draft-ietf-ippm-delay-03.txt   draft-ietf-ippm-delay-04.txt 
Network Working Group G. Almes Network Working Group G. Almes
Internet Draft S. Kalidindi Internet Draft S. Kalidindi
Expiration Date: December 1998 M. Zekauskas Expiration Date: March 1999 M. Zekauskas
Advanced Network & Services Advanced Network & Services
June 1998 August 1998
A One-way Delay Metric for IPPM A One-way Delay Metric for IPPM
<draft-ietf-ippm-delay-03.txt> <draft-ietf-ippm-delay-04.txt>
1. Status of this Memo 1. Status of this Memo
This document is an Internet-Draft. Internet-Drafts are working This document is an Internet-Draft. Internet-Drafts are working
documents of the Internet Engineering Task Force (IETF), its areas, documents of the Internet Engineering Task Force (IETF), its areas,
and its working groups. Note that other groups may also distribute and its working groups. Note that other groups may also distribute
working documents as Internet Drafts. working 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
skipping to change at page 1, line 38 skipping to change at page 1, line 38
Rim), ftp.ietf.org (US East Coast), or ftp.isi.edu (US West Coast). Rim), ftp.ietf.org (US East Coast), or 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 This memo defines a metric for one-way delay of packets across
Internet paths. It builds on notions introduced and discussed in the Internet paths. It builds on notions introduced and discussed in the
IPPM Framework document, RFC 2223 [1]; the reader is assumed to be IPPM Framework document, RFC 2330 [1]; the reader is assumed to be
familiar with that document. familiar with that document.
This memo is intended to be parallel in structure to a companion This memo is intended to be parallel in structure to a companion
document for Packet Loss ("A Packet Loss Metric for IPPM" document for Packet Loss ("A Packet Loss Metric for IPPM"
<draft-ietf-ippm-loss-02.txt>) [2]. <draft-ietf-ippm-loss-04.txt>) [2].
The structure of the memo is as follows: The structure of the memo is as follows:
+ 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-Poisson-Stream, will be introduced to measure a sequence of Delay-Poisson-Stream, will be introduced to measure a sequence of
singleton delays measured at times taken from a Poisson process. singleton delays measured at times taken from a Poisson process.
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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. separation among them, is important.
Whenever a technical term from the IPPM Framework document is first Whenever a technical term from the IPPM Framework document is first
used in this memo, it will be tagged with a trailing asterisk. For used in this memo, it will be tagged with a trailing asterisk. For
example, "term*" indicates that "term" is defined in the Framework. example, "term*" indicates that "term" is defined in the Framework.
2.1. Motivation: 2.1. Motivation:
One-way delay of a type-P packet from a source host* to a destination One-way delay of a Type-P* packet from a source host* to a
host is useful for several reasons: destination host is useful for several reasons:
+ Some applications do not perform well (or at all) if end-to-end + Some applications do not perform well (or at all) if end-to-end
delay between hosts is large relative to some threshold value. delay between hosts is large relative to some threshold value.
+ Erratic variation in delay makes it difficult (or impossible) to + Erratic variation in delay makes it difficult (or impossible) to
support many real-time applications. support many real-time applications.
+ The larger the value of delay, the more difficult it is for + The larger the value of delay, the more difficult it is for
transport-layer protocols to sustain high bandwidths. transport-layer protocols to sustain high bandwidths.
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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
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 is dT<< means that Src sent the first bit of a type-P Src to Dst at T is dT<< means that Src sent the first bit of a Type-P
packet to Dst at wire-time* T and that Dst received the last bit of packet to Dst at wire-time* T and that Dst received the last bit of
that packet at wire-time T+dT. that packet at wire-time T+dT.
>>The *Type-P-One-way-Delay* from Src to Dst at T is undefined >>The *Type-P-One-way-Delay* from Src to Dst at T is undefined
(informally, infinite)<< means that Src sent the first bit of a type- (informally, infinite)<< means that Src sent the first bit of a Type-
P packet to Dst at wire-time T and that Dst did not receive that P packet to Dst at wire-time T and that Dst did not receive that
packet. packet.
Suggestions for what to report along with metric values appear in
Section 3.8 after a discussion of the metric, methodologies for
measuring the metric, and error analysis.
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 large (and the packet is yet to arrive at Dst). As noted by
Mahdavi and Paxson [4], simple upper bounds (such as the 255 Mahdavi and Paxson [4], simple upper bounds (such as the 255
seconds theoretical upper bound on the lifetimes of IP seconds theoretical upper bound on the lifetimes of IP
packets [5]) could be used, but good engineering, including an packets [5]) could be used, but good engineering, including an
understanding of packet lifetimes, will be needed in practice. understanding of packet lifetimes, will be needed in practice.
{Comment: Note that, for many applications of these metrics, the {Comment: Note that, for many applications of these metrics, the
harm in treating a large delay as infinite might be zero or very harm in treating a large delay as infinite might be zero or very
small. A TCP data packet, for example, that arrives only after small. A TCP data packet, for example, that arrives only after
several multiples of the RTT may as well have been lost.} several multiples of the RTT may as well have been lost.}
+ The context in which the metric is measured must be carefully
considered, and should always be reported along with metric
results.
As noted in the Framework document [1], the value of the metric
may depend on the type of IP packets used to make the measurement,
or "type-P". The value of Type-P-One-way-Delay could change if
the protocol (UDP or TCP), port number, size, or arrangement for
special treatment (e.g., IP precedence or RSVP) changes. The
exact Type-P used to make the measurements must be accurately
reported.
In addition, the threshold (or methodology to distinguish) between
a large finite delay and loss should be reported.
Finally, the path traversed by the packet should be reported, if
possible. In general it is impractical to know the precise path a
given packet takes through the network. The precise path may be
known for certain Type-P on short or stable paths. If Type-P
includes the record route (or loose-source route) option in the IP
header, and the path is short enough, and all routers* on the path
support record (or loose-source) route, then the path will be
precisely recorded. This is impractical because the route must be
short enough, many routers do not support (or are not configured
for) record route, and use of this feature would often
artificially worsen the performance observed by removing the
packet from common-case processing. However, partial information
is still valuable context. For example, if a host can choose
between two links* (and hence two separate routes from src to
dst), then the initial link used is valuable context. {Comment:
For example, with Merit's NetNow setup, a Src on one NAP can reach
a Dst on another NAP by either of several different backbone
networks.}
The above list is not exhaustive; any additional information that
could be useful in interpreting applications of the metrics should
be reported.
+ If the packet is duplicated along the path (or paths) so that + If the packet is duplicated along the path (or paths) so that
multiple non-corrupt copies arrive at the destination, then the multiple non-corrupt copies arrive at the destination, then the
packet is counted as received, and the first copy to arrive packet is counted as received, and the first copy to arrive
determines the packet's one-way delay. determines the packet's one-way delay.
+ If the packet is fragmented and if, for whatever reason, + If the packet is fragmented and if, for whatever reason,
reassembly does not occur, then the packet will be deemed lost. reassembly does not occur, then the packet will be deemed lost.
3.6. Methodologies: 3.6. Methodologies:
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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. See the next section, "Errors and Uncertainties",
for a more detailed discussion.
+ 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' is a parameter of the
methodology. methodology.
Issues such as the packet format, the means by which Dst knows when Issues such as the packet format, the means by which Dst knows when
to expect the test packet, and the means by which Src and Dst are to expect the test packet, and the means by which Src and Dst are
synchronized are outside the scope of this document. {Comment: We synchronized are outside the scope of this document. {Comment: We
plan to document elsewhere our own work in describing such more plan to document elsewhere our own work in describing such more
detailed implementation techniques and we encourage others to as detailed implementation techniques and we encourage others to as
well.} 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 or uncertainty.
Framework document provides general guidence on this point, but we The Framework document provides general guidence on this point, but
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 Src + Errors or uncertainties due to uncertainties in the clocks of the
and Dst hosts. Src and Dst hosts.
+ Errors/uncertainties due to the difference between 'wire time' and + Errors or uncertainties due to the difference between 'wire time'
'host time'. and 'host time'.
Each of these are discussed in more detail below. In addition, the loss threshold may affect the results. Each of
these are discussed in more detail below, along with a section
("Calibration") on accounting for these errors and uncertainties.
3.7.1. Errors/uncertainties related to Clocks 3.7.1. Errors or uncertainties related to Clocks
The uncertainty in a measurement of one-way delay is related, in The uncertainty in a measurement of one-way delay is related, in
part, to uncertainties in the clocks of the Src and Dst hosts. In part, to uncertainties in the clocks of the Src and Dst hosts. In
the following, we refer to the clock used to measure when the packet the following, we refer to the clock used to measure when the packet
was sent from Src as the source clock, we refer to the clock used to was sent from Src as the source clock, we refer to the clock used to
measure when the packet was received by Dst as the dest clock, we measure when the packet was received by Dst as the dest clock, we
refer to the observed time when the packet was sent by the source refer to the observed time when the packet was sent by the source
clock as Tsource, and the observed time when the packet was received clock as Tsource, and the observed time when the packet was received
by the dest clock as Tdest. Alluding to the notions of by the dest clock as Tdest. Alluding to the notions of
synchronization, accuracy, resolution, and skew mentioned in the synchronization, accuracy, resolution, and skew mentioned in the
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+ 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 say that the source clock and the dest clock have a
synchronization error of Tsynch if the source clock is Tsynch synchronization error of Tsynch if the source clock is Tsynch
ahead of the dest clock. Thus, if we know the value of Tsynch ahead of the dest clock. Thus, if we know the value of Tsynch
exactly, we could correct for clock synchronization by adding exactly, we could correct for clock synchronization by adding
Tsynch to the uncorrected value of Tdest-Tsource. Tsynch to the uncorrected value of Tdest-Tsource.
+ 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. When
because, when computing delays, we are interested only in the computing delays, we are interested only in the differences
differences between clock values. between clock values, not the values themselves.
+ The resolution of a clock adds to uncertainty about any time + The resolution of a clock adds to uncertainty about any time
measured with it. Thus, if the source clock has a resolution of measured with it. Thus, if the source clock has a resolution of
10 msec, then this adds 10 msec of uncertainty to any time value 10 msec, then this adds 10 msec of uncertainty to any time value
measured with it. We will denote the resolution of the source measured with it. We will denote the resolution of the source
clock and the dest clock as Rsource and Rdest, respectively. clock and the dest clock as Rsource and Rdest, respectively.
+ The skew of a clock is not so much an additional issue as it is a + The skew of a clock is not so much an additional issue as it is a
realization of the fact that Tsynch is itself a function of time. realization of the fact that Tsynch is itself a function of time.
Thus, if we attempt to measure or to bound Tsynch, this needs to Thus, if we attempt to measure or to bound Tsynch, this needs to
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Esynch(t) to denote an upper bound on the uncertainty in Esynch(t) to denote an upper bound on the uncertainty in
synchronization. Thus, |Tsynch(t)| <= Esynch(t). synchronization. Thus, |Tsynch(t)| <= Esynch(t).
Taking these items together, we note that naive computation Tdest- Taking these items together, we note that naive computation Tdest-
Tsource will be off by Tsynch(t) +/- (|Rsource|+|Rdest|). Using the Tsource will be off by Tsynch(t) +/- (|Rsource|+|Rdest|). Using the
notion of Esynch(t), we note that these clock-related problems notion of Esynch(t), we note that these clock-related problems
introduce a total uncertainty of Esynch(t)+|Rsource|+|Rdest|. This introduce a total uncertainty of Esynch(t)+|Rsource|+|Rdest|. This
estimate of total clock-related uncertainty should be included in the estimate of total clock-related uncertainty should be included in the
error/uncertainty analysis of any measurement implementation. error/uncertainty analysis of any measurement implementation.
3.7.2. Errors/uncertainties related to Wire-time vs Host-time 3.7.2. Errors or uncertainties related to Wire-time vs Host-time
As we've defined one-way delay, we'd like to measure the time between As we have defined one-way delay, we would like to measure the time
when the test packet leaves the network interface of Src and when it between when the test packet leaves the network interface of Src and
(completely) arrives at the network interface of Dst, and we refer to when it (completely) arrives at the network interface of Dst, and we
this as 'wire time'. If the timings are themselves performed by refer to this as 'wire time'. If the timings are themselves
software on Src and Dst, however, then this software can only performed by software on Src and Dst, however, then this software can
directly measure the time between when Src grabs a timestamp just only directly measure the time between when Src grabs a timestamp
prior to sending the test packet and when Dst grabs a timestamp just just prior to sending the test packet and when Dst grabs a timestamp
after having received the test packet, and we refer to this as 'host just after having received the test packet, and we refer to this as
time'. 'host time'.
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
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 should be included in the error/uncertainty analysis of any
measurement implementation. measurement implementation.
3.7.3. Calibration
Generally, the measured values can be decomposed as follows:
measured value = true value + systematic error + random error
If the systematic error (the constant bias in measured values) can be
determined, it can be compensated for in the reported results.
reported value = measured value - systematic error
therefore
reported value = true value + random error
The goal of calibration is to determine the systematic and random
error in as much detail as possible. At a minimum, a bound ("e")
should be found such that the reported value is in the range (true
value - e) to (true value + e) at least 95 percent of the time. We
call "e" the error bar for the measurements. {Comment: 95 percent
was chosen because (1) some confidence level is desirable to be able
to remove outliers which will be found in measuring any physical
property; (2) a particular confidence level should be specified so
that the results of independent implementations can be compared; and
(3) even with a prototype user-level implementation, 95% was loose
enough to exclude outliers.}
From the discussion in the previous two sections, the error in
measurements could be bounded by determining all the individual
uncertainties, and adding them together to form
Esynch(t) + |Rsource| + |Rdest| + Hsource + Hdest.
However, reasonable bounds on both the clock-related uncertainty
captured by the first three terms and the host-related uncertainty
captured by the last two terms should be possible by careful design
techniques and calibrating the instruments using a known, isolated,
network in a lab.
For example, the clock-related uncertainties are greatly reduced
through the use of a GPS time source. The sum of Esynch(t) +
|Rsource| + |Rdest| is small, and is also bounded for the duration of
the measurement because of the global time source.
The host-related uncertainties, Hsource + Hdest, could be bounded by
connecting two instruments back-to-back with a high-speed serial link
or isolated LAN (depending on the intended network connection for
actual measurement), and performing repeated measurements. In this
case, unlike measuring live networks, repeated measurements are
measuring the same wire time. (When measuring live networks, the
wire time is what you are measuring, and varies with the load
encountered on the path traversed by the test packets.)
If the test packets are small, such a network connection has a
minimal wire time that may be approximated by zero. The measured
delay therefore contains only systematic and random error in the
instrumentation. The "average value" of repeated measurements is the
systematic error, and the variation is the random error.
One way to compute the systematic error, and the random error to a
95% confidence is to repeat the experiment many times - at least
hundreds of tests. The systematic error would then be the median,
and likely the mode (the most frequently occuring value). {Comment:
It's likely the systematic error is represented by the minimum value
(which is also the median and the mode); with unloaded instruments on
a single test path all the random error will tend to be increased
time due to host processing. The only error resulting an a delay
less than the systematic error would be due to clock-related
uncertainties (resolution and relative skew).} The random error could
then be found by removing the systematic error from the measured
values. The 95% confidence interval would be the range from the 2nd
percentile to the 97th percentile of these deviations from the true
value. The error bar "e" could then be taken to be the largest
absolute value of these two numbers, plus the clock-related
uncertainty. If all of the deviations are positive, then the 95%
confidence interval is simply the 95th percentile, and that value
should be used instead of the larger of the 2nd and 97th percentiles.
{Comment: as described, this bound is relatively loose since the
uncertainties are added, and the absolute value of the largest
deviation is used. As long as the resulting value is not a
significant fraction of the measured values, it is a reasonable
bound. If the resulting value is a significant fraction of the
measured values, then more exact methods will be needed to compute an
error bar.}
Note that random error is a function of measurement load. For
example, if many paths will be measured by one instrument, this might
increase interrupts, process scheduling, and disk I/O (for example,
recording the measurements), all of which may increase the random
error in measured singletons. Therefore, in addition to minimal load
measurements to find the systematic error, calibration measurements
should be performed with the same measurement load that the
instruments will see in the field.
In addition to calibrating the instruments for finite one-way delay,
two checks should be made to ensure that packets reported as losses
were really lost. First, the threshold for loss should be verified.
In particular, ensure the "reasonable" threshold is reasonable: that
it is very unlikely a packet will arrive after the threshold value,
and therefore the number of packets lost over an interval is not
sensitive to the error bound on measurements. Second, consider the
probability that a packet arrives at the network interface, but is
lost due to congestion on that interface or to other resource
exhaustion (e.g. buffers) in the instrument.
3.8. Reporting the metric:
The calibration and context in which the metric is measured must be
carefully considered, and should always be reported along with metric
results. We now present four items to consider: the Type-P of test
packets, the threshold of infinite delay (if any), error calibration,
and the path traversed by the test packets. This list is not
exhaustive; any additional information that could be useful in
interpreting applications of the metrics should also be reported.
3.8.1. Type-P
As noted in the Framework document [1], the value of the metric may
depend on the type of IP packets used to make the measurement, or
"type-P". The value of Type-P-One-way-Delay could change if the
protocol (UDP or TCP), port number, size, or arrangement for special
treatment (e.g., IP precedence or RSVP) changes. The exact Type-P
used to make the measurements must be accurately reported.
3.8.2. Loss threshold
In addition, the threshold (or methodology to distinguish) between a
large finite delay and loss should be reported.
3.8.3. Calibration results
+ If the systematic error can be determined, it should be removed
from the measured values.
+ Report an error bar, e, such that the true value is the reported
value plus or minus e, with 95% confidence.
+ If possible, report the probability that a test packet with finite
delay is reported as lost due to resource exhaustion on the
measurement instrument.
3.8.4. Path
Finally, the path traversed by the packet should be reported, if
possible. In general it is impractical to know the precise path a
given packet takes through the network. The precise path may be
known for certain Type-P on short or stable paths. If Type-P
includes the record route (or loose-source route) option in the IP
header, and the path is short enough, and all routers* on the path
support record (or loose-source) route, then the path will be
precisely recorded. This is impractical because the route must be
short enough, many routers do not support (or are not configured for)
record route, and use of this feature would often artificially worsen
the performance observed by removing the packet from common-case
processing. However, partial information is still valuable context.
For example, if a host can choose between two links* (and hence two
separate routes from src to dst), then the initial link used is
valuable context. {Comment: For example, with Merit's NetNow setup,
a Src on one NAP can reach a Dst on another NAP by either of several
different backbone networks.}
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, and Type-P, select a particular binding of the parameters Src, Dst, and Type-P,
then define a sample of values of parameter T. The means for then define a sample of values of parameter T. The means for
defining the values of T is to select a beginning time T0, a final defining the values of T is to select a beginning time T0, a final
time Tf, and an average rate lambda, then define a pseudo-random time Tf, and an average rate lambda, then define a pseudo-random
Poisson arrival process of rate lambda, whose values fall between T0 Poisson arrival process of rate lambda, whose values fall between T0
and Tf. The time interval between successive values of T will then and Tf. The time interval between successive values of T will then
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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].
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 several things,
things, including problems with the pseudo-random number techniques including problems with the pseudo-random number techniques used to
used to generate the Poisson arrival process, or with jitter in the generate the Poisson arrival process, or with jitter in the value of
value of Hsource (mentioned above as uncertainty in the singleton Hsource (mentioned above as uncertainty in the singleton delay
delay metric). The Framework document shows how to use an Anderson- metric). The Framework document shows how to use the Anderson-
Darling test for this. Darling test to verify the accuracy of the Poisson process.
4.8. Reporting the metric:
You should report the calibration and context for the underlying
singletons along with the stream. (See "Reporting the metric" for
Type-P-One-way-Delay.)
5. Some Statistics Definitions for One-way Delay 5. Some Statistics Definitions for One-way Delay
Given the sample metric Type-P-One-way-Delay-Poisson-Stream, we now Given the sample metric Type-P-One-way-Delay-Poisson-Stream, we now
offer several statistics of that sample. These statistics are offer several statistics of that sample. These statistics are
offered mostly to be illustrative of what could be done. offered mostly to be illustrative of what could be done.
5.1. Type-P-One-way-Delay-Percentile 5.1. Type-P-One-way-Delay-Percentile
Given a Type-P-One-way-Delay-Poisson-Stream and a percent X between Given a Type-P-One-way-Delay-Poisson-Stream and a percent X between
skipping to change at page 12, line 16 skipping to change at page 15, line 25
Stream1 = < Stream1 = <
<T1, 100 msec> <T1, 100 msec>
<T2, 110 msec> <T2, 110 msec>
<T3, undefined> <T3, undefined>
<T4, 90 msec> <T4, 90 msec>
<T5, 500 msec> <T5, 500 msec>
> >
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.
Note that if the probability that a finite packet is reported as lost
is significant, then a high percentile (90th or 95th) might be
reported as infinite instead of finite.
5.2. Type-P-One-way-Delay-Median 5.2. Type-P-One-way-Delay-Median
Given a Type-P-One-way-Delay-Poisson-Stream, the median of all the dT Given a Type-P-One-way-Delay-Poisson-Stream, the median of all the dT
values in the Stream. In computing the median, undefined values are values in the Stream. In computing the median, undefined values are
treated as infinitely large. treated as infinitely large.
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.
skipping to change at page 14, line 9 skipping to change at page 17, line 17
be used where appropriate to guard against injected traffic attacks. be used where appropriate to guard against injected traffic attacks.
The privacy concerns of network measurement are limited by the active The privacy concerns of network measurement are limited by the active
measurements described in this memo. Unlike passive measurements, measurements described in this memo. Unlike passive measurements,
there can be no release of existing user data. there can be no release of existing user data.
7. Acknowledgements 7. Acknowledgements
Special thanks are due to Vern Paxson of Lawrence Berkeley Labs for Special thanks are due to Vern Paxson of Lawrence Berkeley Labs for
his helpful comments on issues of clock uncertainty and statistics. his helpful comments on issues of clock uncertainty and statistics.
Thanks also to Sean Shapira and to Roland Wittig for several useful Thanks also to Will Leland, Sean Shapira, and Roland Wittig for
suggestions. several useful suggestions.
8. References 8. References
[1] V. Paxson, G. Almes, J. Mahdavi, and M. Mathis, "Framework for [1] V. Paxson, G. Almes, J. Mahdavi, and M. Mathis, "Framework for
IP Performance Metrics", RFC 2330, May 1998. IP Performance Metrics", RFC 2330, May 1998.
[2] G. Almes, S. Kalidindi, and M. Zekauskas, "A One-way Delay [2] G. Almes, S. Kalidindi, and M. Zekauskas, "A Packet Loss Metric
Metric for IPPM", Internet-Draft <draft-ietf-ippm-delay-02.txt>, for IPPM", Internet-Draft <draft-ietf-ippm-loss-04.txt>, August
June 1998. 1998.
[3] D. Mills, "Network Time Protocol (v3)", RFC 1305, April 1992. [3] D. Mills, "Network Time Protocol (v3)", RFC 1305, April 1992.
[4] J. Mahdavi and V. Paxson, "Connectivity", Work in Progress, [4] J. Mahdavi and V. Paxson, "IPPM Metrics for Measuring
November 1997. Connectivity", Internet-Draft <draft-ietf-ippm-
connectivity-02.txt>, August 1998.
[5] J. Postel, "Internet Protocol", RFC 791, September 1981. [5] J. Postel, "Internet Protocol", RFC 791, September 1981.
9. Authors' Addresses 9. Authors' Addresses
Guy Almes Guy Almes
Advanced Network & Services, Inc. Advanced Network & Services, Inc.
200 Business Park Drive 200 Business Park Drive
Armonk, NY 10504 Armonk, NY 10504
USA USA
Phone: +1 914 765 1120 Phone: +1 914 765 1120
EMail: almes@advanced.org EMail: almes@advanced.org
Sunil Kalidindi Sunil Kalidindi
skipping to change at page 15, line 4 skipping to change at page 18, line 21
EMail: almes@advanced.org EMail: almes@advanced.org
Sunil Kalidindi Sunil Kalidindi
Advanced Network & Services, Inc. Advanced Network & Services, Inc.
200 Business Park Drive 200 Business Park Drive
Armonk, NY 10504 Armonk, NY 10504
USA USA
Phone: +1 914 765 1128 Phone: +1 914 765 1128
EMail: kalidindi@advanced.org EMail: kalidindi@advanced.org
Matthew J. Zekauskas Matthew J. Zekauskas
Advanced Network & Services, Inc. Advanced Network & Services, Inc.
200 Buisiness Park Drive 200 Buisiness Park Drive
Armonk, NY 10504 Armonk, NY 10504
USA USA
Phone: +1 914 765 1112 Phone: +1 914 765 1112
EMail: matt@advanced.org EMail: matt@advanced.org
Expiration date: December, 1998 Expiration date: March, 1999
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