-1) | |||

The mean value of ipdv distribution will result in | The mean value of ipdv distribution will result in | |||

E(ipdv) = (D(n) - D(0))/n | E(ipdv) = (D(n) - D(0))/n | |||

If an actual measurement is performed, that lasts a period of time | If an actual measurement is performed, that lasts a period of time | |||

long enough to contain a number "n" sufficiently large and, supposing | long enough to contain a number "n" sufficiently large and, supposing | |||

synchronized clocks, such that the network conditions (traffic) allow | 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 | to find a D(n) not too different from D(0), e.g. a time of n x 24 | |||

n x 24 hours, E(ipdv) will tend to zero, since the difference | hours, E(ipdv) will tend to zero, since the difference D(n) - D(0) will | |||

D(n) - D(0) will remain finite. | remain finite and little. | |||

7.2. Effects of a varying traffic | 7.2. Effects of a varying traffic | |||

If the mean values of delay D are changing inside a given period of | 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, | time, for example they are increasing due to an increment of traffic, | |||

we can consider, as a first approximation, the ipdv values as decom- | we can consider, as a first approximation, the ipdv values as decom- | |||

posed into two components, one being instantaneous and another one | posed into two components, one being instantaneous and another one | |||

as having a constant rate dD and corresponding to the increment "per | 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 | 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 | will be shifted of the value dD corresponding to the mean value of | |||

the interval between test packets. When the conditions will come back | 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 | to the initial ones, the distribution will resume a mean value around | |||

zero. At any time the distribution will correctly describe the | zero. As for the case of drift, also in this case a monotonic varia- | |||

effects of the path on the packet flow. | -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 | 7.3. 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 relative "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" | |||

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

that the total 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. | ||||

I-D Ipdv Metric July 1998 | I-D Ipdv Metric November 1998 | |||

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 | 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. In order to analyze the effects produced by this | the same time T0. | |||

situation we suppose that packets are transferred, from Src to Dst, | ||||

with a constant delay D. In this conditions the measured ipdv should | In order to analyze the effects produced by this situation we suppose | |||

always be zero, and what is actually measured is the error. | 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 | 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. | 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 time- | It is then possible to calculate the values of the Tx and Rx time- | |||

stamps as they are seen by the two clocks, and the related values of | stamps as they are seen by the two clocks, and the related two ipdv | |||

the two ipdv values. | 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 amount of variation during the time inter- | The error is given by the effect of the skew during the time inter- | |||

val Ti(i) between the two packets of the pair, and a second order | val Ti(i) between the two packets of the pair, and a second order | |||

term due to the variation of that variation in the same interval. | term due to the variation of that skew in the same interval. | |||

If, as in practical cases, the drift can be considered zero, then | If, as in the most of practical cases, the drift can be considered | |||

ts1 = ts2, and the error is not depending on the time at which the | close to zero, then ts1 = ts2, and the error is not depending on the | |||

measurement is done. | 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 | ||||

discussed in Appendix A. | ||||

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 | ||||

packets. | ||||

I-D Ipdv Metric November 1998 | ||||

7.4. 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 | 1) + 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 | ||||

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 avai- | ||||

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

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

2) + Considering the total skew as subdivided into a fixed part and a | 2) + Considering the total skew as subdivided into a fixed part and a | |||

variable part (skew and drift),respectively, ts and + or - td, and | variable part (skew and drift),respectively, ts and + or - td, | |||

a minimum time T in which the drift can go from -td to +td or vice | from the mean ipdv value and the mean emission interval the average | |||

-versa, each ipdv(i) value will be increased of the fixed quantity | skew can be derived in the period of interest (Appendix A). The | |||

Ti(i)*ts plus or minus, as a maximum, the quantity 2*td*Ti(i)/T | preceding correction can then be applied. The maximum residual er- | |||

-ror on an ipdv value is given by the difference between the actual | ||||

I-D Ipdv Metric July 1998 | skew at the time in which the value has been measured and the ave- | |||

-rage 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. | ||||

3) + If the duration of the measurement is such that it is possible | 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, | to consider that the effect of the items at points 7.1 and 7.2, | |||

and the effect of the drift are negligible (related average ten- | are close to zero, the mean value of the ipdv distribution will | |||

ding to zero), the mean value of the ipdv distribution will have | have the value of the average skew multiplied by the mean value of | |||

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

interval. | ||||

4) + We observe that the displacement due to the skew does not change | 4) + We observe that the displacement due to the skew does not change | |||

the shape of the distribution, and, for example the Standard Devi- | the shape of the distribution, and, for example the Standard Devi- | |||

ation remains the same. What introduces a distortion is the effect | ation remains the same. What introduces a distortion is the effect | |||

of the drift, even if the mean value of this effect is zero at the | of the drift, also when the mean value of this effect is zero at | |||

end of the measurement. The value of this distortion is limited to | the end of the measurement. The value of this distortion is limited | |||

the effect of the total skew variation on the emission interval. | to the effect of the total skew variation on the emission interval. | |||

5) + 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 | ||||

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 | ||||

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 fixed action of the skew has modified the measured mean value. It | the action of the average skew has modified the measured mean value. | |||

is therefore expected that on one direction that value is equal and | It is therefore expected that on one direction that value is equal and | |||

opposite to the one measured in the other direction. | 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 host E and an host W is reached at time Tf such that for each time | an host E and an host W is reached at time Tf such that for each time | |||

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

epsilon is what we can consider as zero, is always verified. | epsilon is what we can consider as zero, is always verified. This is | |||

one, but not the only method for verifying that the mean ipdv value | ||||

has reached the value of the average reciprocal skew. | ||||

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

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

between consecutive packets, that can be calculated over the trans- | ||||

-mitted 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-ways 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 intervals in the | ||||

backward direction. They would be produced by the combination of the | ||||

original Poisson arrival process and the effect of ipdv on the forward | ||||

direction. It has to be studied if this sequence of intervals is still | ||||

suitable for the measurement. also other possibilities can be | ||||

envisaged for obtaining a proper backward sequence and still maintain | ||||

the loopback concept. | ||||

I-D Ipdv Metric July 1998 | I-D Ipdv Metric November 1998 | |||

9. References | 9. References | |||

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

Metrics", Internet Draft <draft-ietf-ippm-framework-01.txt> Feb. 1998 | Metrics", Internet Draft <draft-ietf-ippm-framework-01.txt> Feb. 1998 | |||

G.Almes, S.Kalidindi - "A One-way Delay Metric for IPPM", Internet | G.Almes, S.Kalidindi - "A One-Way-Delay Metric for IPPM", Internet | |||

Draft <draft-ietf-ippm-delay-01.txt> Nov. 1997 | Draft <draft-ietf-ippm-delay-01.txt> Nov. 1997 | |||

10. Author's Address | 10. Author's Address | |||

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 | ||||

APPENDIX A | ||||

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

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

-pendent way and at the same time in both direction an ipdv measure- | ||||

-ment 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. | ||||

A.1 - Initial positions | ||||

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

-ments 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. | ||||

A.2 - 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. | ||||

A.2.1 - 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. | ||||

I-D Ipdv Metric November 1998 | ||||

For the evaluation that we want to do, it is not a limitation to con- | ||||

-sider 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. | ||||

I-D Ipdv Metric November 1998 | ||||

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 rela- | ||||

-tive 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 signi- | ||||

-ficant for the statistics. | ||||

A.2.2 - 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: | ||||

I-D Ipdv Metric November 1998 | ||||

+ 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. | ||||

A.2.2.1 - 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 measu- | ||||

-red 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. | ||||

A.2.2.2 - 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 correc- | ||||

-tion will be effective, while over the remaining few values the error | ||||

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

I-D Ipdv Metric November 1998 | ||||

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 | ||||

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

-nized 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 impre- | ||||

cision 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. | ||||

A.4 - Bidirectional measurement and components of ipdv | ||||

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

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 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. | ||||

A.4.1 - 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 suc- | ||||

-cessive 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 instanta- | ||||

-neous 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). | ||||

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- | ||||

-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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