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rfc:rfc2679

Network Working Group G. Almes Request for Comments: 2679 S. Kalidindi Category: Standards Track M. Zekauskas

                                           Advanced Network & Services
                                                        September 1999
                  A One-way Delay Metric for IPPM

1. Status of this Memo

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

Copyright Notice

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

2. Introduction

 This memo defines a metric for one-way delay of packets across
 Internet paths.  It builds on notions introduced and discussed in the
 IPPM Framework document, RFC 2330 [1]; the reader is assumed to be
 familiar with that document.
 This memo is intended to be parallel in structure to a companion
 document for Packet Loss ("A One-way Packet Loss Metric for IPPM")
 [2].
 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
 document are to be interpreted as described in 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-One-way-Delay, will
    be introduced to measure a single observation of one-way delay.

Almes, et al. Standards Track [Page 1] 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 of
    singleton delays measured at times taken from a Poisson process.
 +  Using this sample, several 'statistics' of the sample will be
    defined and discussed.
 This progression from singleton to sample to statistics, with clear
 separation among them, is important.
 Whenever a technical term from the IPPM Framework document is first
 used in this memo, it will be tagged with a trailing asterisk.  For
 example, "term*" indicates that "term" is defined in the Framework.

2.1. Motivation:

 One-way delay of a Type-P* packet from a source host* to a
 destination host is useful for several reasons:
 +  Some applications do not perform well (or at all) if end-to-end
    delay between hosts is large relative to some threshold value.
 +  Erratic variation in delay makes it difficult (or impossible) to
    support many real-time applications.
 +  The larger the value of delay, the more difficult it is for
    transport-layer protocols to sustain high bandwidths.
 +  The minimum value of this metric provides an indication of the
    delay due only to propagation and transmission delay.
 +  The minimum value of this metric provides an indication of the
    delay that will likely be experienced when the path* traversed is
    lightly loaded.
 +  Values of this metric above the minimum provide an indication of
    the congestion present in the path.
 The measurement of one-way delay instead of round-trip delay is
 motivated by the following factors:
 +  In today's Internet, the path from a source to a destination may
    be different than the path from the destination back to the source
    ("asymmetric paths"), such that different sequences of routers are
    used for the forward and reverse paths.  Therefore round-trip
    measurements actually measure the performance of two distinct
    paths together.  Measuring each path independently highlights the
    performance difference between the two paths which may traverse

Almes, et al. Standards Track [Page 2] RFC 2679 A One-way Delay Metric for IPPM September 1999

    different Internet service providers, and even radically different
    types of networks (for example, research versus commodity
    networks, or ATM versus packet-over-SONET).
 +  Even when the two paths are symmetric, they may have radically
    different performance characteristics due to asymmetric queueing.
 +  Performance of an application may depend mostly on the performance
    in one direction.  For example, a file transfer using TCP may
    depend more on the performance in the direction that data flows,
    rather than the direction in which acknowledgements travel.
 +  In quality-of-service (QoS) enabled networks, provisioning in one
    direction may be radically different than provisioning in the
    reverse direction, and thus the QoS guarantees differ.  Measuring
    the paths independently allows the verification of both
    guarantees.
 It is outside the scope of this document to say precisely how delay
 metrics would be applied to specific problems.

2.2. General Issues Regarding Time

 {Comment: the terminology below differs from that defined by ITU-T
 documents (e.g., G.810, "Definitions and terminology for
 synchronization networks" and I.356, "B-ISDN ATM layer cell transfer
 performance"), but is consistent with the IPPM Framework document.
 In general, these differences derive from the different backgrounds;
 the ITU-T documents historically have a telephony origin, while the
 authors of this document (and the Framework) have a computer systems
 background.  Although the terms defined below have no direct
 equivalent in the ITU-T definitions, after our definitions we will
 provide a rough mapping.  However, note one potential confusion: our
 definition of "clock" is the computer operating systems definition
 denoting a time-of-day clock, while the ITU-T definition of clock
 denotes a frequency reference.}
 Whenever a time (i.e., a moment in history) is mentioned here, it is
 understood to be measured in seconds (and fractions) relative to UTC.
 As described more fully in the Framework document, there are four
 distinct, but related notions of clock uncertainty:

Almes, et al. Standards Track [Page 3] RFC 2679 A One-way Delay Metric for IPPM September 1999

 synchronization*
       measures the extent to which two clocks agree on what time it
       is.  For example, the clock on one host might be 5.4 msec ahead
       of the clock on a second host.  {Comment: A rough ITU-T
       equivalent is "time error".}
 accuracy*
       measures the extent to which a given clock agrees with UTC.
       For example, the clock on a host might be 27.1 msec behind UTC.
       {Comment: A rough ITU-T equivalent is "time error from UTC".}
 resolution*
       measures the precision of a given clock.  For example, the
       clock on an old Unix host might tick only once every 10 msec,
       and thus have a resolution of only 10 msec.  {Comment: A very
       rough ITU-T equivalent is "sampling period".}
 skew*
       measures the change of accuracy, or of synchronization, with
       time.  For example, the clock on a given host might gain 1.3
       msec per hour and thus be 27.1 msec behind UTC at one time and
       only 25.8 msec an hour later.  In this case, we say that the
       clock of the given host has a skew of 1.3 msec per hour
       relative to UTC, which threatens accuracy.  We might also speak
       of the skew of one clock relative to another clock, which
       threatens synchronization.  {Comment: A rough ITU-T equivalent
       is "time drift".}

3. A Singleton Definition for One-way Delay

3.1. Metric Name:

 Type-P-One-way-Delay

3.2. Metric Parameters:

 +  Src, the IP address of a host
 +  Dst, the IP address of a host
 +  T, a time

Almes, et al. Standards Track [Page 4] RFC 2679 A One-way Delay Metric for IPPM September 1999

3.3. Metric Units:

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

3.4. Definition:

 For a real number dT, >>the *Type-P-One-way-Delay* from Src to Dst at
 T is dT<< means that Src sent the first bit of a Type-P packet to Dst
 at wire-time* T and that Dst received the last bit of that packet at
 wire-time T+dT.
 >>The *Type-P-One-way-Delay* from Src to Dst at T is undefined
 (informally, infinite)<< means that Src sent the first bit of a
 Type-P packet to Dst at wire-time T and that Dst did not receive that
 packet.
 Suggestions for what to report along with metric values appear in
 Section 3.8 after a discussion of the metric, methodologies for
 measuring the metric, and error analysis.

3.5. Discussion:

 Type-P-One-way-Delay is a relatively simple analytic metric, and one
 that we believe will afford effective methods of measurement.
 The following issues are likely to come up in practice:
 +  Real delay values will be positive.  Therefore, it does not make
    sense to report a negative value as a real delay.  However, an
    individual zero or negative delay value might be useful as part of
    a stream when trying to discover a distribution of a stream of
    delay values.
 +  Since delay values will often be as low as the 100 usec to 10 msec
    range, it will be important for Src and Dst to synchronize very
    closely.  GPS systems afford one way to achieve synchronization to
    within several 10s of usec.  Ordinary application of NTP may allow
    synchronization to within several msec, but this depends on the
    stability and symmetry of delay properties among those NTP agents
    used, and this delay is what we are trying to measure.  A
    combination of some GPS-based NTP servers and a conservatively
    designed and deployed set of other NTP servers should yield good
    results, but this is yet to be tested.
 +  A given methodology will have to include a way to determine
    whether a delay value is infinite or whether it is merely very
    large (and the packet is yet to arrive at Dst).  As noted by

Almes, et al. Standards Track [Page 5] 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 packets
    [5]) could be used, but good engineering, including an
    understanding of packet lifetimes, will be needed in practice.
    {Comment: Note that, for many applications of these metrics, the
    harm in treating a large delay as infinite might be zero or very
    small.  A TCP data packet, for example, that arrives only after
    several multiples of the RTT may as well have been lost.}
 +  If the packet is duplicated along the path (or paths) so that
    multiple non-corrupt copies arrive at the destination, then the
    packet is counted as received, and the first copy to arrive
    determines the packet's one-way delay.
 +  If the packet is fragmented and if, for whatever reason,
    reassembly does not occur, then the packet will be deemed lost.

3.6. Methodologies:

 As with other Type-P-* metrics, the detailed methodology will depend
 on the Type-P (e.g., protocol number, UDP/TCP port number, size,
 precedence).
 Generally, for a given Type-P, the methodology would proceed as
 follows:
 +  Arrange that Src and Dst are synchronized; that is, that they have
    clocks that are very closely synchronized with each other and each
    fairly close to the actual time.
 +  At the Src host, select Src and Dst IP addresses, and form a test
    packet of Type-P with these addresses.  Any 'padding' portion of
    the packet needed only to make the test packet a given size should
    be filled with randomized bits to avoid a situation in which the
    measured delay is lower than it would otherwise be due to
    compression techniques along the path.
 +  At the Dst host, arrange to receive the packet.
 +  At the Src host, place a timestamp in the prepared Type-P packet,
    and send it towards Dst.
 +  If the packet arrives within a reasonable period of time, take a
    timestamp as soon as possible upon the receipt of the packet.  By
    subtracting the two timestamps, an estimate of one-way delay can
    be computed.  Error analysis of a given implementation of the
    method must take into account the closeness of synchronization
    between Src and Dst.  If the delay between Src's timestamp and the

Almes, et al. Standards Track [Page 6] RFC 2679 A One-way Delay Metric for IPPM September 1999

    actual sending of the packet is known, then the estimate could be
    adjusted by subtracting this amount; uncertainty in this value
    must be taken into account in error analysis.  Similarly, if the
    delay between the actual receipt of the packet and Dst's timestamp
    is known, then the estimate could be adjusted by subtracting this
    amount; uncertainty in this value must be taken into account in
    error analysis.  See the next section, "Errors and Uncertainties",
    for a more detailed discussion.
 +  If the packet fails to arrive within a reasonable period of time,
    the one-way delay is taken to be undefined (informally, infinite).
    Note that the threshold of 'reasonable' is a parameter of the
    methodology.
 Issues such as the packet format, the means by which Dst knows when
 to expect the test packet, and the means by which Src and Dst are
 synchronized are outside the scope of this document.  {Comment: We
 plan to document elsewhere our own work in describing such more
 detailed implementation techniques and we encourage others to as
 well.}

3.7. Errors and Uncertainties:

 The description of any specific measurement method should include an
 accounting and analysis of various sources of error or uncertainty.
 The Framework document provides general guidance on this point, but
 we note here the following specifics related to delay metrics:
 +  Errors or uncertainties due to uncertainties in the clocks of the
    Src and Dst hosts.
 +  Errors or uncertainties due to the difference between 'wire time'
    and 'host time'.
 In addition, the loss threshold may affect the results.  Each of
 these are discussed in more detail below, along with a section
 ("Calibration") on accounting for these errors and uncertainties.

3.7.1. Errors or uncertainties related to Clocks

 The uncertainty in a measurement of one-way delay is related, in
 part, to uncertainties in the clocks of the Src and Dst hosts.  In
 the following, we refer to the clock used to measure when the packet
 was sent from Src as the source clock, we refer to the clock used to
 measure when the packet was received by Dst as the destination clock,
 we refer to the observed time when the packet was sent by the source
 clock as Tsource, and the observed time when the packet was received
 by the destination clock as Tdest.  Alluding to the notions of

Almes, et al. Standards Track [Page 7] RFC 2679 A One-way Delay Metric for IPPM September 1999

 synchronization, accuracy, resolution, and skew mentioned in the
 Introduction, we note the following:
 +  Any error in the synchronization between the source clock and the
    destination clock will contribute to error in the delay
    measurement.  We say that the source clock and the destination
    clock have a synchronization error of Tsynch if the source clock
    is Tsynch ahead of the destination clock.  Thus, if we know the
    value of Tsynch exactly, we could correct for clock
    synchronization by adding Tsynch to the uncorrected value of
    Tdest-Tsource.
 +  The accuracy of a clock is important only in identifying the time
    at which a given delay was measured.  Accuracy, per se, has no
    importance to the accuracy of the measurement of delay.  When
    computing delays, we are interested only in the differences
    between clock values, not the values themselves.
 +  The resolution of a clock adds to uncertainty about any time
    measured with it.  Thus, if the source clock has a resolution of
    10 msec, then this adds 10 msec of uncertainty to any time value
    measured with it.  We will denote the resolution of the source
    clock and the destination clock as Rsource and Rdest,
    respectively.
 +  The skew of a clock is not so much an additional issue as it is a
    realization of the fact that Tsynch is itself a function of time.
    Thus, if we attempt to measure or to bound Tsynch, this needs to
    be done periodically.  Over some periods of time, this function
    can be approximated as a linear function plus some higher order
    terms; in these cases, one option is to use knowledge of the
    linear component to correct the clock.  Using this correction, the
    residual Tsynch is made smaller, but remains a source of
    uncertainty that must be accounted for.  We use the function
    Esynch(t) to denote an upper bound on the uncertainty in
    synchronization.  Thus, |Tsynch(t)| <= Esynch(t).
 Taking these items together, we note that naive computation Tdest-
 Tsource will be off by Tsynch(t) +/- (Rsource + Rdest).  Using the
 notion of Esynch(t), we note that these clock-related problems
 introduce a total uncertainty of Esynch(t)+ Rsource + Rdest.  This
 estimate of total clock-related uncertainty should be included in the
 error/uncertainty analysis of any measurement implementation.

Almes, et al. Standards Track [Page 8] RFC 2679 A One-way Delay Metric for IPPM September 1999

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

 As we have defined one-way delay, we would like to measure the time
 between when the test packet leaves the network interface of Src and
 when it (completely) arrives at the network interface of Dst, and we
 refer to these as "wire times."  If the timings are themselves
 performed by software on Src and Dst, however, then this software can
 only directly measure the time between when Src grabs a timestamp
 just prior to sending the test packet and when Dst grabs a timestamp
 just after having received the test packet, and we refer to these two
 points as "host times".
 To the extent that the difference between wire time and host time is
 accurately known, this knowledge can be used to correct for host time
 measurements and the corrected value more accurately estimates the
 desired (wire time) metric.
 To the extent, however, that the difference between wire time and
 host time is uncertain, this uncertainty must be accounted for in an
 analysis of a given measurement method.  We denote by Hsource an
 upper bound on the uncertainty in the difference between wire time
 and host time on the Src host, and similarly define Hdest for the Dst
 host.  We then note that these problems introduce a total uncertainty
 of Hsource+Hdest.  This estimate of total wire-vs-host uncertainty
 should be included in the error/uncertainty analysis of any
 measurement implementation.

3.7.3. Calibration

 Generally, the measured values can be decomposed as follows:
    measured value = true value + systematic error + random error
 If the systematic error (the constant bias in measured values) can be
 determined, it can be compensated for in the reported results.
    reported value = measured value - systematic error
 therefore
    reported value = true value + random error
 The goal of calibration is to determine the systematic and random
 error generated by the instruments themselves in as much detail as
 possible.  At a minimum, a bound ("e") should be found such that the
 reported value is in the range (true value - e) to (true value + e)
 at least 95 percent of the time.  We call "e" the calibration error
 for the measurements.  It represents the degree to which the values

Almes, et al. Standards Track [Page 9] RFC 2679 A One-way Delay Metric for IPPM September 1999

 produced by the measurement instrument are repeatable; that is, how
 closely an actual delay of 30 ms is reported as 30 ms.  {Comment: 95
 percent was chosen because (1) some confidence level is desirable to
 be able to remove outliers, which will be found in measuring any
 physical property; (2) a particular confidence level should be
 specified so that the results of independent implementations can be
 compared; and (3) even with a prototype user-level implementation,
 95% was loose enough to exclude outliers.}
 From the discussion in the previous two sections, the error in
 measurements could be bounded by determining all the individual
 uncertainties, and adding them together to form
     Esynch(t) + Rsource + Rdest + Hsource + Hdest.
 However, reasonable bounds on both the clock-related uncertainty
 captured by the first three terms and the host-related uncertainty
 captured by the last two terms should be possible by careful design
 techniques and calibrating the instruments using a known, isolated,
 network in a lab.
 For example, the clock-related uncertainties are greatly reduced
 through the use of a GPS time source.  The sum of Esynch(t) + Rsource
 + Rdest is small, and is also bounded for the duration of the
 measurement because of the global time source.
 The host-related uncertainties, Hsource + Hdest, could be bounded by
 connecting two instruments back-to-back with a high-speed serial link
 or isolated LAN segment.  In this case, repeated measurements are
 measuring the same one-way delay.
 If the test packets are small, such a network connection has a
 minimal delay that may be approximated by zero.  The measured delay
 therefore contains only systematic and random error in the
 instrumentation.  The "average value" of repeated measurements is the
 systematic error, and the variation is the random error.
 One way to compute the systematic error, and the random error to a
 95% confidence is to repeat the experiment many times - at least
 hundreds of tests.  The systematic error would then be the median.
 The random error could then be found by removing the systematic error
 from the measured values.  The 95% confidence interval would be the
 range from the 2.5th percentile to the 97.5th percentile of these
 deviations from the true value.  The calibration error "e" could then
 be taken to be the largest absolute value of these two numbers, plus
 the clock-related uncertainty.  {Comment: as described, this bound is
 relatively loose since the uncertainties are added, and the absolute
 value of the largest deviation is used.  As long as the resulting

Almes, et al. Standards Track [Page 10] RFC 2679 A One-way Delay Metric for IPPM September 1999

 value is not a significant fraction of the measured values, it is a
 reasonable bound.  If the resulting value is a significant fraction
 of the measured values, then more exact methods will be needed to
 compute the calibration error.}
 Note that random error is a function of measurement load.  For
 example, if many paths will be measured by one instrument, this might
 increase interrupts, process scheduling, and disk I/O (for example,
 recording the measurements), all of which may increase the random
 error in measured singletons.  Therefore, in addition to minimal load
 measurements to find the systematic error, calibration measurements
 should be performed with the same measurement load that the
 instruments will see in the field.
 We wish to reiterate that this statistical treatment refers to the
 calibration of the instrument; it is used to "calibrate the meter
 stick" and say how well the meter stick reflects reality.
 In addition to calibrating the instruments for finite one-way delay,
 two checks should be made to ensure that packets reported as losses
 were really lost.  First, the threshold for loss should be verified.
 In particular, ensure the "reasonable" threshold is reasonable: that
 it is very unlikely a packet will arrive after the threshold value,
 and therefore the number of packets lost over an interval is not
 sensitive to the error bound on measurements.  Second, consider the
 possibility that a packet arrives at the network interface, but is
 lost due to congestion on that interface or to other resource
 exhaustion (e.g. buffers) in the instrument.

3.8. Reporting the metric:

 The calibration and context in which the metric is measured MUST be
 carefully considered, and SHOULD always be reported along with metric
 results.  We now present four items to consider: the Type-P of test
 packets, the threshold of infinite delay (if any), error calibration,
 and the path traversed by the test packets.  This list is not
 exhaustive; any additional information that could be useful in
 interpreting applications of the metrics should also be reported.

3.8.1. Type-P

 As noted in the Framework document [1], the value of the metric may
 depend on the type of IP packets used to make the measurement, or
 "type-P".  The value of Type-P-One-way-Delay could change if the
 protocol (UDP or TCP), port number, size, or arrangement for special
 treatment (e.g., IP precedence or RSVP) changes.  The exact Type-P
 used to make the measurements MUST be accurately reported.

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3.8.2. Loss threshold

 In addition, the threshold (or methodology to distinguish) between a
 large finite delay and loss MUST be reported.

3.8.3. Calibration results

 +  If the systematic error can be determined, it SHOULD be removed
    from the measured values.
 +  You SHOULD also report the calibration error, e, such that the
    true value is the reported value plus or minus e, with 95%
    confidence (see the last section.)
 +  If possible, the conditions under which a test packet with finite
    delay is reported as lost due to resource exhaustion on the
    measurement instrument SHOULD be reported.

3.8.4. Path

 Finally, the path traversed by the packet SHOULD be reported, if
 possible.  In general it is impractical to know the precise path a
 given packet takes through the network.  The precise path may be
 known for certain Type-P on short or stable paths.  If Type-P
 includes the record route (or loose-source route) option in the IP
 header, and the path is short enough, and all routers* on the path
 support record (or loose-source) route, then the path will be
 precisely recorded.  This is impractical because the route must be
 short enough, many routers do not support (or are not configured for)
 record route, and use of this feature would often artificially worsen
 the performance observed by removing the packet from common-case
 processing.  However, partial information is still valuable context.
 For example, if a host can choose between two links* (and hence two
 separate routes from Src to Dst), then the initial link used is
 valuable context.  {Comment: For example, with Merit's NetNow setup,
 a Src on one NAP can reach a Dst on another NAP by either of several
 different backbone networks.}

4. A Definition for Samples of One-way Delay

 Given the singleton metric Type-P-One-way-Delay, we now define one
 particular sample of such singletons.  The idea of the sample is to
 select a particular binding of the parameters Src, Dst, and Type-P,
 then define a sample of values of parameter T.  The means for
 defining the values of T is to select a beginning time T0, a final
 time Tf, and an average rate lambda, then define a pseudo-random

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 Poisson process of rate lambda, whose values fall between T0 and Tf.
 The time interval between successive values of T will then average
 1/lambda.
 {Comment: Note that Poisson sampling is only one way of defining a
 sample.  Poisson has the advantage of limiting bias, but other
 methods of sampling might be appropriate for different situations.
 We encourage others who find such appropriate cases to use this
 general framework and submit their sampling method for
 standardization.}

4.1. Metric Name:

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

4.2. Metric Parameters:

 +  Src, the IP address of a host
 +  Dst, the IP address of a host
 +  T0, a time
 +  Tf, a time
 +  lambda, a rate in reciprocal seconds

4.3. Metric Units:

 A sequence of pairs; the elements of each pair are:
 +  T, a time, and
 +  dT, either a real number or an undefined number of seconds.
 The values of T in the sequence are monotonic increasing.  Note that
 T would be a valid parameter to Type-P-One-way-Delay, and that dT
 would be a valid value of Type-P-One-way-Delay.

4.4. Definition:

 Given T0, Tf, and lambda, we compute a pseudo-random Poisson process
 beginning at or before T0, with average arrival rate lambda, and
 ending at or after Tf.  Those time values greater than or equal to T0
 and less than or equal to Tf are then selected.  At each of the times
 in this process, we obtain the value of Type-P-One-way-Delay at this
 time.  The value of the sample is the sequence made up of the
 resulting <time, delay> pairs.  If there are no such pairs, the

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

4.5. Discussion:

 The reader should be familiar with the in-depth discussion of Poisson
 sampling in the Framework document [1], which includes methods to
 compute and verify the pseudo-random Poisson process.
 We specifically do not constrain the value of lambda, except to note
 the extremes.  If the rate is too large, then the measurement traffic
 will perturb the network, and itself cause congestion.  If the rate
 is too small, then you might not capture interesting network
 behavior.  {Comment: We expect to document our experiences with, and
 suggestions for, lambda elsewhere, culminating in a "best current
 practices" document.}
 Since a pseudo-random number sequence is employed, the sequence of
 times, and hence the value of the sample, is not fully specified.
 Pseudo-random number generators of good quality will be needed to
 achieve the desired qualities.
 The sample is defined in terms of a Poisson process both to avoid the
 effects of self-synchronization and also capture a sample that is
 statistically as unbiased as possible.  {Comment: there is, of
 course, no claim that real Internet traffic arrives according to a
 Poisson arrival process.}  The Poisson process is used to schedule
 the delay measurements.  The test packets will generally not arrive
 at Dst according to a Poisson distribution, since they are influenced
 by the network.
 All the singleton Type-P-One-way-Delay metrics in the sequence will
 have the same values of Src, Dst, and Type-P.
 Note also that, given one sample that runs from T0 to Tf, and given
 new time values T0' and Tf' such that T0 <= T0' <= Tf' <= Tf, the
 subsequence of the given sample whose time values fall between T0'
 and Tf' are also a valid Type-P-One-way-Delay-Poisson-Stream sample.

4.6. Methodologies:

 The methodologies follow directly from:
 +  the selection of specific times, using the specified Poisson
    arrival process, and
 +  the methodologies discussion already given for the singleton
    Type-P-One-way-Delay metric.

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 Care must, of course, be given to correctly handle out-of-order
 arrival of test packets; it is possible that the Src could send one
 test packet at TS[i], then send a second one (later) at TS[i+1],
 while the Dst could receive the second test packet at TR[i+1], and
 then receive the first one (later) at TR[i].

4.7. Errors and Uncertainties:

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

4.8. Reporting the metric:

 You MUST report the calibration and context for the underlying
 singletons along with the stream.  (See "Reporting the metric" for
 Type-P-One-way-Delay.)

5. Some Statistics Definitions for One-way Delay

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

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

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

Almes, et al. Standards Track [Page 15] RFC 2679 A One-way Delay Metric for IPPM September 1999

 Example: suppose we take a sample and the results are:
    Stream1 = <
    <T1, 100 msec>
    <T2, 110 msec>
    <T3, undefined>
    <T4, 90 msec>
    <T5, 500 msec>
    >
 Then the 50th percentile would be 110 msec, since 90 msec and 100
 msec are smaller and 110 msec and 'undefined' are larger.
 Note that if the possibility that a packet with finite delay is
 reported as lost is significant, then a high percentile (90th or
 95th) might be reported as infinite instead of finite.

5.2. Type-P-One-way-Delay-Median

 Given a Type-P-One-way-Delay-Poisson-Stream, the median of all the dT
 values in the Stream.  In computing the median, undefined values are
 treated as infinitely large.  As with Type-P-One-way-Delay-
 Percentile, Type-P-One-way-Delay-Median is undefined if the sample is
 empty.
 As noted in the Framework document, the median differs from the 50th
 percentile only when the sample contains an even number of values, in
 which case the mean of the two central values is used.
 Example: suppose we take a sample and the results are:
 Stream2 = <
    <T1, 100 msec>
    <T2, 110 msec>
    <T3, undefined>
    <T4, 90 msec>
    >
 Then the median would be 105 msec, the mean of 100 msec and 110 msec,
 the two central values.

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

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

Almes, et al. Standards Track [Page 16] RFC 2679 A One-way Delay Metric for IPPM September 1999

 undefined if the sample is empty.
 In the above example, the minimum would be 90 msec.

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

 Given a Type-P-One-way-Delay-Poisson-Stream and a time duration
 threshold, the fraction of all the dT values in the Stream less than
 or equal to the threshold.  The result could be as low as 0% (if all
 the dT values exceed threshold) or as high as 100%.  Type-P-One-way-
 Delay-Inverse-Percentile is undefined if the sample is empty.
 In the above example, the Inverse-Percentile of 103 msec would be
 50%.

6. Security Considerations

 Conducting Internet measurements raises both security and privacy
 concerns.  This memo does not specify an implementation of the
 metrics, so it does not directly affect the security of the Internet
 nor of applications which run on the Internet.  However,
 implementations of these metrics must be mindful of security and
 privacy concerns.
 There are two types of security concerns: potential harm caused by
 the measurements, and potential harm to the measurements.  The
 measurements could cause harm because they are active, and inject
 packets into the network.  The measurement parameters MUST be
 carefully selected so that the measurements inject trivial amounts of
 additional traffic into the networks they measure.  If they inject
 "too much" traffic, they can skew the results of the measurement, and
 in extreme cases cause congestion and denial of service.
 The measurements themselves could be harmed by routers giving
 measurement traffic a different priority than "normal" traffic, or by
 an attacker injecting artificial measurement traffic.  If routers can
 recognize measurement traffic and treat it separately, the
 measurements will not reflect actual user traffic.  If an attacker
 injects artificial traffic that is accepted as legitimate, the loss
 rate will be artificially lowered.  Therefore, the measurement
 methodologies SHOULD include appropriate techniques to reduce the
 probability measurement traffic can be distinguished from "normal"
 traffic.  Authentication techniques, such as digital signatures, may
 be used where appropriate to guard against injected traffic attacks.
 The privacy concerns of network measurement are limited by the active
 measurements described in this memo.  Unlike passive measurements,
 there can be no release of existing user data.

Almes, et al. Standards Track [Page 17] RFC 2679 A One-way Delay Metric for IPPM September 1999

7. Acknowledgements

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

8. References

 [1]  Paxson, V., Almes, G., Mahdavi, J. and M. Mathis, "Framework for
      IP Performance Metrics", RFC 2330, May 1998.
 [2]  Almes, G., Kalidindi, S. and M. Zekauskas, "A One-way Packet
      Loss Metric for IPPM", RFC 2680, 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.
 [7]  Bradner, S., "The Internet Standards Process -- Revision 3", BCP
      9, RFC 2026, October 1996.

Almes, et al. Standards Track [Page 18] RFC 2679 A One-way Delay Metric for IPPM September 1999

9. Authors' Addresses

 Guy Almes
 Advanced Network & Services, Inc.
 200 Business Park Drive
 Armonk, NY  10504
 USA
 Phone: +1 914 765 1120
 EMail: almes@advanced.org
 Sunil Kalidindi
 Advanced Network & Services, Inc.
 200 Business Park Drive
 Armonk, NY  10504
 USA
 Phone: +1 914 765 1128
 EMail: kalidindi@advanced.org
 Matthew J. Zekauskas
 Advanced Network & Services, Inc.
 200 Business Park Drive
 Armonk, NY 10504
 USA
 Phone: +1 914 765 1112
 EMail: matt@advanced.org

Almes, et al. Standards Track [Page 19] RFC 2679 A One-way Delay Metric for IPPM September 1999

10. Full Copyright Statement

 Copyright (C) The Internet Society (1999).  All Rights Reserved.
 This document and translations of it may be copied and furnished to
 others, and derivative works that comment on or otherwise explain it
 or assist in its implementation may be prepared, copied, published
 and distributed, in whole or in part, without restriction of any
 kind, provided that the above copyright notice and this paragraph are
 included on all such copies and derivative works.  However, this
 document itself may not be modified in any way, such as by removing
 the copyright notice or references to the Internet Society or other
 Internet organizations, except as needed for the purpose of
 developing Internet standards in which case the procedures for
 copyrights defined in the Internet Standards process must be
 followed, or as required to translate it into languages other than
 English.
 The limited permissions granted above are perpetual and will not be
 revoked by the Internet Society or its successors or assigns.
 This document and the information contained herein is provided on an
 "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
 TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
 BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
 HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
 MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

Acknowledgement

 Funding for the RFC Editor function is currently provided by the
 Internet Society.

Almes, et al. Standards Track [Page 20]

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