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   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
   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-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].

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
   arrival process of the wire-times of the sending of the test packets.
   Problems with this process could be caused by several things,
   including problems with the pseudo-random number techniques used to
   generate the Poisson arrival process.  The Framework document shows
   how to use the Anderson-Darling test verify the accuracy of the
   Poisson process over small time frames.  {Comment: The goal is to
   ensure that the test packets are sent "close enough" to a Poisson
   schedule, and avoid periodic behavior.}

3.8. Reporting the metric:

   The calibration and context for the underlying singletons MUST be
   reported along with the stream.  (See "Reporting the metric" for
   Type-P-One-way-Packet-Loss.)



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4. 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.

4.1. 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.

   Note that although the loss threshold should be set such that any
   errors in loss are not significant, if the possibility that a packet
   which arrived is counted as lost due to resource exhaustion is
   significant compared to the loss rate of interest, Type-P-One-way-
   Packet-Loss-Average will be meaningless.

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.





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   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

   Thanks are due to Matt Mathis for encouraging this work and for
   calling attention on so many occasions to the significance of packet
   loss.

   Thanks are due also to Vern Paxson for his valuable comments on early
   drafts, and to Garry Couch and Will Leland for several useful
   suggestions.

7. References

   [1]  Paxson, V.,  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]  Mahdavi, J. and V. Paxson, "IPPM Metrics for Measuring
        Connectivity", RFC 2678, September 1999.






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   [4]  Postel, J., "Internet Protocol", STD 5, RFC 791, September 1981.

   [5]  Bradner, S., "Key words for use in RFCs to Indicate Requirement
        Levels", BCP 14, RFC 2119, March 1997.

   [6]  Bradner, S., "The Internet Standards Process -- Revision 3", BCP
        9, RFC 2026, October 1996.

8. Authors' Addresses

   Guy Almes
   Advanced Network & Services, Inc.
   200 Business Park Drive
   Armonk, NY  10504
   USA

   Phone: [phone]
   EMail: [e-mail]


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

   Phone: [phone]
   EMail: [e-mail]


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

   Phone: [phone]
   EMail: [e-mail]













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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.



















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