RFC2679 - A One-way Delay Metric for IPPM

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　　Network Working Group G. Almes
Request for Comments: 2679 S. Kalidindi
Category: Standards Track M. Zekauskas
Advanced Network & Services
September 1999

A One-way Delay Metric for IPPM

1. Status of this Memo

This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.

Copyright Notice

Copyright (C) The Internet Society (1999). All Rights Reserved.

2. Introduction

This memo defines a metric for one-way delay of packets across
Internet paths. It builds on notions introduced and discussed in the
IPPM Framework document, RFC2330 [1]; the reader is assumed to be
familiar with that document.

This memo is intended to be parallel in structure to a companion
document for Packet Loss ("A One-way Packet Loss Metric for IPPM")
[2].

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC2119 [6].
Although RFC2119 was written with protocols in mind, the key words
are used in this document for similar reasons. They are used to
ensure the results of measurements from two different implementations
are comparable, and to note instances when an implementation could
perturb the network.

The structure of the memo is as follows:

+ A 'singleton' analytic metric, called Type-P-One-way-Delay, will
be introduced to measure a single observation of one-way delay.

+ Using this singleton metric, a 'sample', called Type-P-One-way-
Delay-Poisson-Stream, will be introduced to measure a sequence of
singleton delays measured at times taken from a Poisson process.

+ Using this sample, several 'statistics' of the sample will be
defined and discussed.

This progression from singleton to sample to statistics, with clear
separation among them, is important.

Whenever a technical term from the IPPM Framework document is first
used in this memo, it will be tagged with a trailing asterisk. For
example, "term*" indicates that "term" is defined in the Framework.

2.1. Motivation:

One-way delay of a Type-P* packet from a source host* to a
destination host is useful for several reasons:

+ Some applications do not perform well (or at all) if end-to-end
delay between hosts is large relative to some threshold value.

+ Erratic variation in delay makes it difficult (or impossible) to
support many real-time applications.

+ The larger the value of delay, the more difficult it is for
transport-layer protocols to sustain high bandwidths.

+ The minimum value of this metric provides an indication of the
delay due only to propagation and transmission delay.

+ The minimum value of this metric provides an indication of the
delay that will likely be experienced when the path* traversed is
lightly loaded.

+ Values of this metric above the minimum provide an indication of
the congestion present in the path.

The measurement of one-way delay instead of round-trip delay is
motivated by the following factors:

+ In today's Internet, the path from a source to a destination may
be different than the path from the destination back to the source
("asymmetric paths"), such that different sequences of routers are
used for the forward and reverse paths. Therefore round-trip
measurements actually measure the performance of two distinct
paths together. Measuring each path independently highlights the
performance difference between the two paths which may traverse

different Internet service providers, and even radically different
types of networks (for example, research versus commodity
networks, or ATM versus packet-over-SONET).

+ Even when the two paths are symmetric, they may have radically
different performance characteristics due to asymmetric queueing.

+ Performance of an application may depend mostly on the performance
in one direction. For example, a file transfer using TCP may
depend more on the performance in the direction that data flows,
rather than the direction in which acknowledgements travel.

+ In quality-of-service (QoS) enabled networks, provisioning in one
direction may be radically different than provisioning in the
reverse direction, and thus the QoS guarantees differ. Measuring
the paths independently allows the verification of both
guarantees.

It is outside the scope of this document to say precisely how delay
metrics would be applied to specific problems.

2.2. General Issues Regarding Time

{Comment: the terminology below differs from that defined by ITU-T
documents (e.g., G.810, "Definitions and terminology for
synchronization networks" and I.356, "B-ISDN ATM layer cell transfer
performance"), but is consistent with the IPPM Framework document.
In general, these differences derive from the different backgrounds;
the ITU-T documents historically have a telephony origin, while the
authors of this document (and the Framework) have a computer systems
background. Although the terms defined below have no direct
equivalent in the ITU-T definitions, after our definitions we will
provide a rough mapping. However, note one potential confusion: our
definition of "clock" is the computer operating systems definition
denoting a time-of-day clock, while the ITU-T definition of clock
denotes a frequency reference.}

Whenever a time (i.e., a moment in history) is mentioned here, it is
understood to be measured in seconds (and fractions) relative to UTC.

As described more fully in the Framework document, there are four
distinct, but related notions of clock uncertainty:

synchronization*

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 clock on a second host. {Comment: A rough ITU-T
equivalent is "time error".}

accuracy*

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.
{Comment: A rough ITU-T equivalent is "time error from UTC".}

resolution*

measures the precision of a given clock. For example, the
clock on an old Unix host might tick only once every 10 msec,
and thus have a resolution of only 10 msec. {Comment: A very
rough ITU-T equivalent is "sampling period".}

skew*

measures the change of accuracy, or of synchronization, with
time. For example, the clock on a given host might gain 1.3
msec per hour and thus be 27.1 msec behind UTC at one time and
only 25.8 msec an hour later. In this case, we say that the
clock of the given host has a skew of 1.3 msec per hour
relative to UTC, which threatens accuracy. We might also speak
of the skew of one clock relative to another clock, which
threatens synchronization. {Comment: A rough ITU-T equivalent
is "time drift".}

3. A Singleton Definition for One-way Delay

3.1. Metric Name:

Type-P-One-way-Delay

3.2. Metric Parameters:

+ Src, the IP address of a host

+ Dst, the IP address of a host

+ T, a time

3.3. Metric Units:

The value of a Type-P-One-way-Delay is either a real number, or an
undefined (informally, infinite) number of seconds.

3.4. Definition:

For a 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 packet to Dst
at wire-time* T and that Dst received the last bit of that packet at
wire-time T+dT.

>>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-P packet to Dst at wire-time T and that Dst did not receive that
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:

Type-P-One-way-Delay is a relatively simple analytic metric, and one
that we believe will afford effective methods of measurement.

The following issues are likely to come up in practice:

+ Real delay values will be positive. Therefore, it does not make
sense to report a negative value as a real delay. However, an
individual zero or negative delay value might be useful as part of
a stream when trying to discover a distribution of a stream of
delay values.

+ 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
closely. GPS systems afford one way to achieve synchronization to
within several 10s of usec. Ordinary application of NTP may allow
synchronization to within several msec, but this depends on the
stability and symmetry of delay properties among those NTP agents
used, and this delay is what we are trying to measure. A
combination of some GPS-based NTP servers and a conservatively
designed and deployed set of other NTP servers should yield good
results, but this is yet to be tested.

+ A given methodology will have to include a way to determine
whether a delay value is infinite or whether it is merely very
large (and the packet is yet to arrive at Dst). As noted by

Mahdavi and Paxson [4], simple upper bounds (such as the 255
seconds theoretical upper bound on the lifetimes of IP packets
[5]) could be used, but good engineering, including an
understanding of packet lifetimes, will be needed in practice.
{Comment: Note that, for many applications of these metrics, the
harm in treating a large delay as infinite might be zero or very
small. A TCP data packet, for example, that arrives only after
several multiples of the RTT may as well have been lost.}

+ 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
determines the packet's one-way delay.

+ If the packet is fragmented and if, for whatever reason,
reassembly does not occur, then the packet will be deemed lost.

3.6. Methodologies:

As with other Type-P-* metrics, the detailed methodology will depend
on the Type-P (e.g., protocol number, UDP/TCP port number, size,
precedence).

Generally, for a given Type-P, the methodology would proceed as
follows:

+ Arrange that Src and Dst are synchronized; that is, that they have
clocks that are very closely synchronized with each other and each
fairly close to the actual time.

+ 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
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
measured delay is lower than it would otherwise be due to
compression techniques along the path.

+ At the Dst host, arrange to receive the packet.

+ At the Src host, place a timestamp in the prepared Type-P packet,
and send it towards Dst.

+ If the packet arrives within a reasonable period of time, take a
timestamp as soon as possible upon the receipt of the packet. By
subtracting the two timestamps, an estimate of one-way delay can
be computed. Error analysis of a given implementation of the
method must take into account the closeness of synchronization
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
adjusted by subtracting this amount; uncertainty in this value
must be taken into account in error analysis. Similarly, if the
delay between the actual receipt of the packet and Dst's timestamp
is known, then the estimate could be adjusted by subtracting this
amount; uncertainty in this value must be taken into account in
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,
the one-way delay is taken to be undefined (informally, infinite).
Note that the threshold of 'reasonable' is a parameter of the
methodology.

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
synchronized are outside the scope of this document. {Comment: We
plan to document elsewhere our own work in describing such more
detailed implementation techniques and we encourage others to as
well.}

3.7. Errors and Uncertainties:

The description of any specific measurement method should include an
accounting and analysis of various sources of error or uncertainty.
The Framework document provides general guidance on this point, but
we note here the following specifics related to delay metrics:

+ Errors or uncertainties due to uncertainties in the clocks of the
Src and Dst hosts.

+ Errors or uncertainties due to the difference between 'wire time'
and 'host time'.

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 or uncertainties related to Clocks

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
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
measure when the packet was received by Dst as the destination clock,
we 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
by the destination clock as Tdest. Alluding to the notions of

synchronization, accuracy, resolution, and skew mentioned in the
Introduction, we note the following:

+ Any error in the synchronization between the source clock and the
destination clock will contribute to error in the delay
measurement. We say that the source clock and the destination
clock have a synchronization error of Tsynch if the source clock
is Tsynch ahead of the destination clock. Thus, if we know the
value of Tsynch exactly, we could correct for clock
synchronization by adding Tsynch to the uncorrected value of
Tdest-Tsource.

+ The accuracy of a clock is important only in identifying the time
at which a given delay was measured. Accuracy, per se, has no
importance to the accuracy of the measurement of delay. When
computing delays, we are interested only in the differences
between clock values, not the values themselves.

+ The resolution of a clock adds to uncertainty about any time
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
measured with it. We will denote the resolution of the source
clock and the destination clock as Rsource and Rdest,
respectively.

+ 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.
Thus, if we attempt to measure or to bound Tsynch, this needs to
be done periodically. Over some periods of time, this function
can be approximated as a linear function plus some higher order
terms; in these cases, one option is to use knowledge of the
linear component to correct the clock. Using this correction, the
residual Tsynch is made smaller, but remains a source of
uncertainty that must be accounted for. We use the function
Esynch(t) to denote an upper bound on the uncertainty in
synchronization. Thus, |Tsynch(t)| <= Esynch(t).

Taking these items together, we note that naive computation Tdest-
Tsource will be off by Tsynch(t) +/- (Rsource + Rdest). Using the
notion of Esynch(t), we note that these clock-related problems
introduce a total uncertainty of Esynch(t)+ Rsource + Rdest. This
estimate of total clock-related uncertainty should be included in the
error/uncertainty analysis of any measurement implementation.

3.7.2. Errors or uncertainties related to Wire-time vs Host-time

As we have defined one-way delay, we would like to measure the time
between when the test packet leaves the network interface of Src and
when it (completely) arrives at the network interface of Dst, and we
refer to these as "wire times." If the timings are themselves
performed by software on Src and Dst, however, then this software can
only directly measure the time between when Src grabs a timestamp
just prior to sending the test packet and when Dst grabs a timestamp
just after having received the test packet, and we refer to these two
points as "host times".

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
measurements and the corrected value more accurately estimates the
desired (wire time) metric.

To the extent, however, that the difference between wire time and
host time is uncertain, this uncertainty must be accounted for in an
analysis of a given measurement method. We denote by Hsource an
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
host. We then note that these problems introduce a total uncertainty
of Hsource+Hdest. This estimate of total wire-vs-host uncertainty
should be included in the error/uncertainty analysis of any
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 generated by the instruments themselves 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 calibration error
for the measurements. It represents the degree to which the values

produced by the measurement instrument are repeatable; that is, how
closely an actual delay of 30 ms is reported as 30 ms. {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 segment. In this case, repeated measurements are
measuring the same one-way delay.

If the test packets are small, such a network connection has a
minimal delay 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.
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 2.5th percentile to the 97.5th percentile of these
deviations from the true value. The calibration error "e" could then
be taken to be the largest absolute value of these two numbers, plus
the clock-related uncertainty. {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 the calibration error.}

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.

We wish to reiterate that this statistical treatment refers to the
calibration of the instrument; it is used to "calibrate the meter
stick" and say how well the meter stick reflects reality.

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
possibility 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 MUST be reported.

3.8.3. Calibration results

+ If the systematic error can be determined, it SHOULD be removed
from the measured values.

+ You SHOULD also report the calibration error, e, such that the
true value is the reported value plus or minus e, with 95%
confidence (see the last section.)

+ If possible, the conditions under which a test packet with finite
delay is reported as lost due to resource exhaustion on the
measurement instrument SHOULD be reported.

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

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
select a particular binding of the parameters Src, Dst, and Type-P,
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
time Tf, and an average rate lambda, then define a pseudo-random

Poisson process of rate lambda, whose values fall between T0 and Tf.
The time interval between successive values of T will then average
1/lambda.

{Comment: Note that Poisson sampling is only one way of defining a
sample. Poisson has the advantage of limiting bias, but other
methods of sampling might be appropriate for different situations.
We encourage others who find such appropriate cases to use this
general framework and submit their sampling method for
standardization.}

4.1. Metric Name:

Type-P-One-way-Delay-Poisson-Stream

4.2. Metric Parameters:

+ Src, the IP address of a host

+ Dst, the IP address of a host

+ T0, a time

+ Tf, a time

+ lambda, a rate in reciprocal seconds

4.3. Metric Units:

A sequence of pairs; the elements of each pair are:

+ T, a time, and

+ dT, either a real number or an undefined number of seconds.

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
would be a valid value of Type-P-One-way-Delay.

4.4. Definition:

Given T0, Tf, and lambda, we compute a pseudo-random Poisson process
beginning at or before T0, with average arrival rate lambda, and
ending 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
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
resulting <time, delay> pairs. If there are no such pairs, the

sequence is of length zero and the sample is said to be empty.

4.5. Discussion:

The reader should be familiar with the in-depth discussion of Poisson
sampling in the Framework document [1], which includes methods to
compute and verify the pseudo-random Poisson process.

We specifically do not constrain the value of lambda, except to note
the extremes. If the rate is too large, then the measurement traffic
will perturb the network, and itself cause congestion. If the rate
is too small, then you might not capture interesting network
behavior. {Comment: We expect to document our experiences with, and
suggestions for, lambda elsewhere, culminating in a "best current
practices" document.}

Since a pseudo-random number sequence is employed, the sequence of
times, and hence the value of the sample, is not fully specified.
Pseudo-random number generators of good quality will be needed to
achieve the desired qualities.

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
statistically as unbiased as possible. {Comment: there is, of
course, no claim that real Internet traffic arrives according to a
Poisson arrival process.} The Poisson process is used to schedule
the delay measurements. The test packets will generally not arrive
at Dst according to a Poisson distribution, since they are influenced
by the network.

All the singleton Type-P-One-way-Delay metrics in the sequence will
have the same values of Src, Dst, and Type-P.

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
subsequence of the given sample whose time values fall between T0'
and Tf' are also a valid Type-P-One-way-Delay-Poisson-Stream sample.

4.6. Methodologies:

The methodologies follow directly from:

+ the selection of specific times, using the specified Poisson
arrival process, and

+ the methodologies discussion already given for the singleton
Type-P-One-way-Delay metric.

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
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
then receive the first one (later) at TR[i].

4.7. Errors and Uncertainties:

In addition to sources of errors and uncertainties associated with
methods employed to measure the singleton values that make up the
sample, care must be given to analyze the accuracy of the Poisson
process with respect to the wire-times of the sending of the test
packets. Problems with this process could be caused by several
things, including problems with the pseudo-random number techniques
used to generate the Poisson arrival process, or with jitter in the
value of Hsource (mentioned above as uncertainty in the singleton
delay metric). The Framework document shows how to use the
Anderson-Darling test to verify the accuracy of a Poisson process
over small time frames. {Comment: The goal is to ensure that test
packets are sent "close enough" to a Poisson schedule, and avoid
periodic behavior.}

4.8. Reporting the metric:

You MUST 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

Given the sample metric Type-P-One-way-Delay-Poisson-Stream, we now
offer several statistics of that sample. These statistics are
offered mostly to be illustrative of what could be done.

5.1. Type-P-One-way-Delay-Percentile

Given a Type-P-One-way-Delay-Poisson-Stream and a percent X between
0% and 100%, the Xth percentile of all the dT values in the Stream.
In computing this percentile, undefined values are treated as
infinitely large. Note that this means that the percentile could
thus be undefined (informally, infinite). In addition, the Type-P-
One-way-Delay-Percentile is undefined if the sample is empty.

Example: suppose we take a sample and the results are:

Stream1 = <
<T1, 100 msec>
<T2, 110 msec>
<T3, undefined>
<T4, 90 msec>
<T5, 500 msec>
>

Then the 50th percentile would be 110 msec, since 90 msec and 100
msec are smaller and 110 msec and 'undefined' are larger.

Note that if the possibility that a packet with finite delay 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

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
treated as infinitely large. As with Type-P-One-way-Delay-
Percentile, Type-P-One-way-Delay-Median is undefined if the sample is
empty.

As noted in the Framework document, the median differs from the 50th
percentile only when the sample contains an even number of values, in
which case the mean of the two central values is used.

Example: suppose we take a sample and the results are:

Stream2 = <
<T1, 100 msec>
<T2, 110 msec>
<T3, undefined>
<T4, 90 msec>
>

Then the median would be 105 msec, the mean of 100 msec and 110 msec,
the two central values.

5.3. Type-P-One-way-Delay-Minimum

Given a Type-P-One-way-Delay-Poisson-Stream, the minimum of all the
dT values in the Stream. In computing this, undefined values are
treated as infinitely large. Note that this means that the minimum
could thus be undefined (informally, infinite) if all the dT values
are undefined. In addition, the Type-P-One-way-Delay-Minimum is

undefined if the sample is empty.

In the above example, the minimum would be 90 msec.

5.4. Type-P-One-way-Delay-Inverse-Percentile

Given a Type-P-One-way-Delay-Poisson-Stream and a time duration
threshold, the fraction of all the dT values in the Stream less than
or equal to the threshold. The result could be as low as 0% (if all
the dT values exceed threshold) or as high as 100%. Type-P-One-way-
Delay-Inverse-Percentile is undefined if the sample is empty.

In the above example, the Inverse-Percentile of 103 msec would be
50%.

6. Security Considerations

Conducting Internet measurements raises both security and privacy
concerns. This memo does not specify an implementation of the
metrics, so it does not directly affect the security of the Internet
nor of applications which run on the Internet. However,
implementations of these metrics must be mindful of security and
privacy concerns.

There are two types of security concerns: potential harm caused by
the measurements, and potential harm to the measurements. The
measurements could cause harm because they are active, and inject
packets into the network. The measurement parameters MUST be
carefully selected so that the measurements inject trivial amounts of
additional traffic into the networks they measure. If they inject
"too much" traffic, they can skew the results of the measurement, and
in extreme cases cause congestion and denial of service.

The measurements themselves could be harmed by routers giving
measurement traffic a different priority than "normal" traffic, or by
an attacker injecting artificial measurement traffic. If routers can
recognize measurement traffic and treat it separately, the
measurements will not reflect actual user traffic. If an attacker
injects artificial traffic that is accepted as legitimate, the loss
rate will be artificially lowered. Therefore, the measurement
methodologies SHOULD include appropriate techniques to reduce the
probability measurement traffic can be distinguished from "normal"
traffic. Authentication techniques, such as digital signatures, may
be used where appropriate to guard against injected traffic attacks.

The privacy concerns of network measurement are limited by the active
measurements described in this memo. Unlike passive measurements,
there can be no release of existing user data.

7. Acknowledgements

Special thanks are due to Vern Paxson of Lawrence Berkeley Labs for
his helpful comments on issues of clock uncertainty and statistics.
Thanks also to Garry Couch, Will Leland, Andy Scherrer, Sean Shapira,
and Roland Wittig for several useful suggestions.

8. References

[1] Paxson, V., Almes, G., Mahdavi, J. and M. Mathis, "Framework for
IP Performance Metrics", RFC2330, May 1998.

[2] Almes, G., Kalidindi, S. and M. Zekauskas, "A One-way Packet
Loss Metric for IPPM", RFC2680, September 1999.

[3] Mills, D., "Network Time Protocol (v3)", RFC1305, April 1992.

[4] Mahdavi J. and V. Paxson, "IPPM Metrics for Measuring
Connectivity", RFC2678, September 1999.

[5] Postel, J., "Internet Protocol", STD 5, RFC791, September 1981.

[6] Bradner, S., "Key words for use in RFCs to Indicate Requirement
Levels", BCP 14, RFC2119, March 1997.

[7] Bradner, S., "The Internet Standards Process -- Revision 3", BCP
9, RFC2026, October 1996.

9. Authors' Addresses

Guy Almes
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA

Phone: +1 914 765 1120
EMail: almes@advanced.org

Sunil Kalidindi
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA

Phone: +1 914 765 1128
EMail: kalidindi@advanced.org

Matthew J. Zekauskas
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA

Phone: +1 914 765 1112
EMail: matt@advanced.org

10. Full Copyright Statement

Copyright (C) The Internet Society (1999). All Rights Reserved.

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or assist in its implementation may be prepared, copied, published
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included on all such copies and derivative works. However, this
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Acknowledgement

Funding for the RFCEditor function is currently provided by the
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