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

                     A Packet Loss Metric for IPPM

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
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   To learn the current status of any Internet Draft, please  check  the
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   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 packet loss across Internet paths.  It
   builds on notions introduced and discussed in the IPPM Framework doc-
   ument (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  One-way  Delay  (currently ''A One-way Delay Metric for
   IPPM'' <draft-ietf-ippm-delay-01.txt>); the reader is  assumed  to  be
   familiar with that document.

   The structure of the memo is as follows:

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 +    A 'singleton' analytic metric, called Type-P-One-way-Loss, will be
      introduced to measure a single observation of packet  transmission
      or loss.
 +    Using  this  singleton  metric, a 'sample', called Type-P-One-way-
      Loss-Stream, will be introduced to measure a sequence of singleton
      transmissions and/or losses measured at times taken from a Poisson
 +    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:

   Understanding one-way packet loss of type-P  packets  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
      loss between hosts is large relative to some threshold value.
 +    Excessive packet loss may make it  difficult  to  support  certain
      real-time applications (where the precise threshold of 'excessive'
      depends on the application).
 +    The larger the value of packet loss, the more difficult it is  for
      transport-layer protocols to sustain high bandwidths.
 +    The  sensitivity  of real-time applications and of transport-layer
      protocols to loss become  especially  important  when  very  large
      delay-bandwidth products must be supported.
   It  is  outside  the scope of this document to say precisely how loss
   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:

     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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     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.

     measures the precision of a given clock.  For example, the clock on
     an  old  Unix  host might advance 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 Packet Loss

3.1. Metric Name:


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

3.3. Metric Units:

   The value of a type-P-One-way-Packet-Loss is either a zero  (signify-
   ing  successful  transmission  of  the  packet)  or a one (signifying

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3.4. Definition:

   >>The *Type-P-One-way-Packet-Loss* from Src to Dst at T [via path] is
   0<<  means  that Src sent the first bit of a type-P packet [via path]
   to Dst at wire-time T and that Dst received that packet.

   >>The *Type-P-One-way-Packet-Loss* from Src to Dst at T [via path] is
   1<<  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:

   Thus, Type-P-One-way-Packet-Loss is 0  exactly  when  Type-P-One-way-
   Delay  is  a  finite positive value, and it is 1 exactly when Type-P-
   One-way-Delay is undefined.

   The following issues are likely to come up in practice:
 +    A given methodology will have to  include  a  way  to  distinguish
      between  a  packet  loss  and a very large (but finite) delay.  As
      noted by Mahdavi and Paxson, simple upper bounds (such as the  255
      seconds  theoretical  upper  bound  on the lifetimes of IP packets
      [Postel: RFC 791]) 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, there
      may be no harm in treating a large delay as packet loss.  An audio
      playback packet, for example, that arrives only after the playback
      point 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).
 +    If the packet arrives, but is corrupted, then  it  is  counted  as
      lost.   {Comment:  one  is tempted to count the packet as received
      since corruption and packet loss are related but distinct  phenom-
      ena.   If  the IP header is corrupted, however, one cannot be sure
      about the source or destination IP addresses and is thus on  shaky
      grounds  about  knowing  that the corrupted received packet corre-
      sponds to a given sent test packet.  Similarly, if other parts  of
      the  packet  needed  by the methodology to know that the corrupted
      received packet corresponds to a given sent test packet, then such
      a packet would have to be counted as lost.  Counting these packets
      as lost but packet with corruption in other parts of the packet as
      not lost would be confusing.}

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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.
 +    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,

   Generally, for a given Type-P, one possible methodology would proceed
   as follows:
 +    Arrange  that  Src  and  Dst are moderately synchronized; that is,
      that they have clocks that  are  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.
 +    Optionally, select a specific path and arrange for Src to send the
      packet over that path.  {Comment: This could be done, for example,
      by installing a temporary host-route  for  Dst  in  Src's  routing
 +    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].
 +    If the packet arrives within a reasonable period of time, the one-
      way packet-loss is taken to be zero.
 +    If  the packet fails to arrive within a reasonable period of time,
      the one-way packet-loss is taken to be one.  Note that the thresh-
      old of 'reasonable' here is a parameter of the methodology.  {Com-
      ment: Or it could be part of the metric.  If, however, we make  it
      part of the metric, so that packets arriving after a given reason-
      able period must be counted as lost, then we reintroduce the  need
      for  a  degree of clock synchronization similar to that needed for
      one-way delay.  If a measure of packet  loss  parameterized  by  a
      specific  non-huge  'reasonable' time-out value is needed, one can
      always measure one-way delay and see what  percentage  of  packets
      from a given stream exceed a given time-out value.}
   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.}

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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 guidance on this point.

   Errors due to gross lack of synchronization between the Src  and  Dst
   hosts  should  be  dealt  with.  Since the sensitivity of packet loss
   measurement to lack of synchronization is much less than  for  delay,
   we refer the reader to the treatment of synchronization errors in the
   One-way Delay metric.

4. A Definition for Samples of One-way Packet Loss

   Given the singleton metric Type-P-One-way-Packet-Loss, 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:


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:

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 +    T, a time, and
 +    L, either a zero or a one
   The  values of T in the sequence are monotonic increasing.  Note that
   T would be a valid parameter to Type-P-One-way-Packet-Loss, and  that
   L would be a valid value of Type-P-One-way-Packet-Loss.

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-Packet-Loss at
   this time.  The value of the sample is the sequence made  up  of  the
   resulting  <time,  loss>  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.

   It  is important to note that, in contrast to this metric, loss rates
   observed by transport connections do not  reflect  unbiased  samples.
   For  example,  TCP  transmissions both (1) occur in bursts, which can
   induce loss due to the burst volume that  would  not  otherwise  have
   been observed, and (2) adapt their transmission rate in an attempt to
   minimize the loss rate observed by the connection.}

   All the singleton Type-P-One-way-Packet-Loss 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-Packet-Loss-Stream sample.

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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-Packet-Loss metric.

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

4.7. Errors and Uncertainties:

   In addition to sources of errors and  uncertainties  associated  with
   methods  employed  to  measure  the singleton values that make up the
   sample, care must be given to analyze the  accuracy  of  the  Poisson
   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.  The Framework document
   shows how to use an Anderson-Darling test for this.

5. Some Statistics Definitions for One-way Packet Loss

   Given  the  sample  metric  Type-P-One-way-Packet-Loss-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-Packet-Loss-Average

   Given  a  Type-P-One-way-Packet-Loss-Stream, the average of all the L
   values in the Stream.  In addition,  the  Type-P-One-way-Packet-Loss-
   Average is undefined if the sample is empty.

   Example: suppose we take a sample and the results are:
        Stream1 = <
        <T1, 0>
        <T2, 0>
        <T3, 1>
        <T4, 0>
        <T5, 0>

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   Then the average would be 0.2.

   Note  that,  since healthy Internet paths should be operating at loss
   rates below 1% (particularly if high delay-bandwidth products are  to
   be  sustained), the sample sizes needed might be largr than one would
   like.  Thus, for example, if one wants to discriminate between  vari-
   ous  fractions  of  1%  over one-minute periods, then several hundred
   samples per minute might be needed.  This would result in larger val-
   ues of lambda than one would ordinarily want.

6. Security Considerations

   This memo raises no security issues.

7. Acknowledgements

   Thanks are due to Matt Mathis for encouraging this work and for call-
   ing attention on so many occasions  to  the  significance  of  packet

   Thanks are due also to Vern Paxson for his valuable comments on early

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.

   G. Almes and S. Kalidindi, "A One-way Delay Metric for IPPM",  Inter-
   net Draft <draft-ietf-ippm-delay-01.txt>, November 1997.

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

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

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9. Authors' Addresses

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

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

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