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Versions: 01 03 04 05 06 07 RFC 2679

Network Working Group              G. Almes, Advanced Network & Services
Internet Draft                 S. Kalidindi, Advanced Network & Services
Expiration Date: April 1998                                November 1997


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


1. Status of this Memo

   This document is an Internet Draft.  Internet Drafts are working doc-
   uments  of the Internet Engineering Task Force (IETF), its areas, and
   its working groups.  Note that other groups may also distribute work-
   ing documents as Internet Drafts.

   Internet  Drafts  are  draft  documents  valid  for  a maximum of six
   months, and may be updated, replaced, or obsoleted by other documents
   at any time.  It is inappropriate to use Internet Drafts as reference
   material or to cite them other than as ``work in progress''.

   To learn the current status of any Internet Draft, please  check  the
   ``1id-abstracts.txt'' listing contained in the Internet Drafts shadow
   directories  on  ftp.is.co.za   (Africa),   nic.nordu.net   (Europe),
   munnari.oz.au  (Pacific  Rim),  ds.internic.net  (US  East Coast), or
   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 IPPM
   Framework document (currently ''Framework for IP Performance  Metrics''
   <draft-ietf-ippm-framework-01.txt>);  the  reader  is  assumed  to be
   familiar with that document.

   This memo is intended to be very parallel in structure to a companion
   document  for  Packet  Loss  (''A Packet Loss Metric for IPPM'' <draft-
   ietf-ippm-loss-01.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.

   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 (and fractions) relative to UTC.

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

synchronization
     measures  the  extent to which two clocks agree on what time it is.
     For example, the clock on one host might be 5.4 msec ahead  of  the
     clock on a second host.



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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
 +    Path, the path* from Src to Dst; in cases where there is only  one
      path from Src to Dst, this optional parameter can be omitted
   {Comment:  the  presence  of  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.  Gener-
   ally, this optional parameter is useful only when  several  different
   routes are possible from Src to Dst.  Using the 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.}


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.





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3.4. Definition:

   For  a non-negative real number dT, >>the *Type-P-One-way-Delay* from
   Src to Dst at T [via path] is dT<< means that Src sent the first  bit
   of  a  type-P  packet  [via  path] 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 [via path] is unde-
   fined (informally, infinite)<< means that Src sent the first bit of a
   type-P packet [via path] to Dst at wire-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.}
 +    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).







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 +    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-
      mines the packet's one-way delay.
 +    If  the packet is fragmented and if, for whatever reason, reassem-
      bly 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  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 specific path and arrange for Src to send the
      packet  to  that 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 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.
   Issues  such  as  the  packet  format, the means by which the 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.
 +    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

   As we've defined one-way delay, 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



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   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 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,  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
   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
 +    Path, the path* from Src to Dst; in cases where there is only  one
      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, [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.


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

   Given  a Type-P-One-way-Delay-Stream and a non-negative 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%.

   In the above example, the Inverse-Percentile of  103  msec  would  be
   50%.


6. Security Considerations

   This memo raises no security issues.









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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 and to Roland Wittig for several useful
   suggestions.


8. References

   V. Paxson, G. Almes, J. Mahdavi, and M.  Mathis,  "Framework  for  IP
   Performance     Metrics",     Internet     Draft    <draft-ietf-ippm-
   framework-01.txt>, November 1997.

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

   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















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