Network Working Group                                           G. Almes
INTERNET-DRAFT                                              S. Kalidindi
Expiration Date: December 1998                              M. Zekauskas
                                             Advanced Network & Services
                                                               June 1998

                     A Packet Loss Metric for IPPM

1. Status of this Memo

   This document is an Internet-Draft.  Internet-Drafts are working
   documents of the Internet Engineering Task Force (IETF), its areas,
   and its working groups.  Note that other groups may also distribute
   working 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 view the entire list of current Internet-Drafts, please check the
   "1id-abstracts.txt" listing contained in the Internet-Drafts shadow
   directories on (Africa), (Northern
   Europe), (Southern Europe), (Pacific
   Rim), (US East Coast), or (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 packet loss across Internet paths.  It
   builds on notions introduced and discussed in the IPPM Framework
   document, RFC 2330 [1]; the reader is assumed to be familiar with
   that document.

   This memo is intended to be parallel in structure to a companion
   document for One-way Delay (currently "A One-way Delay Metric for
   IPPM" <draft-ietf-ippm-delay-02.txt>) [2]; 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, is
      introduced to measure a single observation of packet transmission
      or loss.

   +  Using this singleton metric, a 'sample', called Type-P-One-way-
      Loss-Poisson-Stream, is introduced to measure a sequence of
      singleton transmissions and/or losses measured at times taken from
      a Poisson process.

   +  Using this sample, several 'statistics' of the sample are defined
      and discussed.

   This progression from singleton to sample to statistics, with clear
   separation among them, is important.

   Whenever a technical term from the IPPM Framework document is first
   used in this memo, it will be tagged with a trailing asterisk.  For
   example, "term*" indicates that "term" is defined in the Framework.

2.1. Motivation:

   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.

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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.


        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


        Resolution 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

3. A Singleton Definition for One-way Packet Loss

3.1. Metric Name:


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3.2. Metric Parameters:

   +  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  T, a time

3.3. Metric Units:

   The value of a Type-P-One-way-Packet-Loss is either a zero
   (signifying successful transmission of the packet) or a one
   (signifying loss).

3.4. Definition:

   >>The *Type-P-One-way-Packet-Loss* from Src to Dst at T is 0<< means
   that Src sent the first bit of a type-P packet 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 is 1<< means
   that Src sent the first bit of a type-P packet to Dst at wire-time T
   and that Dst did not receive that packet.

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 [3], simple upper bounds (such as the
      255 seconds theoretical upper bound on the lifetimes of IP
      packets [4]) 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.}

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   +  The context in which the metric is measured must be carefully
      considered, and should always be reported along with metric

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

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

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

      The above list is not exhaustive; any additional information that
      could be useful in interpreting applications of the metrics should
      be reported.

   +  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
      phenomena.  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
      corresponds 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

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      these packets as lost but packet with corruption in other parts of
      the packet as not lost would be inconsistent.}

   +  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,
      reassembly does not occur, then the packet will be deemed lost.

3.6. Methodologies:

   As with other Type-P-* metrics, the detailed methodology will depend
   on the Type-P (e.g., protocol number, UDP/TCP port number, size,

   Generally, for a given Type-P, one possible methodology would proceed
   as follows:

   +  Arrange that Src and Dst have clocks that are synchronized with
      each other.  The degree of synchronization is a parameter of the
      methodology, and depends on the threshold used to determine loss
      (see below).

   +  At the Src host, select Src and Dst IP addresses, and form a test
      packet of Type-P with these addresses.

   +  At the Dst host, arrange to receive the packet.

   +  At the Src host, place a timestamp in the prepared Type-P packet,
      and send it towards Dst.

   +  If the packet arrives within a reasonable period of time, 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
      threshold of "reasonable" here is a parameter of the methodology.

      {Comment: The definition of reasonable is intentionally vague, and
      is intended to indicate a value "Th" so large that any value in
      (Th-delta,Th+delta) is an equivalent threshold for loss.  Here,
      delta encompasses all error in clock synchronization along the
      measured path.  If there is a single value after which the packet
      must be counted as lost, then we reintroduce the need for a degree
      of clock synchronization similar to that needed for one-way delay.
      Therefore, if a measure of packet loss parameterized by a specific

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      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 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

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, 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:


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4.2. Metric Parameters:

   +  Src, the IP address of a host

   +  Dst, the IP address of a host

   +  T0, a time

   +  Tf, a time

   +  lambda, a rate in reciprocal seconds

4.3. Metric Units:

   A sequence of pairs; the elements of each pair are:

   +  T, a time, and

   +  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
   ending at or after Tf.  Those time values greater than or equal to T0
   and less than or equal to Tf are then selected.  At each of the times
   in this process, we obtain the value of Type-P-One-way-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

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   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, 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-Poisson-Stream

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.

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5. Some Statistics Definitions for One-way Packet Loss

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

5.1. Type-P-One-way-Packet-Loss-Average

   Given a Type-P-One-way-Packet-Loss-Poisson-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>
   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 larger than one would
   like.  Thus, for example, if one wants to discriminate between
   various fractions of 1% over one-minute periods, then several hundred
   samples per minute might be needed.  This would result in larger
   values of lambda than one would ordinarily want.

6. Security Considerations

   Conducting Internet measurements raises both security and privacy
   concerns.  This memo does not specify an implementation of the
   metrics, so it does not directly affect the security of the Internet
   nor of applications which run on the Internet.  However,
   implementations of these metrics must be mindful of security and
   privacy concerns.

   There are two types of security concerns: potential harm caused by
   the measurements, and potential harm to the measurements.  The
   measurements could cause harm because they are active, and inject
   packets into the network.  The measurement parameters must be
   carefully selected so that the measurements inject trivial amounts of
   additional traffic into the networks they measure.  If they inject
   "too much" traffic, they can skew the results of the measurement, and

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   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.

7. Acknowledgements

   Thanks are due to Matt Mathis for encouraging this work and for
   calling 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

   [1]  V. Paxson, G. Almes, J. Mahdavi, and M. Mathis, "Framework for
        IP Performance Metrics", RFC 2330, May 1998.

   [2]  G. Almes, S. Kalidindi, and M. Zekauskas, "A One-way Delay
        Metric for IPPM", Internet-Draft <draft-ietf-ippm-delay-02.txt>,
        June 1998.

   [3]  J. Mahdavi and V. Paxson, "Connectivity", Work in Progress,
        November 1997.

   [4]  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: +1 914 765 1120

   Sunil Kalidindi
   Advanced Network & Services, Inc.
   200 Business Park Drive
   Armonk, NY  10504

   Phone: +1 914 765 1128

   Matthew J. Zekauskas
   Advanced Network & Services, Inc.
   200 Buisiness Park Drive
   Armonk, NY 10504

   Phone: +1 914 765 1112

   Expiration date: December, 1998

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