This memo defines a metric for one-way delay of packets Internet paths. It builds on notions introduced and discussed in
IPPM Frameworkdocument, RFC 2330 [1]; the reader is assumed to
familiar with that document
This memo is intended to be parallel in structure to a 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 document are to be interpreted as described in RFC 2119 [6].
Although RFC 2119 was written with protocols in mind, the key
are used in this document for similar reasons. They are used
ensure the results of measurements from two different
are comparable, and to note instances when an implementation
perturb the network
RFC 2679 A One-way Delay Metric for IPPM September 1999
+ Using this singleton metric, a 'sample', called Type-P-One-way
Delay-Poisson-Stream, will be introduced to measure a sequence
singleton delays measured at times taken from a Poisson process
+ Using this sample, several 'statistics' of the sample will
defined and discussed
This progression from singleton to sample to statistics, with
separation among them, is important
Whenever a technical term from the IPPM Frameworkdocument is
used in this memo, it will be tagged with a trailing asterisk.
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 destination host is useful for several reasons
+ Some applications do not perform well (or at all) if end-to-
delay between hosts is large relative to some threshold value
+ Erratic variation in delay makes it difficult (or impossible)
support many real-time applications
+ The larger the value of delay, the more difficult it is transport-layer protocols to sustain high bandwidths
+ In quality-of-service (QoS) enabled networks, provisioning in direction may be radically different than provisioning in
reverse direction, and thus the QoS guarantees differ.
the paths independently allows the verification of
guarantees
It is outside the scope of this document to say precisely how
metrics would be applied to specificproblems
measures the extent to which two clocks agree on what time
is. For example, the clock on one host might be 5.4 msec
of the clock on a second host. {Comment: A rough ITU- equivalent is "time error".}
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".}
measures the precision of a given clock. For example,
clock on an old Unix host might tick only once every 10 msec
and thus have a resolution of only 10 msec. {Comment: A
rough ITU-T equivalent is "sampling period".}
skew
measures the change of accuracy, or of synchronization,
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
only 25.8 msec an hour later. In this case, we say that
clock of the given host has a skew of 1.3 msec per relative to UTC, which threatens accuracy. We might also
of the skew of one clock relative to another clock,
threatens synchronization. {Comment: A rough ITU-T
is "time drift".}
For a real number dT, >>the *Type-P-One-way-Delay* from Src to Dst
T is dT<< means that Src sent the first bit of a Type-P packet to
at wire-time* T and that Dst received the last bit of that packet
wire-time T+dT
>>The *Type-P-One-way-Delay* from Src to Dst at T is
(informally, infinite)<< means that Src sent the first bit of
Type-P packet to Dst at wire-time T and that Dst did not receive
packet
Suggestions for what to report along with metric values appear
Section 3.8 after a discussion of the metric, methodologies
measuring the metric, and error analysis
+ Real delay values will be positive. Therefore, it does not
sense to report a negative value as a real delay. However, individual zero or negative delay value might be useful as part
a stream when trying to discover a distribution of a stream
delay values
+ Since delay values will often be as low as the 100 usec to 10
range, it will be important for Src and Dst to synchronize
closely. GPS systems afford one way to achieve synchronization
within several 10s of usec. Ordinary application of NTP may synchronization to within several msec, but this depends on
stability and symmetry of delay properties among those NTP
used, and this delay is what we are trying to measure. combination of some GPS-based NTP servers and a
designed and deployed set of other NTP servers should yield
results, but this is yet to be tested
+ A given methodology will have to include a way to
whether a delay value is infinite or whether it is merely
large (and the packet is yet to arrive at Dst). As noted
RFC 2679 A One-way Delay Metric for IPPM September 1999
Mahdavi and Paxson [4], simple upper bounds (such as the 255
seconds theoretical upper bound on the lifetimes of IP
[5]) could be used, but good engineering, including
understanding of packet lifetimes, will be needed in practice
{Comment: Note that, for many applications of these metrics,
harm in treating a large delay as infinite might be zero or
small. A TCP data packet, for example, that arrives only
several multiples of the RTT may as well have been lost.}
+ If the packet is duplicated along the path (or paths) so multiple non-corrupt copies arrive at the destination, then
packet is counted as received, and the first copy to
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
on the Type-P (e.g., protocol number, UDP/TCP port number, size precedence).
Generally, for a given Type-P, the methodology would proceed
follows
+ Arrange that Src and Dst are synchronized; that is, that they
clocks that are very closely synchronized with each other and
fairly close to the actual time
+ At the Src host, select Src and Dst IP addresses, and form a
packet of Type-P with these addresses. Any 'padding' portion
the packet needed only to make the test packet a given size
be filled with randomized bits to avoid a situation in which measured delay is lower than it would otherwise be due compressiontechniques 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 timestamp as soon as possible upon the receipt of the packet.
subtracting the two timestamps, an estimate of one-way delay
be computed. Error analysis of a given implementation of
method must take into account the closeness of
between Src and Dst. If the delay between Src's timestamp and
RFC 2679 A One-way Delay Metric for IPPM September 1999
actual sending of the packet is known, then the estimate could
adjusted by subtracting this amount; uncertainty in this
must be taken into account in error analysis. Similarly, if
delay between the actual receipt of the packet and Dst's
is known, then the estimate could be adjusted by subtracting
amount; uncertainty in this value must be taken into account
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 methodology
Issues such as the packet format, the means by which Dst knows
to expect the test packet, and the means by which Src and Dst
synchronized are outside the scope of this document. {Comment:
plan to document elsewhere our own work in describing such
detailed implementationtechniques and we encourage others to
well.}
+ Errors or uncertainties due to uncertainties in the clocks of
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
these are discussed in more detail below, along with a
("Calibration") on accounting for these errors and uncertainties
3.7.1. Errors or uncertainties related to
The uncertainty in a measurement of one-way delay is related,
part, to uncertainties in the clocks of the Src and Dst hosts.
the following, we refer to the clock used to measure when the
was sent from Src as the source clock, we refer to the clock used
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
clock as Tsource, and the observed time when the packet was
by the destination clock as Tdest. Alluding to the notions
+ Any error in the synchronization between the source clock and destination clock will contribute to error in the measurement. We say that the source clock and the
clock have a synchronization error of Tsynch if the source
is Tsynch ahead of the destination clock. Thus, if we know
value of Tsynch exactly, we could correct for synchronization by adding Tsynch to the uncorrected value
Tdest-Tsource
+ The accuracy of a clock is important only in identifying the
at which a given delay was measured. Accuracy, per se, has
importance to the accuracy of the measurement of delay. computing delays, we are interested only in the
between clock values, not the values themselves
+ The skew of a clock is not so much an additional issue as it is
realization of the fact that Tsynch is itself a function of time
Thus, if we attempt to measure or to bound Tsynch, this needs
be done periodically. Over some periods of time, this
can be approximated as a linear function plus some higher
terms; in these cases, one option is to use knowledge of
linear component to correct the clock. Using this correction,
residual Tsynch is made smaller, but remains a source uncertainty that must be accounted for. We use the
Esynch(t) to denote an upper bound on the uncertainty synchronization. Thus, |Tsynch(t)| <= Esynch(t).
RFC 2679 A One-way Delay Metric for IPPM September 1999
3.7.2. Errors or uncertainties related to Wire-time vs Host-
As we have defined one-way delay, we would like to measure the
between when the test packet leaves the network interface of Src
when it (completely) arrives at the network interface of Dst, and
refer to these as "wire times." If the timings are
performed by software on Src and Dst, however, then this software
only directly measure the time between when Src grabs a
just prior to sending the test packet and when Dst grabs a
just after having received the test packet, and we refer to these
points as "host times".
To the extent that the difference between wire time and host time
accurately known, this knowledge can be used to correct for host
measurements and the corrected value more accurately estimates
desired (wire time) metric
The goal of calibration is to determine the systematic and
error generated by the instruments themselves in as much detail possible. At a minimum, a bound ("e") should be found such that 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
for the measurements. It represents the degree to which the
RFC 2679 A One-way Delay Metric for IPPM September 1999
produced by the measurementinstrument are repeatable; that is,
closely an actual delay of 30 ms is reported as 30 ms. {Comment: 95
percent was chosen because (1) some confidence level is desirable
be able to remove outliers, which will be found in measuring physicalproperty; (2) a particular confidence level should specified so that the results of independent implementations can
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
measurements could be bounded by determining all the
uncertainties, and adding them together to
Esynch(t) + Rsource + Rdest + Hsource + Hdest
However, reasonable bounds on both the clock-related
captured by the first three terms and the host-related
captured by the last two terms should be possible by careful techniques and calibrating the instruments using a known, isolated
network in a lab
For example, the clock-related uncertainties are greatly
through the use of a GPS time source. The sum of Esynch(t) +
+ Rdest is small, and is also bounded for the duration of measurement because of the global time source
The host-related uncertainties, Hsource + Hdest, could be bounded connecting two instruments back-to-back with a high-speed serial
or isolated LAN segment. In this case, repeated measurements
measuring the same one-way delay
If the test packets are small, such a network connection has
minimal delay that may be approximated by zero. The measured thereforecontains only systematic and random error in instrumentation. The "average value" of repeated measurements is
systematic error, and the variation is the random error
One way to compute the systematic error, and the random error to
95% confidence is to repeat the experiment many times - at
hundreds of tests. The systematic error would then be the median
The random error could then be found by removing the systematic
from the measured values. The 95% confidence interval would be
range from the 2.5th percentile to the 97.5th percentile of
deviations from the true value. The calibration error "e" could
be taken to be the largest absolute value of these two numbers,
the clock-related uncertainty. {Comment: as described, this bound
relatively loose since the uncertainties are added, and the
value of the largest deviation is used. As long as the
RFC 2679 A One-way Delay Metric for IPPM September 1999
value is not a significant fraction of the measured values, it is
reasonable bound. If the resulting value is a significant
of the measured values, then more exact methods will be needed
compute the calibration error.}
Note that random error is a function of measurement load.
example, if many paths will be measured by one instrument, this increase interrupts, process scheduling, and disk I/O (for example recording the measurements), all of which may increase the
error in measured singletons. Therefore, in addition to minimal
measurements to find the systematic error, calibration
should be performed with the same measurement load that
instruments will see in the field
We wish to reiterate that this statistical treatment refers to
calibration of the instrument; it is used to "calibrate the
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
were really lost. First, the threshold for loss should be verified
In particular, ensure the "reasonable" threshold is reasonable:
it is very unlikely a packet will arrive after the threshold value
and therefore the number of packets lost over an interval is
sensitive to the error bound on measurements. Second, consider
possibility that a packet arrives at the network interface, but
lost due to congestion on that interface or to other exhaustion (e.g. buffers) in the instrument
The calibration and context in which the metric is measured MUST
carefully considered, and SHOULD always be reported along with
results. We now present four items to consider: the Type-P of
packets, the threshold of infinite delay (if any), error calibration
and the path traversed by the test packets. This list is
exhaustive; any additionalinformation that could be useful
interpreting applications of the metrics should also be reported
3.8.1. Type-
As noted in the Frameworkdocument [1], the value of the metric
depend on the type of IP packets used to make the measurement,
"type-P". The value of Type-P-One-way-Delay could change if protocol (UDP or TCP), port number, size, or arrangement for
treatment (e.g., IP precedence or RSVP) changes. The exact Type-
used to make the measurements MUST be accurately reported
+ If the systematic error can be determined, it SHOULD be
from the measured values
+ You SHOULD also report the calibration error, e, such that
true value is the reported value plus or minus e, with 95%
confidence (see the last section.)
Finally, the path traversed by the packet SHOULD be reported, possible. In general it is impractical to know the precise path
given packet takes through the network. The precise path may
known for certain Type-P on short or stable paths. If Type-
includes the record route (or loose-source route) option in the
header, and the path is short enough, and all routers* on the
support record (or loose-source) route, then the path will
precisely recorded. This is impractical because the route must
short enough, many routers do not support (or are not configured for
record route, and use of this feature would often artificially
the performance observed by removing the packet from common- processing. However, partial information is still valuable context
For example, if a host can choose between two links* (and hence separate routes from Src to Dst), then the initial link used
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 differentbackbonenetworks.}
Given the singleton metric Type-P-One-way-Delay, we now define particular sample of such singletons. The idea of the sample is
select a particular binding of the parameters Src, Dst, and Type-P
then define a sample of values of parameter T. The means defining the values of T is to select a beginning time T0, a
time Tf, and an average rate lambda, then define a pseudo-
RFC 2679 A One-way Delay Metric for IPPM September 1999
Poisson process of rate lambda, whose values fall between T0 and Tf
The time interval between successive values of T will then
1/lambda
{Comment: Note that Poisson sampling is only one way of defining
sample. Poisson has the advantage of limiting bias, but
methods of sampling might be appropriate for different situations
We encourage others who find such appropriate cases to use
general framework and submit their sampling method
standardization.}
+ dT, either a real number or an undefined number of seconds
The values of T in the sequence are monotonic increasing. Note
T would be a valid parameter to Type-P-One-way-Delay, and that
would be a valid value of Type-P-One-way-Delay
Given T0, Tf, and lambda, we compute a pseudo-random Poisson
beginning at or before T0, with average arrival rate lambda,
ending at or after Tf. Those time values greater than or equal to T
and less than or equal to Tf are then selected. At each of the
in this process, we obtain the value of Type-P-One-way-Delay at
time. The value of the sample is the sequence made up of
resulting