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Network Working Group G. Almes, Advanced Network & Services
Internet Draft S. Kalidindi, Advanced Network & Services
Expiration Date: January 1998 July 1997
A One-way Delay Metric for IPPM
<draft-ietf-bmwg-ippm-delay-02.txt>
1. Status of this Memo
This document is an Internet Draft. Internet Drafts are working doc-
uments of the Internet Engineering Task Force (IETF), its areas, and
its working groups. Note that other groups may also distribute work-
ing documents as Internet Drafts.
Internet Drafts are draft documents valid for a maximum of six
months, and may be updated, replaced, or obsoleted by other documents
at any time. It is inappropriate to use Internet Drafts as reference
material or to cite them other than as ``work in progress''.
To learn the current status of any Internet Draft, please check the
``1id-abstracts.txt'' listing contained in the Internet Drafts shadow
directories on ftp.is.co.za (Africa), nic.nordu.net (Europe),
munnari.oz.au (Pacific Rim), ds.internic.net (US East Coast), or
ftp.isi.edu (US West Coast).
This memo provides information for the Internet community. This memo
does not specify an Internet standard of any kind. Distribution of
this memo is unlimited.
2. Introduction
This memo defines a metric for one-way delay of packets across Inter-
net paths. It builds on notions introduced and discussed in the IPPM
Framework document (currently 'Framework for IP Provider Metrics'
<draft-ietf-bmwg-ippm-framework-01.txt>); the reader is assumed to be
familiar with that document.
This memo is intended to be very parallel in structure to a companion
document for Packet Loss ('A Packet Loss Metric for IPPM' <draft-
ietf-bmwg-ippm-loss-01.txt>).
The structure of the memo is as follows:
Almes and Kalidindi [Page 1]
ID One-way Delay Metric July 1997
+ 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-Stream, will be introduced to measure a sequence of single-
ton 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, as
with >>term*<<.
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 trans-
port-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.
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
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.
Almes and Kalidindi [Page 2]
ID One-way Delay Metric July 1997
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.
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.
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, and this threatens
accuracy. We might also speak of the skew of one clock relative to
another clock, and this threatens synchronization.
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
+ Path, the path* from Src to Dst; in cases where there is only one
path from Src to Dst, this optional parameter can be omitted
{Comment: the presence of path is motivated by cases such as with
Merit's NetNow setup, in which a Src on one NAP can reach a Dst on
another NAP by either of several different backbone networks. Gener-
ally, this optional parameter is useful only when several different
routes are possible from Src to Dst. Using the loose source route IP
option is avoided since it would often artificially worsen the per-
formance observed, and since it might not be supported along some
paths.}
3.3. Metric Units:
The value of a type-P-One-way-Delay is either a non-negative real
number or an undefined (informally, infinite) number of seconds.
Almes and Kalidindi [Page 3]
ID One-way Delay Metric July 1997
3.4. Definition:
For a non-negative real number dT, >>the *Type-P-One-way-Delay* from
Src to Dst at T [via path] is dT<< means that Src sent a type-P
packet [via path] to Dst at time T and that Dst received that packet
at time T+dT.
>>The *Type-P-One-way-Delay* from Src to Dst at T [via path] is unde-
fined (informally, infinite)<< means that Src sent a type-P packet
[via path] to Dst at time T and that Dst did not receive that packet.
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:
+ 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 combina-
tion 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 Mah-
davi and Paxson, simple upper bounds (such as the 255 seconds the-
oretical upper bound on the lifetimes of IP packets [Postel: RFC
791]) could be used, but good engineering, including an under-
standing of packet lifetimes, will be needed in practice. {Com-
ment: 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.}
+ 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
number, size, and arrangement for special treatment (as with IP
precedence or with RSVP).
Almes and Kalidindi [Page 4]
ID One-way Delay Metric July 1997
+ 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:
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 fol-
lows:
+ 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 compres-
sion techniques along the path.
+ Optionally, select a specific path and arrange for Src to send the
packet to that path. {Comment: This could be done, for example,
by installing a temporary host-route for Dst in Src's routing
table.}
+ 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 [via path].
+ 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.
Almes and Kalidindi [Page 5]
ID One-way Delay Metric July 1997
+ 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' here is a parameter of the
methodology. {Comment: or should it be a parameter of the met-
ric?}
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,
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/uncertainty. The
Framework document provides general guidence on this point, but we
note here the following specifics related to delay metrics:
+ Errors/uncertainties due to uncertainties in the clocks of the Src
and Dst hosts.
+ Errors/uncertainties due to the difference between 'wire time' and
'host time'.
Each of these are discussed in more detail below.
3.7.1. Errors/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 dest 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 dest clock as Tdest. Alluding to the notions of synchroniza-
tion, accuracy, resolution, and skew mentioned in the Introduction,
we note the following:
+ Any error in the synchronization between the source clock and the
dest clock will contribute to error in the delay measurement. We
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
dest 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.
Almes and Kalidindi [Page 6]
ID One-way Delay Metric July 1997
+ 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. This is
because, when computing delays, we are interested only in the dif-
ferences between clock values.
+ 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
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
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
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 lin-
ear component to correct the clock. Using this correction, the
residual Tsynch is made smaller, but remains a source of uncer-
tainty 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 intro-
duce a total uncertainty of Esynch(t)+|Rsource|+|Rdest|. This esti-
mate of total clock-related uncertainty should be included in the
error/uncertainty analysis of any measurement implementation.
3.7.2. Errors/uncertainties related to Wire-time vs Host-time
Ideally, we'd 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 this as 'wire time'.
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 this as 'host time'.
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
Almes and Kalidindi [Page 7]
ID One-way Delay Metric July 1997
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 measure-
ment implementation.
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, path, 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 arrival process of rate lambda, whose values fall between T0
and Tf. The time interval between successive values of T will then
average 1/lambda.
4.1. Metric Name:
Type-P-One-way-Delay-Stream
4.2. Metric Parameters:
+ Src, the IP address of a host
+ Dst, the IP address of a host
+ Path, the path* from Src to Dst; in cases where there is only one
path from Src to Dst, this optional parameter can be omitted
+ 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 non-negative 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.
Almes and Kalidindi [Page 8]
ID One-way Delay Metric July 1997
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 end-
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
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-
ing <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:
Note first that, 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.}
All the singleton Type-P-One-way-Delay metrics in the sequence will
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
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-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].
Almes and Kalidindi [Page 9]
ID One-way Delay Metric July 1997
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
arrival process of the wire-time of the sending of the test packets.
Problems with this process could be caused by either of 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 an Anderson-
Darling test for this.
5. Some Statistics Definitions for One-way Delay
Given the sample metric Type-P-One-way-Delay-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-Stream and a percent X between 0% and
100%, the Xth percentile of all the dT values in the Stream. In com-
puting this percentile, undefined values are treated as infinitely
large. Note that this means that the percentile could thus be unde-
fined (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.
5.2. Type-P-One-way-Delay-Median
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
as infinitely large.
Almes and Kalidindi [Page 10]
ID One-way Delay Metric July 1997
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-Minumum
Given a Type-P-One-way-Delay-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 unde-
fined. 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-Stream and a non-negative 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%.
In the above example, the Inverse-Percentile of 103 msec would be
50%.
6. Security Considerations
This memo raises no security issues.
Almes and Kalidindi [Page 11]
ID One-way Delay Metric July 1997
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 Sean Shapira for several useful suggestions.
8. References
V. Paxson, G. Almes, J. Mahdavi, and M. Mathis, "Framework for IP
Provider Metrics", Internet Draft <draft-ietf-bmwg-ippm-
framework-01.txt>, July 1997.
J. Postel, "Internet Protocol", RFC 791, September 1981.
D. Mills, "Network Time Protocol (v3)", RFC 1305, April 1992.
9. Authors' Addresses
Guy Almes <almes@advanced.org>
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA
Phone: +1 914/273-7863
Sunil Kalidindi <kalidindi@advanced.org>
Advanced Network & Services, Inc.
200 Business Park Drive
Armonk, NY 10504
USA
Phone: +1 914/273-1219
Almes and Kalidindi [Page 12]
