draft-ietf-bmwg-ippm-delay-00.txt   draft-ietf-bmwg-ippm-delay-01.txt 
Network Working Group G. Almes, Advanced Network & Services Network Working Group G. Almes, Advanced Network & Services
Internet Draft S. Kalidindi, Advanced Network & Services Internet Draft S. Kalidindi, Advanced Network & Services
Expiration Date: May 1997 November 1996 Expiration Date: September 1997 March 1997
A One-way Delay Metric for IPPM A One-way Delay Metric for IPPM
<draft-ietf-bmwg-ippm-delay-00.txt> <draft-ietf-bmwg-ippm-delay-01.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
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munnari.oz.au (Pacific Rim), ds.internic.net (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. Introduction 2. Introduction
This memo defines a metric for one-way delay of packets across Inter- This memo defines a metric for one-way delay of packets across Inter-
net paths. It builds on notions introduced and discussed in the net paths. It builds on notions introduced and discussed in the IPPM
revised IPPM Framework document (currently <draft-almes-ippm- Framework document (currently "Framework for IP Provider Metrics"
framework-01.txt>); the reader is assumed to be familiar with that <draft-ietf-bmwg-ippm-framework-00.txt>); the reader is assumed to be
document. {Comment: The revised document, which is being edited in familiar with that document.
parallel with the present document, introduces the notion of 'type-P'
packets, develops some notions of clock uncertainties, develops some This memo is intended to be very parallel in structure to a companion
notions of measurement calibration, and develops some techniques use- document for Packet Loss (soon to be submitted as "A Packet Loss Met-
ful for statistics.} ric for IPPM" <draft-ietf-bmwg-ippm-loss-00.txt>).
The structure of the memo is as follows: The structure of the memo is as follows:
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
+ A 'singleton' analytic metric, called Type-P-One-way-Delay, will + A 'singleton' analytic metric, called Type-P-One-way-Delay, will
be introduced to measure a single observation of one-way delay. be introduced to measure a single observation of one-way delay.
+ Using this singleton metric, a 'sample', called Type-P-One-way- + Using this singleton metric, a 'sample', called Type-P-One-way-
Delay-Stream, will be introduced to measure a sequence of single- Delay-Stream, will be introduced to measure a sequence of single-
ton delays measured at times taken from a Poisson process. ton delays measured at times taken from a Poisson process.
+ Using this sample, several 'statistics' of the sample will be + Using this sample, several 'statistics' of the sample will be
defined and discussed. defined and discussed.
This progression from singleton to sample to statistics, with clear This progression from singleton to sample to statistics, with clear
separation among them, is important. {Comment: In fact, it might be separation among them, is important. {Comment: In fact, it might be
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It is outside the scope of this document to say precisely how delay It is outside the scope of this document to say precisely how delay
metrics would be applied to specific problems. metrics would be applied to specific problems.
2.2. General Issues Regarding Time 2.2. General Issues Regarding Time
Whenever a time (i.e., a moment in history) is mentioned here, it is Whenever a time (i.e., a moment in history) is mentioned here, it is
understood to be measured in seconds relative to 0000 UT on 1 January understood to be measured in seconds relative to 0000 UT on 1 January
1900. {Comment: times will thus be commensurate with NTP timestamps 1900. {Comment: times will thus be commensurate with NTP timestamps
[Mills: RFC 1305].} [Mills: RFC 1305].}
As described more fully in the (revised) Framework document, there As described more fully in the Framework document, there are four
are four distinct, but related notions of clock uncertainty: distinct, but related notions of clock uncertainty:
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
synchronization synchronization
measures the extent to which two clocks agree on what time it is. measures the extent to which two clocks agree on what time it is.
For example, the clock on one host might be 5.4 msec ahead of the For example, the clock on one host might be 5.4 msec ahead of the
clock on a second host. clock on a second host.
accuracy accuracy
measures the extent to which a given clock agrees with UTC. For measures the extent to which a given clock agrees with UTC. For
example, the clock on a host might be 27.1 msec behind UTC. example, the clock on a host might be 27.1 msec behind UTC.
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3. A Singleton Definition for One-way Delay 3. A Singleton Definition for One-way Delay
3.1. Metric Name: 3.1. Metric Name:
Type-P-One-way-Delay Type-P-One-way-Delay
3.2. Metric Parameters: 3.2. Metric Parameters:
+ Src, the IP address of a host + Src, the IP address of a host
+ Dst, the IP address of a host + Dst, the IP address of a host
+ T, a time + T, a time
+ First-hop, the IP address of the first hop router on the path from + Path, the path* from Src to Dst; in cases where there is only one
Src to Dst; this optional parameter defaults to the router one hop path from Src to Dst, this optional parameter can be omitted
from Src whenever there is in fact only one such router {Comment: the presence of path is motivated by cases such as with
{Comment: the presence of first-hop is motivated by cases such as Merit's NetNow setup, in which a Src on one NAP can reach a Dst on
with Merit's NetNow setup, in which a Src on one NAP can reach a Dst another NAP by either of several different backbone networks. Gener-
on another NAP by either of several different backbone networks. ally, this optional parameter is useful only when several different
Generally, this optional step is useful when several different routes routes are possible from Src to Dst. Using the loose source route IP
are possible from Src to Dst and determining the first hop can effec-
tively choose among them. The more flexible loose source route IP
option is avoided since it would often artificially worsen the per- option is avoided since it would often artificially worsen the per-
formance observed, and since it might not be supported along some formance observed, and since it might not be supported along some
paths.} paths.}
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
3.3. Metric Units: 3.3. Metric Units:
The value of a type-P-One-way-Delay is either a non-negative real The value of a type-P-One-way-Delay is either a non-negative real
number or an undefined (informally, infinite) number of seconds. number or an undefined (informally, infinite) number of seconds.
3.4. Definition: 3.4. Definition:
For a non-negative real number dT, >>the *Type-P-One-way-Delay* from For a non-negative real number dT, >>the *Type-P-One-way-Delay* from
Src to Dst at T [via first-hop] is dT<< means that Src sent a type-P Src to Dst at T [via path] is dT<< means that Src sent a type-P
packet [via first-hop] to Dst at time T and that Dst received that packet [via path] to Dst at time T and that Dst received that packet
packet at time T+dT. at time T+dT.
>>The *Type-P-One-way-Delay* from Src to Dst at T [via first-hop] is >>The *Type-P-One-way-Delay* from Src to Dst at T [via path] is unde-
undefined (informally, infinite)<< means that Src sent a type-P fined (informally, infinite)<< means that Src sent a type-P packet
packet [via first-hop] to Dst at time T and that Dst did not receive [via path] to Dst at time T and that Dst did not receive that packet.
that packet.
3.5. Discussion: 3.5. Discussion:
Type-P-One-way-Delay is a relatively simple analytic metric, and one Type-P-One-way-Delay is a relatively simple analytic metric, and one
that we believe will afford effective methods of measurement. that we believe will afford effective methods of measurement.
The following issues are likely to come up in practice: The following issues are likely to come up in practice:
+ Since delay values will often be as low as the 100 usec to 10 msec + Since delay values will often be as low as the 100 usec to 10 msec
range, it will be important for Src and Dst to synchronize very range, it will be important for Src and Dst to synchronize very
closely. GPS systems afford one way to achieve synchronization to closely. GPS systems afford one way to achieve synchronization to
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large (and the packet is yet to arrive at Dst). As noted by Mah- large (and the packet is yet to arrive at Dst). As noted by Mah-
davi and Paxson, simple upper bounds (such as the 255 seconds the- davi and Paxson, simple upper bounds (such as the 255 seconds the-
oretical upper bound on the lifetimes of IP packets [Postel: RFC oretical upper bound on the lifetimes of IP packets [Postel: RFC
791]) could be used, but good engineering, including an under- 791]) could be used, but good engineering, including an under-
standing of packet lifetimes, will be needed in practice. {Com- standing of packet lifetimes, will be needed in practice. {Com-
ment: Note that, for many applications of these metrics, the harm ment: Note that, for many applications of these metrics, the harm
in treating a large delay as infinite might be zero or very small. in treating a large delay as infinite might be zero or very small.
A TCP data packet, for example, that arrives only after several A TCP data packet, for example, that arrives only after several
multiples of the RTT may as well have been lost.} multiples of the RTT may as well have been lost.}
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
+ As with other 'type-P' metrics, the value of the metric may depend + As with other 'type-P' metrics, the value of the metric may depend
on such properties of the packet as protocol, (UDP or TCP) port on such properties of the packet as protocol, (UDP or TCP) port
number, size, and arrangement for special treatment (as with IP number, size, and arrangement for special treatment (as with IP
precedence or with RSVP). precedence or with RSVP).
+ If the packet is duplicated along the path (or paths!) so that
multiple non-corrupt copies arrive at the destination, then the
packet is counted as received, and the first copy to arrive deter-
mintes the packet's one-way delay.
3.6. Methodologies: 3.6. Methodologies:
As with other Type-P-* metrics, the detailed methodology will depend As with other Type-P-* metrics, the detailed methodology will depend
on the Type-P (e.g., protocol number, UDP/TCP port number, size, on the Type-P (e.g., protocol number, UDP/TCP port number, size,
precedence). precedence).
Generally, for a given Type-P, the methodology would proceed as fol- Generally, for a given Type-P, the methodology would proceed as fol-
lows: lows:
+ Arrange that Src and Dst are synchronized; that is, that they have + Arrange that Src and Dst are synchronized; that is, that they have
clocks that are very closely synchronized with each other and each clocks that are very closely synchronized with each other and each
fairly close to the actual time. fairly close to the actual time.
+ At the Src host, select Src and Dst IP addresses, and form a test + At the Src host, select Src and Dst IP addresses, and form a test
packet of Type-P with these addresses. Any 'padding' portion of packet of Type-P with these addresses. Any 'padding' portion of
the packet needed only to make the test packet a given size should the packet needed only to make the test packet a given size should
be filled with randomized bits to avoid a situation in which the be filled with randomized bits to avoid a situation in which the
measured delay is lower than it would otherwise be due to compres- measured delay is lower than it would otherwise be due to compres-
sion techniques along the path. sion techniques along the path.
+ Optionally, select a first-hop router IP address and arrange for + Optionally, select a specific path and arrange for Src to send the
Src to send the packet to that router. {Comment: This could be packet to that path. {Comment: This could be done, for example,
done, for example, by installing a temporary host-route for Dst in by installing a temporary host-route for Dst in Src's routing
Src's routing table.} table.}
+ At the Dst host, arrange to receive the packet. + At the Dst host, arrange to receive the packet.
+ At the Src host, place a timestamp in the prepared Type-P packet, + At the Src host, place a timestamp in the prepared Type-P packet,
and send it towards Dst [via first-hop]. 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. Error analysis of a given implementation of the be computed. Error analysis of a given implementation of the
method must take into account the closeness of synchronization method must take into account the closeness of synchronization
between Src and Dst. If the delay between Src's timestamp and the between Src and Dst. If the delay between Src's timestamp and the
actual sending of the packet is known, then the estimate could be actual sending of the packet is known, then the estimate could be
adjusted by subtracting this amount; uncertainty in this value adjusted by subtracting this amount; uncertainty in this value
must be taken into account in error analysis. Similarly, if the must be taken into account in error analysis. Similarly, if the
delay between the actual receipt of the packet and Dst's timestamp delay between the actual receipt of the packet and Dst's timestamp
is known, then the estimate could be adjusted by subtracting this is known, then the estimate could be adjusted by subtracting this
amount; uncertainty in this value must be taken into account in amount; uncertainty in this value must be taken into account in
error analysis. error analysis.
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
+ If the packet fails to arrive within a reasonable period of time, + If the packet fails to arrive within a reasonable period of time,
the one-way delay is taken to be undefined (informally, infinite). the one-way delay is taken to be undefined (informally, infinite).
Note that the threshold of 'reasonable' here is a parameter of the Note that the threshold of 'reasonable' here is a parameter of the
methodology. {Comment: or should it be a parameter of the met- methodology. {Comment: or should it be a parameter of the met-
ric?} ric?}
Issues such as the packet format, the means by which the first-hop is Issues such as the packet format, the means by which the path is
ensured, the means by which Dst knows when to expect the test packet, ensured, the means by which Dst knows when to expect the test packet,
and the means by which Src and Dst are synchronized are outside the and the means by which Src and Dst are synchronized are outside the
scope of this document. {Comment: We plan to document elsewhere our scope of this document. {Comment: We plan to document elsewhere our
own work in describing such more detailed implementation techniques own work in describing such more detailed implementation techniques
and we encourage others to as well.} and we encourage others to as well.}
3.7. Errors and Uncertainties: 3.7. Errors and Uncertainties:
The description of any specific measurement method should include an The description of any specific measurement method should include an
accounting and analysis of various sources of error/uncertainty. The accounting and analysis of various sources of error/uncertainty. The
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tion, accuracy, resolution, and skew mentioned in the Introduction, tion, accuracy, resolution, and skew mentioned in the Introduction,
we note the following: we note the following:
+ Any error in the synchronization between the source clock and the + Any error in the synchronization between the source clock and the
dest clock will contribute to error in the delay measurement. We dest clock will contribute to error in the delay measurement. We
say that the source clock and the dest clock have a synchroniza- say that the source clock and the dest clock have a synchroniza-
tion error of Tsynch if the source clock is Tsynch ahead of the tion error of Tsynch if the source clock is Tsynch ahead of the
dest clock. Thus, if we know the value of Tsynch exactly, we dest clock. Thus, if we know the value of Tsynch exactly, we
could correct for clock synchronization by adding Tsynch to the could correct for clock synchronization by adding Tsynch to the
uncorrected value of Tdest-Tsource. uncorrected value of Tdest-Tsource.
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
+ The accuracy of a clock is important only in identifying the time + The accuracy of a clock is important only in identifying the time
at which a given delay was measured. Accuracy, per se, has no at which a given delay was measured. Accuracy, per se, has no
importance to the accuracy of the measurement of delay. This is importance to the accuracy of the measurement of delay. This is
because, when computing delays, we are interested only in the dif- because, when computing delays, we are interested only in the dif-
ferences between clock values. ferences between clock values.
+ The resolution of a clock adds to uncertainty about any time mea- + The resolution of a clock adds to uncertainty about any time mea-
sured with it. Thus, if the source clock has a resolution of 10 sured with it. Thus, if the source clock has a resolution of 10
msec, then this adds 10 msec of uncertainty to any time value mea- msec, then this adds 10 msec of uncertainty to any time value mea-
sured with it. We will denote the resolution of the source clock sured with it. We will denote the resolution of the source clock
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To the extent that the difference between wire time and host time is To the extent that the difference between wire time and host time is
accurately known, this knowledge can be used to correct for host time accurately known, this knowledge can be used to correct for host time
measurements and the corrected value more accurately estimates the measurements and the corrected value more accurately estimates the
desired (wire time) metric. desired (wire time) metric.
To the extent, however, that the difference between wire time and To the extent, however, that the difference between wire time and
host time is uncertain, this uncertainty must be accounted for in an host time is uncertain, this uncertainty must be accounted for in an
analysis of a given measurement method. We denote by Hsource an analysis of a given measurement method. We denote by Hsource an
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
upper bound on the uncertainty in the difference between wire time upper bound on the uncertainty in the difference between wire time
and host time on the Src host, and similarly define Hdest for the Dst and host time on the Src host, and similarly define Hdest for the Dst
host. We then note that these problems introduce a total uncertainty host. We then note that these problems introduce a total uncertainty
of Hsource+Hdest. This estimate of total wire-vs-host uncertainty of Hsource+Hdest. This estimate of total wire-vs-host uncertainty
should be included in the error/uncertainty analysis of any measure- should be included in the error/uncertainty analysis of any measure-
ment implementation. ment implementation.
4. A Definition for Samples of One-way Delay 4. A Definition for Samples of One-way Delay
Given the singleton metric Type-P-One-way-Delay, we now define one Given the singleton metric Type-P-One-way-Delay, we now define one
particular sample of such singletons. The idea of the sample is to particular sample of such singletons. The idea of the sample is to
select a particular binding of the parameters Src, Dst, first-hop, select a particular binding of the parameters Src, Dst, path, and
and Type-P, then define a sample of values of parameter T. The means Type-P, then define a sample of values of parameter T. The means for
for defining the values of T is to select a beginning time T0, a defining the values of T is to select a beginning time T0, a final
final time Tf, and an average rate lambda, then define a pseudo- time Tf, and an average rate lambda, then define a pseudo-random
random Poisson arrival process of rate lambda, whose values fall Poisson arrival process of rate lambda, whose values fall between T0
between T0 and Tf. The time interval between successive values of T and Tf. The time interval between successive values of T will then
will then average 1/lambda. average 1/lambda.
4.1. Metric Name: 4.1. Metric Name:
Type-P-One-way-Delay-Stream Type-P-One-way-Delay-Stream
4.2. Metric Parameters: 4.2. Metric Parameters:
+ Src, the IP address of a host + Src, the IP address of a host
+ Dst, the IP address of a host + Dst, the IP address of a host
+ First-hop, the IP address of the first hop router on the path from + Path, the path* from Src to Dst; in cases where there is only one
Src to Dst; this optional parameter defaults to the router one hop path from Src to Dst, this optional parameter can be omitted
from Src whenever there is in fact only one such router
+ T0, a time + T0, a time
+ Tf, a time + Tf, a time
+ lambda, a rate in reciprocal seconds + lambda, a rate in reciprocal seconds
4.3. Metric Units: 4.3. Metric Units:
A sequence of pairs; the elements of each pair are: A sequence of pairs; the elements of each pair are:
+ T, a time, and + T, a time, and
+ dT, either a non-negative real number or an undefined number of + dT, either a non-negative real number or an undefined number of
seconds. seconds.
The values of T in the sequence are monotonic increasing. Note that The values of T in the sequence are monotonic increasing. Note that
T would be a valid parameter to Type-P-One-way-Delay, and that dT T would be a valid parameter to Type-P-One-way-Delay, and that dT
would be a valid value of Type-P-One-way-Delay. would be a valid value of Type-P-One-way-Delay.
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
4.4. Definition: 4.4. Definition:
Given T0, Tf, and lambda, we compute a pseudo-random Poisson process Given T0, Tf, and lambda, we compute a pseudo-random Poisson process
beginning at or before T0, with average arrival rate lambda, and end- beginning at or before T0, with average arrival rate lambda, and end-
ing at or after Tf. Those time values greater than or equal to T0 ing at or after Tf. Those time values greater than or equal to T0
and less than or equal to Tf are then selected. At each of the times and less than or equal to Tf are then selected. At each of the times
in this process, we obtain the value of Type-P-One-way-Delay at this in this process, we obtain the value of Type-P-One-way-Delay at this
time. The value of the sample is the sequence made up of the result- time. The value of the sample is the sequence made up of the result-
ing <time, delay> pairs. If there are no such pairs, the sequence is ing <time, delay> pairs. If there are no such pairs, the sequence is
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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
statistically as unbiased as possible. {Comment: there is, of statistically as unbiased as possible. {Comment: there is, of
course, no claim that real Internet traffic arrives according to a course, no claim that real Internet traffic arrives according to a
Poisson arrival process.} Poisson arrival process.}
All the singleton Type-P-One-way-Delay metrics in the sequence will All the singleton Type-P-One-way-Delay metrics in the sequence will
have the same values of Src, Dst, [first-hop,] and Type-P. have the same values of Src, Dst, [path,] and Type-P.
Note also that, given one sample that runs from T0 to Tf, and given Note also that, given one sample that runs from T0 to Tf, and given
new time values T0' and Tf' such that T0 <= T0' <= Tf' <= Tf, the new time values T0' and Tf' such that T0 <= T0' <= Tf' <= Tf, the
subsequence of the given sample whose time values fall between T0' subsequence of the given sample whose time values fall between T0'
and Tf' are also a valid Type-P-One-way-Delay-Stream sample. and Tf' are also a valid Type-P-One-way-Delay-Stream sample.
4.6. Methodologies: 4.6. Methodologies:
The methodologies follow directly from: The methodologies follow directly from:
+ the selection of specific times, using the specified Poisson + the selection of specific times, using the specified Poisson
arrival process, and arrival process, and
+ the methodologies discussion already given for the singleton Type- + the methodologies discussion already given for the singleton Type-
P-One-way-Delay metric. P-One-way-Delay metric.
Care must, of course, be given to correctly handle out-of-order Care must, of course, be given to correctly handle out-of-order
arrival of test packets; it is possible that the Src could send one arrival of test packets; it is possible that the Src could send one
test packet at TS[i], then send a second one (later) at TS[i+1], test packet at TS[i], then send a second one (later) at TS[i+1],
while the Dst could receive the second test packet at TR[i+1], and while the Dst could receive the second test packet at TR[i+1], and
then receive the first one (later) at TR[i]. then receive the first one (later) at TR[i].
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
4.7. Errors and Uncertainties: 4.7. Errors and Uncertainties:
In addition to sources of errors and uncertainties associated with In addition to sources of errors and uncertainties associated with
methods employed to measure the singleton values that make up the methods employed to measure the singleton values that make up the
sample, care must be given to analyze the accuracy of the Poisson sample, care must be given to analyze the accuracy of the Poisson
arrival process of the wire-time of the sending of the test packets. arrival process of the wire-time of the sending of the test packets.
Problems with this process could be caused by either of several Problems with this process could be caused by either of several
things, including problems with the pseudo-random number techniques things, including problems with the pseudo-random number techniques
used to generate the Poisson arrival process, or with jitter in the used to generate the Poisson arrival process, or with jitter in the
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> >
Then the 50th percentile would be 110 msec, since 90 msec and 100 Then the 50th percentile would be 110 msec, since 90 msec and 100
msec are smaller and 110 msec and 'undefined' are larger. msec are smaller and 110 msec and 'undefined' are larger.
5.2. Type-P-One-way-Delay-Median 5.2. Type-P-One-way-Delay-Median
Given a Type-P-One-way-Delay-Stream, the median of all the dT values Given a Type-P-One-way-Delay-Stream, the median of all the dT values
in the Stream. In computing the median, undefined values are treated in the Stream. In computing the median, undefined values are treated
as infinitely large. as infinitely large.
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
As noted in the Framework document, the median differs from the 50th As noted in the Framework document, the median differs from the 50th
percentile only when the sample contains an even number of values, in percentile only when the sample contains an even number of values, in
which case the mean of the two central values is used. which case the mean of the two central values is used.
Example: suppose we take a sample and the results are: Example: suppose we take a sample and the results are:
Stream2 = < Stream2 = <
<T1, 100 msec> <T1, 100 msec>
<T2, 110 msec> <T2, 110 msec>
<T3, undefined> <T3, undefined>
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Thanks also to Sean Shapira for several useful suggestions. Thanks also to Sean Shapira for several useful suggestions.
8. References 8. References
G. Almes, W. Cerveny, P. Krishnaswamy, J. Mahdavi, M. Mathis, and V. G. Almes, W. Cerveny, P. Krishnaswamy, J. Mahdavi, M. Mathis, and V.
Paxson, "Framework for IP Provider Metrics", Internet Draft <draft- Paxson, "Framework for IP Provider Metrics", Internet Draft <draft-
almes-ippm-framework-00.txt>, July 1996. almes-ippm-framework-00.txt>, July 1996.
J. Postel, "Internet Protocol", RFC 791, September 1981. J. Postel, "Internet Protocol", RFC 791, September 1981.
ID One-way Delay Metric November 1996 ID One-way Delay Metric March 1997
D. Mills, "Network Time Protocol (v3)", RFC 1305, April 1992. D. Mills, "Network Time Protocol (v3)", RFC 1305, April 1992.
9. Authors' Addresses 9. Authors' Addresses
Guy Almes <almes@advanced.org> Guy Almes <almes@advanced.org>
Advanced Network & Services, Inc. Advanced Network & Services, Inc.
200 Business Park Drive 200 Business Park Drive
Armonk, NY 10504 Armonk, NY 10504
USA USA
 End of changes. 

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