This memo defines a metric for round-trip delay of packets Internet paths. It builds on notions introduced and discussed in
IPPM Frameworkdocument, RFC 2330 [1], and follows closely corresponding metric for One-way Delay ("A One-way Delay Metric
IPPM") [2]; the reader is assumed to be familiar with
documents
The memo was largely written by copying material from the One-
Delay metric. The intention is that, where the two metrics
similar, they will be described with similar or identical text,
that where the two metrics differ, new or modified text will be used
This memo is intended to be parallel in structure to a
companion document for Packet Loss
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
+ A 'singleton' analytic metric, called Type-P-Round-trip-Delay
will be introduced to measure a single observation of round-
delay
+ Using this singleton metric, a 'sample', called Type-P-Round-trip
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
1.1.
Round-trip 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
+ 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
On the other hand, the measurement of round-trip delay has specific advantages
+ Ease of interpretation: in some circumstances, the round-trip
is in fact the quantity of interest. Deducing the round-trip
from matching one-way measurements and an assumption of destinationprocessing time is less direct and potentially
accurate
measures the precision of a given clock. For example, the
on an old Unix host might tick only once every 10 msec, and
have a resolution of only 10 msec
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 hour
to UTC, which threatens accuracy. We might also speak of
skew of one clock relative to another clock, which synchronization
For a real number dT, >>the *Type-P-Round-trip-Delay* from Src to
at T is dT<< means that Src sent the first bit of a Type-P packet
Dst at wire-time* T, that Dst received that packet, then
sent a Type-P packet back to Src, and that Src received the last
of that packet at wire-time T+dT
>>The *Type-P-Round-trip-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 (either Dst did
receive the packet, Dst did not send a Type-P packet in response, or
Src did not receive that response packet
>>The *Type-P-Round-trip-Delay between Src and Dst at T<<
either the *Type-P-Round-trip-Delay from Src to Dst at T or
*Type-P-Round-trip-Delay from Dst to Src at T. When this notion
used, it is understood to be specifically ambiguous which host
as Src and which as Dst. {Comment: This ambiguity will usually be
small price to pay for being able to have one measurement,
from either Src or Dst, rather than having two measurements.}
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
+ The timestamp values (T) for the time at which delays are
should be fairly accurate in order to draw meaningful
about the state of the network at a given T. Therefore,
should have an accurate knowledge of time-of-day. NTP [3]
one way to achieve time accuracy to within several milliseconds
Depending on the NTP server, higher accuracy may be achieved,
example when NTP servers make use of GPS systems as a time source
Note that NTP will adjust the instrument's clock. If
adjustment is made between the time the initial timestamp is
and the time the final timestamp is taken the adjustment
affect the uncertainty in the measured delay. This
must be accounted for in the instrument's calibration
RFC 2681 Round-trip for Delay Metric for IPPM September 1999
+ 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
Mahdavi and Paxson [4], simple upper bounds (such as the 255
seconds theoretical upper bound on the lifetimes of
packets [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 so that multiple non-corrupt
of the response arrive back at the source, then the packet
counted as received, and the first instance to arrive back at
source determines the packet's round-trip delay
+ If the packet is fragmented and if, for whatever reason reassembly does not occur, then the packet will be deemed lost
2.6. 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
+ 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. The test packet must
some identifying information so that the response to it can
identified by Src when Src receives the response; one means to
this is by placing the timestampgenerated just before sending
test packet in the packet itself
+ At the Dst host, arrange to receive and respond to the
packet. At the Src host, arrange to receive the response packet
+ If the response packet arrives within a reasonable period of time
take the final timestamp as soon as possible upon the receipt
the packet. By subtracting the two timestamps, an estimate
round-trip delay can be computed. If the delay between
initial 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 analysis. Similarly, if the delay between the actual receipt
the response packet and final timestamp is known, then estimate could be adjusted by subtracting this amount;
in this value must be taken into account in error analysis.
the next section, "Errors and Uncertainties", for a more discussion
+ If the packet fails to arrive within a reasonable period of time
the round-trip delay is taken to be undefined (informally infinite). Note that the threshold of 'reasonable' is a
of the methodology
Issues such as the packet format and the means by which Dst
when to expect the test packet are outside the scope of document
{Comment: Note that you cannot in general add two Type-P-One-way
Delay values (see [2]) to form a Type-P-Round-trip-Delay value.
order to form a Type-P-Round-trip-Delay value, the return packet
be triggered by the reception of a packet from Src.}
{Comment: "ping" would qualify as a round-trip measure under definition, with a Type-P of ICMP echo request/reply with 60-
packets. However, the uncertainties associated with a typical
program must be analyzed as in the next section, including the
of reflecting point (a router may not handle an ICMP request in
fast path) and effects of load on the reflecting point.}
+ Errors or uncertainties due to uncertainty in the clock of the
host
+ Errors or uncertainties due to the difference between 'wire time
and 'host time'.
+ Errors or uncertainties due to time required by the Dst to
the packet from the Src and send the correspondingresponse
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
2.7.1. Errors or Uncertainties Related to
The uncertainty in a measurement of round-trip delay is related,
part, to uncertainty in the clock of the Src host. In the following
we refer to the clock used to measure when the packet was sent
Src as the source clock, and we refer to the observed time when
packet was sent by the source as Tinitial, and the observed time
the packet was received by the source as Tfinal. Alluding to
notions of synchronization, accuracy, resolution, and skew
in the Introduction, we note the following
+ While in one-way delay there is an issue of the synchronization
the source clock and the destination clock, in round-trip
there is an (easier) issue of self-synchronization, as it were
between the source clock at the time the test packet is sent
the (same) source clock at the time the response packet received. Theoretically a very severe case of skew could
this. In practice, the greater threat is anything that
cause a discontinuity in the source clock during the time
the taking of the initial and final timestamp. This might happen
for example, with certain implementations of NTP
+ 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
Taking these items together, we note that naive computation Tfinal
Tinitial will be off by 2*Rsource
2.7.2. Errors or Uncertainties Related to Wire-time vs Host-
As we have defined round-trip delay, we would like to measure
time between when the test packet leaves the network interface of
and when the correspondingresponse packet (completely) arrives
the network interface of Src, and we refer to these as "wire times".
If the timings are themselves performed by software on Src, however
then this software can only directly measure the time between
Src grabs a timestamp just prior to sending the test packet and
it grabs a timestamp just after having received the response packet
and we refer to these two points as "host times".
Another contributor to this problem is time spent at Dst between
receipt there of the test packet and the sending of the
packet. Ideally, this time is zero; it is explored further in
next section
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
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; and (2) a particular confidence level should specified so that the results of independent implementations can
compared.}
From the discussion in the previous three sections, the error
measurements could be bounded by determining all the
uncertainties, and adding them together to
RFC 2681 Round-trip for Delay Metric for IPPM September 1999
However, reasonable bounds on both the clock-related
captured by the first term and the host-related uncertainty
by the last three terms should be possible by careful techniques and calibrating the instruments using a known, isolated
network in a lab
The host-related uncertainties, Hinitial + Hfinal + Hrefl, could
bounded by connecting two instruments back-to-back with a high-
serial link or isolated LAN segment. In this case,
measurements are measuring the same round-trip 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
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
RFC 2681 Round-trip for Delay Metric for IPPM September 1999
In addition to calibrating the instruments for finite delay,
checks should be made to ensure that packets reported as losses
really lost. First, the threshold for loss should be verified. particular, ensure the "reasonable" threshold is reasonable: that
is very unlikely a packet will arrive after the threshold value, 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
2.8.1. 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-Round-trip-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.)
RFC 2681 Round-trip for Delay Metric for IPPM September 1999
2.8.4.
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. For example,
Type-P includes the record route (or loose-source route) option
the IP header, and the path is short enough, and all routers* on
path support record (or loose-source) route, and the Dst host
the path from Src to Dst into the corresponding reply packet,
the path will be precisely recorded. This is impractical because
route must be short enough, many routers do not support (or are configured for) record route, and use of this feature would
artificially worsen the performance observed by removing the
from common-case processing. However, partial information is
valuable context. For example, if a host can choose between
links* (and hence two separate routes from Src to Dst), then
initial link used is valuable context. {Comment: For example,
Merit's NetNow setup, a Src on one NAP can reach a Dst on another
by either of several differentbackbonenetworks.}
Given the singleton metric Type-P-Round-trip-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-
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-Round-trip-Delay, and that
would be a valid value of Type-P-Round-trip-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-Round-trip-Delay
this time. The value of the sample is the sequence made up of
resulting