rfc2681.txt

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   +  T, a time, and

   +  dT, either a 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-Round-trip-Delay, and that dT
   would be a valid value of Type-P-Round-trip-Delay.

3.4. 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-Round-trip-Delay at
   this time.  The value of the sample is the sequence made up of the
   resulting <time, delay> pairs.  If there are no such pairs, the
   sequence is of length zero and the sample is said to be empty.

3.5. Discussion:

   The reader should be familiar with the in-depth discussion of Poisson
   sampling in the Framework document [1], which includes methods to
   compute and verify the pseudo-random Poisson process.

   We specifically do not constrain the value of lambda, except to note
   the extremes.  If the rate is too large, then the measurement traffic
   will perturb the network, and itself cause congestion.  If the rate
   is too small, then you might not capture interesting network
   behavior.  {Comment: We expect to document our experiences with, and
   suggestions for, lambda elsewhere, culminating in a "best current
   practices" document.}



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   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.}  The Poisson process is used to schedule
   the delay measurements.  The test packets will generally not arrive
   at Dst according to a Poisson distribution, nor will response packets
   arrive at Src according to a Poisson distribution, since they are
   influenced by the network.

   All the singleton Type-P-Round-trip-Delay 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-Round-trip-Delay-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-Round-trip-Delay metric.

   Care must, of course, be given to correctly handle out-of-order
   arrival of test or response packets; it is possible that the Src
   could send one test packet at TS[i], then send a second test packet
   (later) at TS[i+1], and it could receive the second response packet
   at TR[i+1], and then receive the first response packet (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
   process with respect to the wire-times of the sending of the test
   packets.  Problems with this process could be caused by several



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   things, including problems with the pseudo-random number techniques
   used to generate the Poisson arrival process, or with jitter in the
   value of Hinitial (mentioned above as uncertainty in the singleton
   delay metric).  The Framework document shows how to use the
   Anderson-Darling test to verify the accuracy of a Poisson process
   over small time frames.  {Comment: The goal is to ensure that test
   packets are sent "close enough" to a Poisson schedule, and avoid
   periodic behavior.}

3.8. Reporting the Metric:

   You MUST report the calibration and context for the underlying
   singletons along with the stream.  (See "Reporting the metric" for
   Type-P-Round-trip-Delay.)

4. Some Statistics Definitions for Round-trip Delay

   Given the sample metric Type-P-Round-trip-Delay-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-Round-trip-Delay-Percentile

   Given a Type-P-Round-trip-Delay-Poisson-Stream and a percent X
   between 0% and 100%, the Xth percentile of all the dT values in the
   Stream.  In computing this percentile, undefined values are treated
   as infinitely large.  Note that this means that the percentile could
   thus be undefined (informally, infinite).  In addition, the Type-P-
   Round-trip-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.

   Note that if the possibility that a packet with finite delay is
   reported as lost is significant, then a high percentile (90th or
   95th) might be reported as infinite instead of finite.





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4.2. Type-P-Round-trip-Delay-Median

   Given a Type-P-Round-trip-Delay-Poisson-Stream, the median of all the
   dT values in the Stream.  In computing the median, undefined values
   are treated as infinitely large.  As with Type-P-Round-trip-Delay-
   Percentile, Type-P-Round-trip-Delay-Median is undefined if the sample
   is empty.

   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.

4.3. Type-P-Round-trip-Delay-Minimum

   Given a Type-P-Round-trip-Delay-Poisson-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 undefined.  In addition, the Type-P-Round-trip-Delay-Minimum is
   undefined if the sample is empty.

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

4.4. Type-P-Round-trip-Delay-Inverse-Percentile

   Given a Type-P-Round-trip-Delay-Poisson-Stream and a 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%.  Type-P-Round-
   trip-Delay-Inverse-Percentile is undefined if the sample is empty.

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






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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.

   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

   Special thanks are due to Vern Paxson and to Will Leland for several
   useful suggestions.

7. References

   [1]  Paxson, D., 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]  Mills, D., "Network Time Protocol (v3)", RFC 1305, April 1992.



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

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

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

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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