Network Working Group              G. Almes, Advanced Network & Services
Internet Draft                 S. Kalidindi, Advanced Network & Services
Expiration Date: May September 1997                               March 1997                                  November 1996

                    A One-way Delay Metric for IPPM
                  <draft-ietf-bmwg-ippm-delay-00.txt>
                  <draft-ietf-bmwg-ippm-delay-01.txt>

1. Status of this Memo

   This document is an Internet Draft.  Internet Drafts are working doc-
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   ftp.isi.edu (US West Coast).

   This memo provides information for the Internet community.  This memo
   does  not  specify an Internet standard of any kind.  Distribution of
   this memo is unlimited.

2. Introduction

   This memo defines a metric for one-way delay of packets across Inter-
   net paths.  It builds on notions introduced and discussed in the
   revised IPPM
   Framework document (currently   <draft-almes-ippm-
   framework-01.txt>); "Framework  for  IP  Provider  Metrics"
   <draft-ietf-bmwg-ippm-framework-00.txt>); the reader is assumed to be
   familiar with that document.  {Comment: The revised document, which

   This memo is being  edited  in intended to be very parallel with the present document, introduces the notion of 'type-P'
   packets, develops some notions of clock uncertainties, develops  some
   notions of measurement calibration, and develops some techniques use-
   ful in structure to a companion
   document for statistics.} Packet Loss (soon to be submitted as "A Packet Loss Met-
   ric for IPPM" <draft-ietf-bmwg-ippm-loss-00.txt>).

   The structure of the memo is as follows:

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 +    A 'singleton' analytic metric, called  Type-P-One-way-Delay,  will
      be introduced to measure a single observation of one-way delay.
 +    Using  this  singleton  metric, a 'sample', called Type-P-One-way-
      Delay-Stream, will be introduced to measure a sequence of  single-
      ton 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.  {Comment: In fact, it might be
   wise to make them separate documents in the future.}

   Whenever a technical term from the IPPM Framework document  is  first
   used  in  this  memo,  it will be tagged with a trailing asterisk, as
   with >>term*<<.

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 trans-
      port-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.
   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

   Whenever  a time (i.e., a moment in history) is mentioned here, it is
   understood to be measured in seconds relative to 0000 UT on 1 January
   1900.   {Comment: times will thus be commensurate with NTP timestamps
   [Mills: RFC 1305].}

   As described more fully in the (revised) Framework  document,  there  are  four
   distinct, but related notions of clock uncertainty:

ID                        One-way Delay Metric             November 1996                March 1997

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, and this threatens
     accuracy.  We might also speak of the skew of one clock relative to
     another clock, and this threatens synchronization.

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
 +    First-hop,    Path, the IP address of the first hop router on the path path* from Src to Dst; this optional parameter defaults to the router one hop
      from Src whenever in cases where there is in fact only  one such router
      path from Src to Dst, this optional parameter can be omitted
   {Comment:  the  presence  of first-hop  path is motivated by cases such as with
   Merit's NetNow setup, in which a Src on one NAP can reach  a  Dst  on
   another NAP by either of several different backbone networks.
   Generally,  Gener-
   ally, this optional step parameter is useful only when  several  different
   routes are possible from Src to Dst and determining Dst.  Using the first hop can effec-
   tively  choose  among  them.  The more flexible loose source route IP
   option is avoided since it would often artificially worsen  the  per-
   formance  observed,  and  since  it might not be supported along some
   paths.}

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3.3. Metric Units:

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

3.4. Definition:

   For  a non-negative real number dT, >>the *Type-P-One-way-Delay* from
   Src to Dst at T [via first-hop] path] is dT<<  means  that  Src  sent  a  type-P
   packet  [via  first-hop] path] to Dst at time T and that Dst received that packet
   at time T+dT.

   >>The *Type-P-One-way-Delay* from Src to Dst at T [via first-hop] path] is
   undefined unde-
   fined  (informally,  infinite)<<  means that Src sent a type-P packet
   [via first-hop] path] to Dst at time T and that Dst did not receive that packet.

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:
 +    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 combina-
      tion  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 Mah-
      davi and Paxson, simple upper bounds (such as the 255 seconds the-
      oretical  upper  bound on the lifetimes of IP packets [Postel: RFC
      791]) could be used, but good  engineering,  including  an  under-
      standing  of  packet lifetimes, will be needed in practice.  {Com-
      ment: 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.}

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 +    As with other 'type-P' metrics, the value of the metric may depend
      on such properties of the packet as protocol, (UDP  or  TCP)  port
      number,  size,  and  arrangement for special treatment (as with IP
      precedence or with RSVP).
 +    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 deter-
      mintes the packet's one-way delay.

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 fol-
   lows:
 +    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 compres-
      sion techniques along the path.
 +    Optionally, select a first-hop router IP address specific path and arrange for Src to send the
      packet to that router. path.  {Comment: This could be done,  for  example,
      by  installing  a  temporary  host-route  for Dst in Src's routing
      table.}
 +    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 [via first-hop]. path].
 +    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
      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.

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 +    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' here is a parameter of the
      methodology.  {Comment: or should it be a parameter  of  the  met-
      ric?}
   Issues  such  as  the  packet  format, the means by which the first-hop path is
   ensured, 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/uncertainty.  The
   Framework document provides general guidence on this  point,  but  we
   note here the following specifics related to delay metrics:
 +    Errors/uncertainties due to uncertainties in the clocks of the Src
      and Dst hosts.  We discuss this in more detail below.
 +    Errors/uncertainties due to the difference between 'wire time' and
      'host time'.
   Each of these are discussed in more detail below.

3.7.1. Errors/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 dest 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 dest clock as Tdest.  Alluding to the notions of  synchroniza-
   tion,  accuracy,  resolution, and skew mentioned in the Introduction,
   we note the following:
 +    Any error in the synchronization between the source clock and  the
      dest  clock will contribute to error in the delay measurement.  We
      say that the source clock and the dest clock have  a  synchroniza-
      tion  error  of  Tsynch if the source clock is Tsynch ahead of the
      dest 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.

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 +    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.   This  is
      because, when computing delays, we are interested only in the dif-
      ferences between clock values.
 +    The resolution of a clock adds to uncertainty about any time  mea-
      sured  with  it.  Thus, if the source clock has a resolution of 10
      msec, then this adds 10 msec of uncertainty to any time value mea-
      sured  with it.  We will denote the resolution of the source clock
      and the dest 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 lin-
      ear component to correct the clock.  Using  this  correction,  the
      residual  Tsynch  is  made smaller, but remains a source of uncer-
      tainty 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 intro-
   duce  a total uncertainty of Esynch(t)+|Rsource|+|Rdest|.  This esti-
   mate of total clock-related uncertainty should  be  included  in  the
   error/uncertainty analysis of any measurement implementation.

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

   Ideally,  we'd  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 this as 'wire time'.
   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 this as 'host time'.

   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

ID                        One-way Delay Metric             November 1996                March 1997

   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  measure-
   ment implementation.

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,  first-hop, path, 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  pseudo-random
   Poisson  arrival process of rate lambda, whose values fall between T0
   and Tf.  The time interval between successive values of T  will  then
   average 1/lambda.

4.1. Metric Name:

   Type-P-One-way-Delay-Stream

4.2. Metric Parameters:
 +    Src, the IP address of a host
 +    Dst, the IP address of a host
 +    First-hop,    Path,  the IP address of the first hop router on the path path* from Src to Dst; this optional parameter defaults to the router one hop
      from Src whenever in cases where there is in fact only one such router
      path from Src to Dst, this optional parameter can be omitted
 +    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 non-negative 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.

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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 end-
   ing  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 result-
   ing <time, delay> pairs.  If there are no such pairs, the sequence is
   of length zero and the sample is said to be empty.

4.5. Discussion:

   Note first that, 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.}

   All  the  singleton Type-P-One-way-Delay metrics in the sequence will
   have the same values of Src, Dst, [first-hop,] [path,] 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-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.

   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].

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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
   arrival process of the wire-time of the sending of the test  packets.
   Problems  with  this  process  could  be  caused by either of 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 an Anderson-
   Darling test for this.

5. Some Statistics Definitions for One-way Delay

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

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

   Given a Type-P-One-way-Delay-Stream, the median of all the dT  values
   in the Stream.  In computing the median, undefined values are treated
   as infinitely large.

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   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-Minumum

   Given a Type-P-One-way-Delay-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  unde-
   fined.  In addition, the Type-P-One-way-Delay-Minimum is undefined if
   the sample is empty.

   In the above example, the minimum would be 90 msec.

6. Security Considerations

   This memo raises no security issues.

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 Sean Shapira for several useful suggestions.

8. References

   G. Almes, W. Cerveny, P. Krishnaswamy, J. Mahdavi, M. Mathis, and  V.
   Paxson,  "Framework  for IP Provider Metrics", Internet Draft <draft-
   almes-ippm-framework-00.txt>, July 1996.

   J. Postel, "Internet Protocol", RFC 791, September 1981.

ID                        One-way Delay Metric             November 1996                March 1997

   D. Mills, "Network Time Protocol (v3)", RFC 1305, April 1992.

9. Authors' Addresses

   Guy Almes <almes@advanced.org>
   Advanced Network & Services, Inc.
   200 Business Park Drive
   Armonk, NY  10504
   USA
   Phone: +1 914/273-7863

   Sunil Kalidindi <kalidindi@advanced.org>
   Advanced Network & Services, Inc.
   200 Business Park Drive
   Armonk, NY  10504
   USA
   Phone: +1 914/273-1219