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rfc:rfc2681

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.

Almes, et al. Standards Track [Page 1] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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.

Almes, et al. Standards Track [Page 2] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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:

Almes, et al. Standards Track [Page 3] RFC 2681 Round-trip for 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.
 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.

Almes, et al. Standards Track [Page 4] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

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.

Almes, et al. Standards Track [Page 5] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 +  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.

Almes, et al. Standards Track [Page 6] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 +  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.}

Almes, et al. Standards Track [Page 7] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

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.

Almes, et al. Standards Track [Page 8] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 +  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

Almes, et al. Standards Track [Page 9] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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.

Almes, et al. Standards Track [Page 10] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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.

Almes, et al. Standards Track [Page 11] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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.

Almes, et al. Standards Track [Page 12] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

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

Almes, et al. Standards Track [Page 13] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

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 seconds

3.3. 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.}

Almes, et al. Standards Track [Page 14] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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

Almes, et al. Standards Track [Page 15] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 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.

Almes, et al. Standards Track [Page 16] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

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%.

Almes, et al. Standards Track [Page 17] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

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.

Almes, et al. Standards Track [Page 18] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

 [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

Almes, et al. Standards Track [Page 19] RFC 2681 Round-trip for Delay Metric for IPPM September 1999

9. 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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