RFC 2681
A Round-trip Delay Metric for IPPM
Network Working Group G. Almes Request for Comments: 2681 S. Kalidindi Category: Standards Track M. Zekauskas Advanced Network & Services September 1999 A Round-trip Delay Metric for IPPM 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.1. Introduction
This memo defines a metric for round-trip delay of packets across Internet paths. It builds on notions introduced and discussed in the IPPM Framework document, RFC 2330 [1], and follows closely the corresponding metric for One-way Delay ("A One-way Delay Metric for IPPM") [2]; the reader is assumed to be familiar with those documents. The memo was largely written by copying material from the One-way Delay metric. The intention is that, where the two metrics are similar, they will be described with similar or identical text, and that where the two metrics differ, new or modified text will be used. This memo is intended to be parallel in structure to a future companion document for Packet Loss. 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 RFC 2119 [6]. Although RFC 2119 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-Round-trip-Delay,
will be introduced to measure a single observation of round-trip
delay.
+ Using this singleton metric, a 'sample', called Type-P-Round-trip-
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.
1.1. Motivation
Round-trip 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 interactive 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 round-trip delay instead of one-way delay has
several weaknesses, summarized here:
+ The Internet path from a source to a destination may differ from
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.
+ 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.
+ 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.
On the other hand, the measurement of round-trip delay has two
specific advantages:
+ Ease of deployment: unlike in one-way measurement, it is often
possible to perform some form of round-trip delay measurement
without installing measurement-specific software at the intended
destination. A variety of approaches are well-known, including
use of ICMP Echo or of TCP-based methodologies (similar to those
outlined in "IPPM Metrics for Measuring Connectivity" [4]).
However, some approaches may introduce greater uncertainty in the
time for the destination to produce a response (see
Section 2.7.3).
+ Ease of interpretation: in some circumstances, the round-trip time
is in fact the quantity of interest. Deducing the round-trip time
from matching one-way measurements and an assumption of the
destination processing time is less direct and potentially less
accurate.
1.2. 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.
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, which threatens accuracy. We might also speak of the
skew of one clock relative to another clock, which threatens
synchronization.
2. A Singleton Definition for Round-trip Delay
2.1. Metric Name:
Type-P-Round-trip-Delay
2.2. Metric Parameters:
+ Src, the IP address of a host
+ Dst, the IP address of a host
+ T, a time
2.3. Metric Units:
The value of a Type-P-Round-trip-Delay is either a real number, or an
undefined (informally, infinite) number of seconds.
2.4. Definition:
For a real number dT, >>the *Type-P-Round-trip-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, that Dst received that packet, then immediately sent a Type-P packet back to Src, and that Src received the last bit of that packet at wire-time T+dT. >>The *Type-P-Round-trip-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 (either Dst did not 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<< means either the *Type-P-Round-trip-Delay from Src to Dst at T or the *Type-P-Round-trip-Delay from Dst to Src at T. When this notion is used, it is understood to be specifically ambiguous which host acts as Src and which as Dst. {Comment: This ambiguity will usually be a small price to pay for being able to have one measurement, launched from either Src or Dst, rather than having two measurements.} 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.2.5. Discussion:
Type-P-Round-trip-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: + The timestamp values (T) for the time at which delays are measured should be fairly accurate in order to draw meaningful conclusions about the state of the network at a given T. Therefore, Src should have an accurate knowledge of time-of-day. NTP [3] affords one way to achieve time accuracy to within several milliseconds. Depending on the NTP server, higher accuracy may be achieved, for example when NTP servers make use of GPS systems as a time source. Note that NTP will adjust the instrument's clock. If an adjustment is made between the time the initial timestamp is taken and the time the final timestamp is taken the adjustment will affect the uncertainty in the measured delay. This uncertainty must be accounted for in the instrument's calibration.
+ 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 so that multiple non-corrupt instances
of the response arrive back at the source, then the packet is
counted as received, and the first instance to arrive back at the
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 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:
+ 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. The test packet must have
some identifying information so that the response to it can be
identified by Src when Src receives the response; one means to do
this is by placing the timestamp generated just before sending the
test packet in the packet itself.
+ At the Dst host, arrange to receive and respond to the test
packet. At the Src host, arrange to receive the corresponding
response packet.
+ At the Src host, take the initial timestamp and then send the
prepared Type-P packet towards Dst. Note that the timestamp could
be placed inside the packet, or kept separately as long as the
packet contains a suitable identifier so the received timestamp
can be compared with the send timestamp.
+ If the packet arrives at Dst, send a corresponding response packet
back from Dst to Src as soon as possible.
+ If the response packet arrives within a reasonable period of time,
take the final timestamp as soon as possible upon the receipt of
the packet. By subtracting the two timestamps, an estimate of
round-trip delay can be computed. If the delay between the
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 error
analysis. Similarly, if the delay between the actual receipt of
the response packet and final 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 round-trip 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 and the means by which Dst knows
when to expect the test packet are outside the scope of this
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. In
order to form a Type-P-Round-trip-Delay value, the return packet must
be triggered by the reception of a packet from Src.}
{Comment: "ping" would qualify as a round-trip measure under this
definition, with a Type-P of ICMP echo request/reply with 60-byte
packets. However, the uncertainties associated with a typical ping
program must be analyzed as in the next section, including the type
of reflecting point (a router may not handle an ICMP request in the
fast path) and effects of load on the reflecting point.}
2.7. 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 uncertainty in the clock of the Src 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 receive the packet from the Src and send the corresponding response. 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.2.7.1. Errors or Uncertainties Related to Clocks
The uncertainty in a measurement of round-trip delay is related, in 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 from Src as the source clock, and we refer to the observed time when the packet was sent by the source as Tinitial, and the observed time when the packet was received by the source as Tfinal. Alluding to the notions of synchronization, accuracy, resolution, and skew mentioned in the Introduction, we note the following: + While in one-way delay there is an issue of the synchronization of the source clock and the destination clock, in round-trip delay there is an (easier) issue of self-synchronization, as it were, between the source clock at the time the test packet is sent and the (same) source clock at the time the response packet is received. Theoretically a very severe case of skew could threaten this. In practice, the greater threat is anything that would cause a discontinuity in the source clock during the time between 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 time at which a given delay was measured. Accuracy, per se, has no importance to the accuracy of the measurement of delay.
+ 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 as Rsource.
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-time
As we have defined round-trip delay, we would like to measure the
time between when the test packet leaves the network interface of Src
and when the corresponding response packet (completely) arrives at
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 when
Src grabs a timestamp just prior to sending the test packet and when
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 the
receipt there of the test packet and the sending of the response
packet. Ideally, this time is zero; it is explored further in the
next section.
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 Hinitial an
upper bound on the uncertainty in the difference between wire time
and host time on the Src host in sending the test packet, and
similarly define Hfinal for the difference on the Src host in
receiving the response packet. We then note that these problems
introduce a total uncertainty of Hinitial + Hfinal. This estimate of
total wire-vs-host uncertainty should be included in the
error/uncertainty analysis of any measurement implementation.
2.7.3. Errors or Uncertainties Related to Dst Producing a Response
Any time spent by the destination host in receiving and recognizing
the packet from Src, and then producing and sending the corresponding
response adds additional error and uncertainty to the round-trip
delay measurement. The error equals the difference between the wire
time the first bit of the packet is received by Dst and the wire time the first bit of the response is sent by Dst. To the extent that this difference is accurately known, this knowledge can be used to correct the desired metric. To the extent, however, that this difference is uncertain, this uncertainty must be accounted for in the error analysis of a measurement implementation. We denote this uncertainty by Hrefl. This estimate of uncertainty should be included in the error/uncertainty analysis of any measurement implementation.2.7.4. 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; and (2) a particular confidence level should be specified so that the results of independent implementations can be compared.} From the discussion in the previous three sections, the error in measurements could be bounded by determining all the individual uncertainties, and adding them together to form 2*Rsource + Hinitial + Hfinal + Hrefl.
However, reasonable bounds on both the clock-related uncertainty
captured by the first term and the host-related uncertainty captured
by the last three terms should be possible by careful design
techniques and calibrating the instruments using a known, isolated,
network in a lab.
The host-related uncertainties, Hinitial + Hfinal + Hrefl, 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 round-trip 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 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.2.8. 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.2.8.1. 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-Round-trip-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.2.8.2. Loss threshold
In addition, the threshold (or methodology to distinguish) between a large finite delay and loss MUST be reported.2.8.3. 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.
2.8.4. 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. For example, 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, and the Dst host copies the path from Src to Dst into the corresponding reply packet, 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.}3. A Definition for Samples of Round-trip Delay
Given the singleton metric Type-P-Round-trip-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.}3.1. Metric Name:
Type-P-Round-trip-Delay-Poisson-Stream
3.2. 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 seconds3.3. 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-Round-trip-Delay, and that dT would be a valid value of Type-P-Round-trip-Delay.3.4. 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-Round-trip-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.3.5. 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, nor will response packets
arrive at Src according to a Poisson distribution, since they are
influenced by the network.
All the singleton Type-P-Round-trip-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-Round-trip-Delay-Poisson-Stream
sample.
3.6. 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-Round-trip-Delay metric.
Care must, of course, be given to correctly handle out-of-order
arrival of test or response packets; it is possible that the Src
could send one test packet at TS[i], then send a second test packet
(later) at TS[i+1], and it could receive the second response packet
at TR[i+1], and then receive the first response packet (later) at
TR[i].
3.7. 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 Hinitial (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.}
3.8. 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-Round-trip-Delay.)
4. Some Statistics Definitions for Round-trip Delay
Given the sample metric Type-P-Round-trip-Delay-Poisson-Stream, we
now offer several statistics of that sample. These statistics are
offered mostly to be illustrative of what could be done.
4.1. Type-P-Round-trip-Delay-Percentile
Given a Type-P-Round-trip-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-
Round-trip-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.
4.2. Type-P-Round-trip-Delay-Median
Given a Type-P-Round-trip-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-Round-trip-Delay- Percentile, Type-P-Round-trip-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.4.3. Type-P-Round-trip-Delay-Minimum
Given a Type-P-Round-trip-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-Round-trip-Delay-Minimum is undefined if the sample is empty. In the above example, the minimum would be 90 msec.4.4. Type-P-Round-trip-Delay-Inverse-Percentile
Given a Type-P-Round-trip-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-Round- trip-Delay-Inverse-Percentile is undefined if the sample is empty. In the above example, the Inverse-Percentile of 103 msec would be 50%.
5. 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.6. Acknowledgements
Special thanks are due to Vern Paxson and to Will Leland for several useful suggestions.7. References
[1] Paxson, D., Almes, G., Mahdavi, J. and M. Mathis, "Framework for IP Performance Metrics", RFC 2330, May 1998. [2] Almes, G., Kalidindi,S. and M. Zekauskas, "A One-way Delay Metric for IPPM", RFC 2679, September 1999. [3] Mills, D., "Network Time Protocol (v3)", RFC 1305, April 1992.
[4] Mahdavi, J. and V. Paxson, "IPPM Metrics for Measuring Connectivity", RFC 2678, September 1999. [5] Postel, J., "Internet Protocol", STD 5, RFC 791, September 1981. [6] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997.8. 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
9. Full Copyright Statement
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