Internet Engineering Task Force                             R. Geib, Ed.
Internet-Draft                                          Deutsche Telekom
Intended status: Standards Track                               A. Morton
Expires: April 27, September 15, 2011                                    AT&T Labs
                                                               R. Fardid
                                                    Cariden Technologies
                                                            A. Steinmitz
                                                                HS Fulda
                                                        October 24, 2010
                                                          March 14, 2011

                   IPPM standard advancement testing


   This document specifies tests to determine if multiple independent
   instantiations of a performance metric RFC have implemented the
   specifications in the same way.  This is the performance metric
   equivalent of interoperability, required to advance RFCs along the
   standards track.  Results from different implementations of metric
   RFCs will be collected under the same underlying network conditions
   and compared using state of the art statistical methods.  The goal is
   an evaluation of the metric RFC itself, whether its definitions are
   clear and unambiguous to implementors and therefore a candidate for
   advancement on the IETF standards track.

Status of this Memo

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   This Internet-Draft will expire on April 27, September 15, 2011.

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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Requirements Language  . . . . . . . . . . . . . . . . . .  6
   2.  Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . .  6
   3.  Verification of conformance to a metric specification  . . . .  8
     3.1.  Tests of an individual implementation against a metric
           specification  . . . . . . . . . . . . . . . . . . . . . .  9
     3.2.  Test setup resulting in identical live network testing
           conditions . . . . . . . . . . . . . . . . . . . . . . . . 11
     3.3.  Tests of two or more different implementations against
           a metric specification . . . . . . . . . . . . . . . . . . 15
     3.4.  Clock synchronisation  . . . . . . . . . . . . . . . . . . 16
     3.5.  Recommended Metric Verification Measurement Process  . . . 17
     3.6.  Miscellaneous  . . . . . . . . . . . . . . . . . . . . . . 20
     3.7.  Proposal to determine an "equivalence" threshold for
           each metric evaluated  . . . . . . . . . . . . . . . . . . 21
   4.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 22
   5.  Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 22
   6.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 22
   7.  Security Considerations  . . . . . . . . . . . . . . . . . . . 22
   8.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 23
     8.1.  Normative References . . . . . . . . . . . . . . . . . . . 23
     8.2.  Informative References . . . . . . . . . . . . . . . . . . 24
   Appendix A.  An example on a One-way Delay metric validation . . . 25
     A.1.  Compliance to Metric specification requirements  . . . . . 25
     A.2.  Examples related to statistical tests for One-way Delay  . 26
   Appendix B.  Anderson-Darling 2 sample C++ code  . . . . . . . . . 28
   Appendix C.  A tunneling set up for remote metric
                implementation testing  . . . . . . . . . . . . . . . 36
   Appendix D.  Glossary  . . . . . . . . . . . . . . . . . . . . . . 38
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 38

1.  Introduction

   The Internet Standards Process RFC2026 [RFC2026] requires that for a
   IETF specification to advance beyond the Proposed Standard level, at
   least two genetically unrelated implementations must be shown to
   interoperate correctly with all features and options.  This
   requirement can be met by supplying:

   o  evidence that (at least a sub-set of) the specification has been
      implemented by multiple parties, thus indicating adoption by the
      IETF community and the extent of feature coverage.

   o  evidence that each feature of the specification is sufficiently
      well-described to support interoperability, as demonstrated
      through testing and/or user experience with deployment.

   In the case of a protocol specification, the notion of
   "interoperability" is reasonably intuitive - the implementations must
   successfully "talk to each other", while exercising all features and
   options.  To achieve interoperability, two implementors need to
   interpret the protocol specifications in equivalent ways.  In the
   case of IP Performance Metrics (IPPM), this definition of
   interoperability is only useful for test and control protocols like
   the One-Way Active Measurement Protocol, OWAMP [RFC4656], and the
   Two-Way Active Measurement Protocol, TWAMP [RFC5357].

   A metric specification RFC describes one or more metric definitions,
   methods of measurement and a way to report the results of
   measurement.  One example would be a way to test and report the One-
   way Delay that data packets incur while being sent from one network
   location to another, One-way Delay Metric.

   In the case of metric specifications, the conditions that satisfy the
   "interoperability" requirement are less obvious, and there was a need
   for IETF agreement on practices to judge metric specification
   "interoperability" in the context of the IETF Standards Process.
   This memo provides methods which should be suitable to evaluate
   metric specifications for standards track advancement.  The methods
   proposed here MAY be generally applicable to metric specification
   RFCs beyond those developed under the IPPM Framework [RFC2330].

   Since many implementations of IP metrics are embedded in measurement
   systems that do not interact with one another (they were built before
   OWAMP and TWAMP), the interoperability evaluation called for in the
   IETF standards process cannot be determined by observing that
   independent implementations interact properly for various protocol
   exchanges.  Instead, verifying that different implementations give
   statistically equivalent results under controlled measurement
   conditions takes the place of interoperability observations.  Even
   when evaluating OWAMP and TWAMP RFCs for standards track advancement,
   the methods described here are useful to evaluate the measurement
   results because their validity would not be ascertained in typical
   interoperability testing.

   The standards advancement process aims at producing confidence that
   the metric definitions and supporting material are clearly worded and
   unambiguous, or reveals ways in which the metric definitions can be
   revised to achieve clarity.  The process also permits identification
   of options that were not implemented, so that they can be removed
   from the advancing specification.  Thus, the product of this process
   is information about the metric specification RFC itself:
   determination of the specifications or definitions that are clear and
   unambiguous and those that are not (as opposed to an evaluation of
   the implementations which assist in the process).

   This document defines a process to verify that implementations (or
   practically, measurement systems) have interpreted the metric
   specifications in equivalent ways, and produce equivalent results.

   Testing for statistical equivalence requires ensuring identical test
   setups (or awareness of differences) to the best possible extent.
   Thus, producing identical test conditions is a core goal of the memo.
   Another important aspect of this process is to test individual
   implementations against specific requirements in the metric
   specifications using customized tests for each requirement.  These
   tests can distinguish equivalent interpretations of each specific

   Conclusions on equivalence are reached by two measures.

   First, implementations are compared against individual metric
   specifications to make sure that differences in implementation are
   minimised or at least known.

   Second, a test setup is proposed ensuring identical networking
   conditions so that unknowns are minimized and comparisons are
   simplified.  The resulting separate data sets may be seen as samples
   taken from the same underlying distribution.  Using state of the art
   statistical methods, the equivalence of the results is verified.  To
   illustrate application of the process and methods defined here,
   evaluation of the One-way Delay Metric [RFC2679] is provided in an
   Appendix.  While test setups will vary with the metrics to be
   validated, the general methodology of determining equivalent results
   will not.  Documents defining test setups to evaluate other metrics
   should be developed once the process proposed here has been agreed
   and approved.

   The metric RFC advancement process begins with a request for protocol
   action accompanied by a memo that documents the supporting tests and
   results.  The procedures of [RFC2026] are expanded in[RFC5657],
   including sample implementation and interoperability reports.
   Section 3 of [morton-advance-metrics-01] can serve as a template for
   a metric RFC report which accompanies the protocol action request to
   the Area Director, including description of the test set-up,
   procedures, results for each implementation and conclusions.

   Changes from WG-01 to WG-02:

   o  Clarification of the number of test streams recommended in section

   o  Clarifications on testing details in sections 3.3 and 3.4.

   o  Spelling corrections throughout.

   Changes from WG -00 to WG -01 draft

   o  Discussion on merits and requirements of a distributed lab test
      using only local load generators.

   o  Proposal of metrics suitable for tests using the proposed
      measurement configuration.

   o  Hint on delay caused by software based L2TPv3 implementation.

   o  Added an appendix with a test configuration allowing remote tests
      comparing different implementations accross across the network.

   o  Proposal for maximum error of "equivalence", based on performance
      comparison of identical implementations.  This may be useful for
      both ADK and non-ADK comparisons.

   Changes from prior ID -02 to WG -00 draft

   o  Incorporation of aspects of reporting to support the protocol
      action request in the Introduction and section 3.5

   o  Overhaul of sectcion section 3.2 regarding tunneling: Added generic
      tunneling requirements and L2TPv3 as an example tunneling
      mechanism fulfilling the tunneling requirements.  Removed and
      adapted some of the prior references to other tunneling protocols

   o  Softened a requirement within section 3.4 (MUST to SHOULD on
      precision) and removed some comments of the authors.

   o  Updated contact information of one author and added a new author.

   o  Added example C++ code of an Anderson-Darling two sample test

   Changes from ID -01 to ID -02 version

   o  Major editorial review, rewording and clarifications on all

   o  Additional text on parrallel parallel testing using VLANs and GRE or
      Pseudowire tunnels.

   o  Additional examples and a glossary.

   Changes from ID -00 to ID -01 version

   o  Addition of a comparison of individual metric implementations
      against the metric specification (trying to pick up problems and
      solutions for metric advancement [morton-advance-metrics]).

   o  More emphasis on the requirement to carefully design and document
      the measurement setup of the metric comparison.

   o  Proposal of testing conditions under identical WAN network
      conditions using IP in IP tunneling or Pseudo Wires and parallel
      measurement streams.

   o  Proposing the requirement to document the smallest resolution at
      which an ADK test was passed by 95%.  As no minimum resolution is
      specified, IPPM metric compliance is not linked to a particular
      performance of an implementation.

   o  Reference to RFC 2330 and RFC 2679 for the 95% confidence interval
      as preferred criterion to decide on statistical equivalence

   o  Reducing the proposed statistical test to ADK with 95% confidence.

1.1.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in RFC 2119 [RFC2119].

2.  Basic idea

   The implementation of a standard compliant metric is expected to meet
   the requirements of the related metric specification.  So before
   comparing two metric implementations, each metric implementation is
   individually compared against the metric specification.

   Most metric specifications leave freedom to implementors on non-
   fundamental aspects of an individual metric (or options).  Comparing
   different measurement results using a statistical test with the
   assumption of identical test path and testing conditions requires
   knowledge of all differences in the overall test setup.  Metric
   specification options chosen by implementors have to be documented.
   It is REQUIRED to use identical implementation options wherever
   possible for any test proposed here.  Calibrations proposed by metric
   standards should be performed to further identify (and possibly
   reduce) potential sources of errors in the test setup.

   The Framework for IP Performance Metrics [RFC2330] expects that a
   "methodology for a metric should have the property that it is
   repeatable: if the methodology is used multiple times under identical
   conditions, it should result in consistent measurements."  This means
   an implementation is expected to repeatedly measure a metric with
   consistent results (repeatability with the same result).  Small
   deviations in the test setup are expected to lead to small deviations
   in results only.  To characterise statistical equivalence in the case
   of small deviations, RFC 2330 and [RFC2679] suggest to apply a 95%
   confidence interval.  Quoting RFC 2679, "95 percent was chosen
   because ... a particular confidence level should be specified so that
   the results of independent implementations can be compared."

   Two different implementations are expected to produce statistically
   equivalent results if they both measure a metric under the same
   networking conditions.  Formulating in statistical terms: separate
   metric implementations collect separate samples from the same
   underlying statistical process (the same network conditions).  The
   statistical hypothesis to be tested is the expectation that both
   samples do not expose statistically different properties.  This
   requires careful test design:

   o  The measurement test setup must be self-consistent to the largest
      possible extent.  To minimize the influence of the test and
      measurement setup on the result, network conditions and paths MUST
      be identical for the compared implementations to the largest
      possible degree.  This includes both the stability and non-
      ambiguity of routes taken by the measurement packets.  See RFC
      2330 for a discussion on self-consistency.

   o  The error induced by the sample size must be small enough to
      minimize its influence on the test result.  This may have to be
      respected, especially if two implementations measure with
      different average probing rates.

   o  Every comparison must be repeated several times based on different
      measurement data to avoid random indications of compatibility (or
      the lack of it).

   o  To minimize the influence of implementation options on the result,
      metric implementations SHOULD use identical options and parameters
      for the metric under evaluation.

   o  The implementation with the lowest probing frequency determines
      the smallest temporal interval for which samples can be compared.

   The metric specifications themselves are the primary focus of
   evaluation, rather than the implementations of metrics.  The
   documentation produced by the advancement process should identify
   which metric definitions and supporting material were found to be
   clearly worded and unambiguous, OR, it should identify ways in which
   the metric specification text should be revised to achieve clarity
   and unified interpretation.

   The process should also permit identification of options that were
   not implemented, so that they can be removed from the advancing
   specification (this is an aspect more typical of protocol advancement
   along the standards track).

   Note that this document does not propose to base interoperability
   indications of performance metric implementations on comparisons of
   individual singletons.  Individual singletons may be impacted by many
   statistical effects while they are measured.  Comparing two
   singletons of different implementations may result in failures with
   higher probability than comparing samples.

3.  Verification of conformance to a metric specification

   This section specifies how to verify compliance of two or more IPPM
   implementations against a metric specification.  This document only
   proposes a general methodology.  Compliance criteria to a specific
   metric implementation need to be defined for each individual metric
   specification.  The only exception is the statistical test comparing
   two metric implementations which are simultaneously tested.  This
   test is applicable without metric specific decision criteria.

   Several testing options exist to compare two or more implementations:

   o  Use a single test lab to compare the implementations and emulate
      the Internet with an impairment generator.

   o  Use a single test lab to compare the implementations and measure
      across the Internet.

   o  Use remotely separated test labs to compare the implementations
      and emulate the Internet with two "identically" configured
      impairment generators.

   o  Use remotely separated test labs to compare the implementations
      and measure across the Internet.

   o  Use remotely separated test labs to compare the implementations
      and measure across the Internet and include a single impairment
      generator to impact all measurement flows in non discriminatory

   The first two approaches work, but cause higher expenses than the
   other ones (due to travel and/or shipping+installation).  For the
   third option, ensuring two identically configured impairment
   generators requires well defined test cases and possibly identical
   hard- and software. >>>Comment: for some specific tests, impairment
   generator accuracy requirements are less-demanding than others, and
   in such cases there is more flexibility in impairment generator
   configuration. <<<

   It is a fair question, whether the last two options can result in any
   applicable test set up at all.  While an experimental approach is
   given in Appendix C, the tradeoff trade off that measurement packets of
   different sites pass the path segments but always in a different
   order of segments probably can't be avoided.

   The question of which option above results in identical networking
   conditions and is broadly accepted can't be answered without more
   practical experience in comparing implementations.  The last proposal
   has the advantage that, while the measurement equipment is remotely
   distributed, a single network impairment generator and the Internet
   can be used in combination to impact all measurement flows.

3.1.  Tests of an individual implementation against a metric

   A metric implementation MUST support the requirements classified as
   "MUST" and "REQUIRED" of the related metric specification to be
   compliant to the latter.

   Further, supported options of a metric implementation SHOULD be
   documented in sufficient detail.  The documentation of chosen options
   is RECOMMENDED to minimise (and recognise) differences in the test
   setup if two metric implementations are compared.  Further, this
   documentation is used to validate and improve the underlying metric
   specification option, to remove options which saw no implementation
   or which are badly specified from the metric specification to be
   promoted to a standard.  This documentation SHOULD be made for all
   implementation relevant
   implementation-relevant specifications of a metric picked for a
   comparison, which aren't
   comparison that are not explicitly marked as "MUST" or "REQUIRED" in
   the metric specification. RFC text.  This applies for the following sections of all metric

   o  Singleton Definition of the Metric.

   o  Sample Definition of the Metric.

   o  Statistics Definition of the Metric.  As statistics are compared
      by the test specified here, this documentation is required even in
      the case, that the metric specification does not contain a
      Statistics Definition.

   o  Timing and Synchronisation related specification (if relevant for
      the Metric).

   o  Any other technical part present or missing in the metric
      specification, which is relevant for the implementation of the

   RFC2330 and RFC2679 emphasise precision as an aim of IPPM metric
   implementations.  A single IPPM conformant implementation MUST under
   otherwise identical network conditions produce precise results for
   repeated measurements of the same metric.

   RFC 2330 prefers the "empirical distribution function" EDF to
   describe collections of measurements.  RFC 2330 determines, that
   "unless otherwise stated, IPPM goodness-of-fit tests are done using
   5% significance."  The goodness of fit test determines by which
   precision two or more samples of a metric implementation belong to
   the same underlying distribution (of measured network performance
   events).  The goodness of fit test to be applied is the Anderson-
   Darling K sample test (ADK sample test, K stands for the number of
   samples to be compared) [ADK].  Please note that RFC 2330 and RFC
   2679 apply an Anderson Darling goodness of fit test too.

   The results of a repeated test with a single implementation MUST pass
   an ADK sample test with confidence level of 95%.  The resolution for
   which the ADK test has been passed with the specified confidence
   level MUST be documented.  To formulate this differently: The
   requirement is to document the smallest resolution, at which the
   results of the tested metric implementation pass an ADK test with a
   confidence level of 95%.  The minimum resolution available in the
   reported results from each implementation MUST be taken into account
   in the ADK test.

3.2.  Test setup resulting in identical live network testing conditions

   Two major issues complicate tests for metric compliance across live
   networks under identical testing conditions.  One is the general
   point that metric definition implementations cannot be conveniently
   examined in field measurement scenarios.  The other one is more
   broadly described as "parallelism in devices and networks", including
   mechanisms like those that achieve load balancing (see [RFC4928]).

   This section proposes two measures to deal with both issues.
   Tunneling mechanisms can be used to avoid parallel processing of
   different flows in the network.  Measuring by separate parallel probe
   flows results in repeated collection of data.  If both measures are
   combined, WAN network conditions are identical for a number of
   independent measurement flows, no matter what the network conditions
   are in detail.

   Any measurement setup MUST be made to avoid the probing traffic
   itself to impede the metric measurement.  The created measurement
   load MUST NOT result in congestion at the access link connecting the
   measurement implementation to the WAN.  The created measurement load
   MUST NOT overload the measurement implementation itself, eg. e.g., by
   causing a high CPU load or by creating imprecisions due to internal
   transmit (receive respectively) probe packet collisions.

   Tunneling multiple flows reaching a network element on a single
   physical port may allow to transmit all packets of the tunnel via the
   same path.  Applying tunnels to avoid undesired influence of standard
   routing for measurement purposes is a concept known from literature,
   see e.g.  GRE encapsulated multicast probing [GU+Duffield].  An
   existing IP in IP tunnel protocol can be applied to avoid Equal-Cost
   Multi-Path (ECMP) routing of different measurement streams if it
   meets the following criteria:

   o  Inner IP packets from different measurement implementations are
      mapped into a single tunnel with single outer IP origin and
      destination address as well as origing origin and destination port numbers
      which are identical for all packets.

   o  An easily accessible commodity tunneling protocol allows to carry
      out a metric test from more test sites.

   o  A low operational overhead may enable a broader audience to set up
      a metric test with the desired properties.

   o  The tunneling protocol should be reliable and stable in set up and
      operation to avoid disturbances or influence on the test results.

   o  The tunneling protocol should not incurr incur any extra cost for those
      interested in setting up a metric test.

   An illustration of a test setup with two tunnels and two flows
   between two linecards of one implementation is given in Figure 1.

           Implementation                   ,---.       +--------+
                               +~~~~~~~~~~~/     \~~~~~~| Remote |
            +------->-----F2->-|          /       \     |->---+  |
            | +---------+      | Tunnel 1(         )    |     |  |
            | | transmit|-F1->-|         (         )    |->+  |  |
            | | LC1     |      +~~~~~~~~~|         |~~~~|  |  |  |
            | | receive |-<--+           (         )    | F1  F2 |
            | +---------+    |           |Internet |    |  |  |  |
            *-------<-----+  F2          |         |    |  |  |  |
              +---------+ |  | +~~~~~~~~~|         |~~~~|  |  |  |
              | transmit|-*  *-|         |         |    |--+<-*  |
              | LC2     |      | Tunnel 2(         )    |  |     |
              | receive |-<-F1-|          \       /     |<-*     |
              +---------+      +~~~~~~~~~~~\     /~~~~~~| Router |
                                            `-+-'       +--------+

   Illustration of a test setup with two tunnels.  For simplicity, only
   two linecards of one implementation and two flows F between them are

                                 Figure 1

   Figure 2 shows the network elements required to set up GRE tunnels or
   as shown by figure 1.


            +-----+                   ,---.
            | LC1 |                  /     \
            +-----+                 /       \              +------+
               |        +-------+  (         )  +-------+  |Remote|
            +--------+  |       |  |         |  |       |  |      |
            |Ethernet|  | Tunnel|  |Internet |  | Tunnel|  |      |
            |Switch  |--| Head  |--|         |--| Head  |--|      |
            +--------+  | Router|  |         |  | Router|  |      |
               |        |       |  (         )  |       |  |Router|
            +-----+     +-------+   \       /   +-------+  +------+
            | LC2 |                  \     /
            +-----+                   `-+-'
        Illustration of a hardware setup to realise the test setup
         illustrated by figure 1 with GRE tunnels or Pseudowires.

                                 Figure 2

   If tunneling is applied, two tunnels MUST carry all test traffic in
   between the test site and the remote site.  For example, if 802.1Q
   Ethernet Virtual LANs (VLAN) are applied and the measurement streams
   are carried in different VLANs, the IP tunnel or Pseudo Wires
   respectively MUST be set up in physical port mode to avoid set up of
   Pseudo Wires per VLAN (which may see different paths due to ECMP
   routing), see RFC 4448.  The remote router and the Ethernet switch
   shown in figure 2 must support 802.1Q in this set up.

   The IP packet size of the metric implementation SHOULD be chosen
   small enough to avoid fragmentation due to the added Ethernet and
   tunnel headers.  Otherwise, the impact of tunnel overhead on
   fragmentation and interface MTU size MUST be understood and taken
   into account (see [RFC4459]).

   An Ethernet port mode IP tunnel carrying several 802.1Q VLANs each
   containing measurement traffic of a single measurement system was set
   up as a proof of concept using RFC4719 [RFC4719], Transport of
   Ethernet Frames over L2TPv3.  Ethernet over L2TPv3 seems to fulfill
   most of the desired tunneling protocol criteria mentioned above.

   The following headers may have to be accounted for when calculating
   total packet length, if VLANs and Ethernet over L2TPv3 tunnels are

   o  Ethernet 802.1Q: 22 Byte.

   o  L2TPv3 Header: 4-16 Byte for L2TPv3 data messages over IP; 16-28
      Byte for L2TPv3 data messages over UDP.

   o  IPv4 Header (outer IP header): 20 Byte.

   o  MPLS Labels may be added by a carrier.  Each MPLS Label has a
      length of 4 Bytes.  By the time of writing, between 1 and 4 Labels
      seems to be a fair guess of what's expectable.

   The applicability of one or more of the following tunneling protocols
   may be investigated by interested parties if Ethernet over L2TPv3 is
   felt to be not suitable: IP in IP [RFC2003] or Generic Routing
   Encapsulation (GRE) [RFC2784].  RFC 4928 [RFC4928] proposes measures
   how to avoid ECMP treatment in MPLS networks.

   L2TP is a commodity tunneling protocol [RFC2661].  By the time of
   writing, L2TPv3 [RFC3931]is the latest version of L2TP.  If L2TPv3 is
   applied, software based implementations of this protocol are not
   suitable for the test set up, as such implementations may cause
   incalculable delay shifts.

   Ethernet Pseudo Wires may also be set up on MPLS networks [RFC4448].
   While there's no technical issue with this solution, MPLS interfaces
   are mostly found in the network provider domain.  Hence not all of
   the above tunneling criteria are met.

   Appendix C provides an experimental tunneling set up for metric
   implementation testing between two (or more) remote sites.

   Each test is repeated several SHOULD be conducted multiple times.  WAN conditions may change over
   time.  Sequential testing is desirable,
   possible, but may not be a useful metric test option. option because WAN
   conditions are likely to change over time.  It is RECOMMENDED that
   tests be carried out by establishing N at least 2 different parallel
   measurement flows.  Two or three linecards per implementation serving to that send or and
   receive measurement flows should be sufficient to create 5 or more 4 parallel
   flows.  If three linecards are used, flows (when each card sends and receives 2
   flows. flows).  Other
   options are to separate flows by DiffServ marks (without deploying
   any QoS in the inner or outer tunnel) or using a single CBR flow and
   evaluating every n-th singleton to belong to a specific measurement

   Some additional rules to calculate and compare samples have to be
   respected to perform a metric test:

   o  To compare different probes of a common underlying distribution in
      terms of metrics characterising a communication network requires
      to respect the temporal nature for which the assumption of common
      underlying distribution may hold.  Any singletons or samples to be
      compared MUST be captured within the same time interval.

   o  Whenever statistical events like singletons or rates are used to
      characterise measured metrics of a time-interval, at least 5
      singletons of a relevant metric SHOULD be present to ensure a
      minimum confidence into the reported value (see Wikipedia on
      confidence [Rule of thumb]).  Note that this criterion also is to
      be respected e.g. when comparing packet loss metrics.  Any packet
      loss measurement interval to be compared with the results of
      another implementation SHOULD contain at least five lost packets
      to have a minimum confidence that the observed loss rate wasn't
      caused by a small number of random packet drops.

   o  The minimum number of singletons or samples to be compared by an
      Anderson-Darling test SHOULD be 100 per tested metric
      implementation.  Note that the Anderson-Darling test detects small
      differences in distributions fairly well and will fail for high
      number of compared results (RFC2330 mentions an example with 8192
      measurements where an Anderson-Darling test always failed).

   o  Generally, the Anderson-Darling test is sensitive to differences
      in the accuracy or bias associated with varying implementations or
      test conditions.  These dissimilarities may result in differing
      averages of samples to be compared.  An example may be different
      packet sizes, resulting in a constant delay difference between
      compared samples.  Therefore samples to be compared by an Anderson
      Anderson-Darling test MAY be calibrated by the difference of the
      average values of the samples.  Any calibration of this kind MUST
      be documented in the test result.

3.3.  Tests of two or more different implementations against a metric

   RFC2330 expects "a methodology for a given metric [to] exhibit
   continuity if, for small variations in conditions, it results in
   small variations in the resulting measurements.  Slightly more
   precisely, for every positive epsilon, there exists a positive delta,
   such that if two sets of conditions are within delta of each other,
   then the resulting measurements will be within epsilon of each
   other."  A small variation in conditions in the context of the metric
   test proposed here can be seen as different implementations measuring
   the same metric along the same path.

   IPPM metric specification specifications however allow for implementor options to
   the largest possible degree.  It can't can not be expected that two
   implementors pick identical value ranges in options for the
   implementations.  Implementors SHOULD to the highest degree possible
   pick the same configurations for their systems when comparing their
   implementations by a metric test.

   In some cases, a goodness of fit test may not be possible or show
   disappointing results.  To clarify the difficulties arising from
   different implementation options, the individual options picked for
   every compared implementation SHOULD be documented in sufficient
   detail.  Based on this documentation, the underlying metric
   specification should be improved before it is promoted to a standard.

   The same statistical test as applicable to quantify precision of a
   single metric implementation MUST be passed used to compare metric
   conformance of result
   equivalence for different implementations.  To document
   compatibility, the smallest measurement resolution at which the
   compared implementations passed the ADK sample test MUST be

   For different implementations of the same metric, "variations in
   conditions" are reasonably expected.  The ADK test comparing samples
   of the different implementations may MAY result in a lower precision than
   the test for precision of each implementation individually. in the same-implementation comparison.

3.4.  Clock synchronisation

   Clock synchronization effects require special attention.  Accuracy of
   one-way active delay measurements for any metrics implementation
   depends on clock synchronization between the source and destination
   of tests.  Ideally, one-way active delay measurement (RFC 2679,
   [RFC2679]) test endpoints either have direct access to independent
   GPS or CDMA-based time sources or indirect access to nearby NTP
   primary (stratum 1) time sources, equipped with GPS receivers.
   Access to these time sources may not be available at all test
   locations associated with different Internet paths, for a variety of
   reasons out of scope of this document.

   When secondary (stratum 2 and above) time sources are used with NTP
   running across the same network, whose metrics are subject to
   comparative implementation tests, network impairments can affect
   clock synchronization, distort sample one-way values and their
   interval statistics.  It is RECOMMENDED to discard sample one-way
   delay values for any implementation, when one of the following
   reliability conditions is met:

   o  Delay is measured and is finite in one direction, but not the

   o  Absolute value of the difference between the sum of one-way
      measurements in both directions and round-trip measurement is
      greater than X% of the latter value.

   Examination of the second condition requires RTT measurement for
   reference, e.g., based on TWAMP (RFC5357, RFC 5357 [RFC5357]), in
   conjunction with one-way delay measurement.

   Specification of X% to strike a balance between identification of
   unreliable one-way delay samples and misidentification of reliable
   samples under a wide range of Internet path RTTs probably requires
   further study.

   An IPPM compliant metric implementation whose measurement of an RFC that requires synchronized clocks is however
   expected to provide precise measurement results.  Any IPPM results in order to claim
   that the metric measured is compliant.

   IF an implementation SHOULD be of publishes a specification of its precision, such
   as "a precision of 1 ms (+/- 500 us) with a confidence of 95% 95%", then
   the specification SHOULD be met over a useful measurement duration.
   For example, if the metric is captured measured along an Internet path which
   is stable and not congested
   during a measurement duration congested, then the precision specification SHOULD
   be met over durations of an hour or more.

3.5.  Recommended Metric Verification Measurement Process

   In order to meet their obligations under the IETF Standards Process
   the IESG must be convinced that each metric specification advanced to
   Draft Standard or Internet Standard status is clearly written, that
   there are the required multiple verifiably a sufficient number of verified equivalent
   implementations, and that all options have been implemented.

   In the context of this document, metrics are designed to measure some
   characteristic of a data network.  An aim of any metric definition
   should be that it should be specified in a way that can reliably
   measure the specific characteristic in a repeatable way across
   multiple independent implementations.

   Each metric, statistic or option of those to be validated MUST be
   compared against a reference measurement or another implementation by
   at least 5 different basic data sets, each one with sufficient size
   to reach the specified level of confidence, as specified by this

   Finally, the metric definitions, embodied in the text of the RFCs,
   are the objects that require evaluation and possible revision in
   order to advance to the next step on the standards track.

   IF two (or more) implementations do not measure an equivalent metric
   as specified by this document,

   AND sources of measurement error do not adequately explain the lack
   of agreement,
   THEN the details of each implementation should be audited along with
   the exact definition text, to determine if there is a lack of clarity
   that has caused the implementations to vary in a way that affects the
   correspondence of the results.

   IF there was a lack of clarity or multiple legitimate interpretations
   of the definition text,

   THEN the text should be modified and the resulting memo proposed for
   consensus and (possible) advancement along the standards track.

   Finally, all the findings MUST be documented in a report that can
   support advancement on the standards track, similar to those
   described in [RFC5657].  The list of measurement devices used in
   testing satisfies the implementation requirement, while the test
   results provide information on the quality of each specification in
   the metric RFC (the surrogate for feature interoperability).

   The complete process of advancing a metric specification to a
   standard as defined by this document is illustrated in Figure 3.

     /     \
    ( Start )
     \     /    Implementations
      `-+-'        +-------+
        |         /|   1   `.
    +---+----+   / +-------+ `.-----------+     ,-------.
    |  RFC   |  /             |Check for  |   ,' was RFC `. YES
    |        | /              |Equivalence....  clause x   ------+
    |        |/    +-------+  |under      |   `. clear?  ,'      |
    | Metric \.....|   2   ....relevant   |     `---+---'   +----+-----+
    | Metric |\    +-------+  |identical  |      No |       |Report    |
    | Metric | \              |network    |      +--+----+  |results + |
    |  ...   |  \             |conditions |      |Modify |  |Advance   |
    |        |   \ +-------+  |           |      |Spec   +--+RFC       |
    +--------+    \|   n   |.'+-----------+      +-------+  |request(?)|
                   +-------+                                +----------+

            Illustration of the metric standardisation process

                                 Figure 3

   Any recommendation for the advancement of a metric specification MUST
   be accompanied by an implementation report, as is the case with all
   requests for the advancement of IETF specifications.  The
   implementation report needs to include the tests performed, the
   applied test setup, the specific metrics in the RFC and reports of
   the tests performed with two or more implementations.  The test plan
   needs to specify the precision reached for each measured metric and
   thus define the meaning of "statistically equivalent" for the
   specific metrics being tested.

   Ideally, the test plan would co-evolve with the development of the
   metric, since that's when people have the most context in their
   thinking regarding the different subtleties that can arise.

   In particular, the implementation report MUST as a minimum document:

   o  The metric compared and the RFC specifying it.  This includes
      statements as required by the section "Tests of an individual
      implementation against a metric specification" of this document.

   o  The measurement configuration and setup.

   o  A complete specification of the measurement stream (mean rate,
      statistical distribution of packets, packet size or mean packet
      size and their distribution), DSCP and any other measurement
      stream properties which could result in deviating results.
      Deviations in results can be caused also if chosen IP addresses
      and ports of different implementations can result in different
      layer 2 or layer 3 paths due to operation of Equal Cost Multi-Path
      routing in an operational network.

   o  The duration of each measurement to be used for a metric
      validation, the number of measurement points collected for each
      metric during each measurement interval (i.e. the probe size) and
      the level of confidence derived from this probe size for each
      measurement interval.

   o  The result of the statistical tests performed for each metric
      validation as required by the section "Tests of two or more
      different implementations against a metric specification" of this

   o  A parameterization of laboratory conditions and applied traffic
      and network conditions allowing reproduction of these laboratory
      conditions for readers of the implementation report.

   o  The documentation helping to improve metric specifications defined
      by this section.

   All of the tests for each set SHOULD be run in a test setup as
   specified in the section "Test setup resulting in identical live
   network testing conditions."

   If a different test set up is chosen, it is RECOMMENDED to avoid
   effects falsifying results of validation measurements caused by real
   data networks (like parallelism in devices and networks).  Data
   networks may forward packets differently in the case of:

   o  Different packet sizes chosen for different metric
      implementations.  A proposed countermeasure is selecting the same
      packet size when validating results of two samples or a sample
      against an original distribution.

   o  Selection of differing IP addresses and ports used by different
      metric implementations during metric validation tests.  If ECMP is
      applied on IP or MPLS level, different paths can result (note that
      it may be impossible to detect an MPLS ECMP path from an IP
      endpoint).  A proposed counter measure is to connect the
      measurement equipment to be compared by a NAT device, or
      establishing a single tunnel to transport all measurement traffic
      The aim is to have the same IP addresses and port for all
      measurement packets or to avoid ECMP based local routing diversion
      by using a layer 2 tunnel.

   o  Different IP options.

   o  Different DSCP.

   o  If the N measurements are captured using sequential measurements
      instead of simultaneous ones, then the following factors come into
      play: Time varying paths and load conditions.

3.6.  Miscellaneous

   A minimum amount of singletons per metric is required if results are
   to be compared.  To avoid accidental singletons from impacting a
   metric comparison, a minimum number of 5 singletons per compared
   interval was proposed above.  Commercial Internet service is not
   operated to reliably create enough rare events of singletons to
   characterize bad measurement engineering or bad implementations.  In
   the case that a metric validation requires capturing rare events, an
   impairment generator may have to be added to the test set up.
   Inclusion of an impairment generator and the parameterisation of the
   impairments generated MUST be documented.

   A metric characterising a common impairment condition would be one,
   which by expectation creates a singleton result for each measured
   packet.  Delay or Delay Variation are examples of this type, and in
   such cases, the Internet may be used to compare metric

   Rare events are those, where by expectation no or a rather low number
   of "event is present" singletons are captured during a measurement
   interval.  Packet duplications, packet loss rates above one digit
   percentages, loss patterns and packet reordering are examples.  Note
   especially that a packet reordering or loss pattern metric
   implementation comparison may require a more sophisticated test set
   up than described here.  Spatial and temporal effects combine in the
   case of packet re-ordering and measurements with different packet
   rates may always lead to different results.

   As specified above, 5 singletons are the recommended basis to
   minimise interference of random events with the statistical test
   proposed by this document.  In the case of ratio measurements (like
   packet loss), the underlying sum of basic events, against the which
   the metric's monitored singletons are "rated", determines the
   resolution of the test.  A packet loss statistic with a resolution of
   1% requires one packet loss statistic-datapoint statistic-data point to consist of 500
   delay singletons (of which at least 5 were lost).  To compare EDFs on
   packet loss requires one hundred such statistics per flow.  That
   means, all in all at least 50 000 delay singletons are required per
   single measurement flow.  Live network packet loss is assumed to be
   present during main traffic hours only.  Let this interval be 5
   hours.  The required minimum rate of a single measurement flow in
   that case is 2.8 packets/sec (assuming a loss of 1% during 5 hours).
   If this measurement is too demanding under live network conditions,
   an impairment generator should be used.

3.7.  Proposal to determine an "equivalence" threshold for each metric

   This section describes a proposal for maximum error of "equivalence",
   based on performance comparison of identical implementations.  This
   comparison may be useful for both ADK and non-ADK comparisons.

   Each metric tested by two or more implementations (cross-
   implementation testing).

   Each metric is also tested twice simultaneously by the *same*
   implementation, using different Src/Dst Address pairs and other
   differences such that the connectivity differences of the cross-
   implementation tests are also experienced and measured by the same

   Comparative results for the same implementation represent a bound on
   cross-implementation equivalence.  This should be particularly useful
   when the metric does *not* produces a continuous distribution of
   singleton values, such as with a loss metric, or a duplication
   metric.  Appendix A indicates how the ADK will work for 0ne-way
   delay, and should be likewise applicable to distributions of delay

   Proposal: the implementation with the largest difference in
   homogeneous comparison results is the lower bound on the equivalence
   threshold, noting that there may be other systematic errors to
   account for when comparing between implementations.

   Thus, when evaluationg evaluating equivalence in cross-implementation results:

   Maximum_Error = Same_Implementation_Error + Systematic_Error

   and only the systematic error need be decided beforehand.

   In the case of ADK comparison, the largest same-implementation
   resolution of distribution equivalence can be used as a limit on
   cross-implementation resolutions (at the same confidence level).

4.  Acknowledgements

   Gerhard Hasslinger commented a first version of this document,
   suggested statistical tests and the evaluation of time series
   information.  Henk Uijterwaal and Lars Eggert have encouraged and
   helped to orgainize this work.  Mike Hamilton, Scott Bradner, David
   Mcdysan and Emile Stephan commented on this draft.  Carol Davids
   reviewed the 01 version of the ID before it was promoted to WG draft.

5.  Contributors

   Scott Bradner, Vern Paxson and Allison Mankin drafted bradner-
   metrictest [bradner-metrictest], and major parts of it are included
   in this document.

6.  IANA Considerations

   This memo includes no request to IANA.

7.  Security Considerations

   This draft does not raise any specific security issues.

8.  References

8.1.  Normative References

   [RFC2003]  Perkins, C., "IP Encapsulation within IP", RFC 2003,
              October 1996.

   [RFC2026]  Bradner, S., "The Internet Standards Process -- Revision
              3", BCP 9, RFC 2026, October 1996.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2330]  Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
              "Framework for IP Performance Metrics", RFC 2330,
              May 1998.

   [RFC2661]  Townsley, W., Valencia, A., Rubens, A., Pall, G., Zorn,
              G., and B. Palter, "Layer Two Tunneling Protocol "L2TP"",
              RFC 2661, August 1999.

   [RFC2679]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Delay Metric for IPPM", RFC 2679, September 1999.

   [RFC2680]  Almes, G., Kalidindi, S., and M. Zekauskas, "A One-way
              Packet Loss Metric for IPPM", RFC 2680, September 1999.

   [RFC2681]  Almes, G., Kalidindi, S., and M. Zekauskas, "A Round-trip
              Delay Metric for IPPM", RFC 2681, September 1999.

   [RFC2784]  Farinacci, D., Li, T., Hanks, S., Meyer, D., and P.
              Traina, "Generic Routing Encapsulation (GRE)", RFC 2784,
              March 2000.

   [RFC3931]  Lau, J., Townsley, M., and I. Goyret, "Layer Two Tunneling
              Protocol - Version 3 (L2TPv3)", RFC 3931, March 2005.

   [RFC4448]  Martini, L., Rosen, E., El-Aawar, N., and G. Heron,
              "Encapsulation Methods for Transport of Ethernet over MPLS
              Networks", RFC 4448, April 2006.

   [RFC4459]  Savola, P., "MTU and Fragmentation Issues with In-the-
              Network Tunneling", RFC 4459, April 2006.

   [RFC4656]  Shalunov, S., Teitelbaum, B., Karp, A., Boote, J., and M.
              Zekauskas, "A One-way Active Measurement Protocol
              (OWAMP)", RFC 4656, September 2006.

   [RFC4719]  Aggarwal, R., Townsley, M., and M. Dos Santos, "Transport
              of Ethernet Frames over Layer 2 Tunneling Protocol Version
              3 (L2TPv3)", RFC 4719, November 2006.

   [RFC4928]  Swallow, G., Bryant, S., and L. Andersson, "Avoiding Equal
              Cost Multipath Treatment in MPLS Networks", BCP 128,
              RFC 4928, June 2007.

   [RFC5657]  Dusseault, L. and R. Sparks, "Guidance on Interoperation
              and Implementation Reports for Advancement to Draft
              Standard", BCP 9, RFC 5657, September 2009.

8.2.  Informative References

   [ADK]      Scholz, F. and M. Stephens, "K-sample Anderson-Darling
              Tests of fit, for continuous and discrete cases",
              University of Washington, Technical Report No. 81,
              May 1986.

              Gu, Y., Duffield, N., Breslau, L., and S. Sen, "GRE
              Encapsulated Multicast Probing: A Scalable Technique for
              Measuring One-Way Loss", SIGMETRICS'07 San Diego,
              California, USA, June 2007.

   [RFC5357]  Hedayat, K., Krzanowski, R., Morton, A., Yum, K., and J.
              Babiarz, "A Two-Way Active Measurement Protocol (TWAMP)",
              RFC 5357, October 2008.

   [Rule of thumb]
              Hardy, M., "Confidence interval", March 2010.

              Bradner, S., Mankin, A., and V. Paxson, "Advancement of
              metrics specifications on the IETF Standards Track",
              draft -bradner-metricstest-03, (work in progress),
              July 2007.

              Morton, A., "Problems and Possible Solutions for Advancing
              Metrics on the Standards Track", draft -morton-ippm-
              advance-metrics-00, (work in progress), July 2009.

              Morton, A., "Lab Test Results for Advancing Metrics on the
              Standards Track", draft -morton-ippm-advance-metrics-01,
              (work in progress), June 2010.

Appendix A.  An example on a One-way Delay metric validation

   The text of this appendix is not binding.  It is an example how parts
   of a One-way Delay metric test could look like.

A.1.  Compliance to Metric specification requirements

   One-way Delay, Loss threshold, RFC 2679

   This test determines if implementations use the same configured
   maximum waiting time delay from one measurement to another under
   different delay conditions, and correctly declare packets arriving in
   excess of the waiting time threshold as lost.  See Section 3.5 of
   RFC2679, 3rd bullet point and also Section 3.8.2 of RFC2679.

   (1)  Configure a path with 1 sec one-way constant delay.

   (2)  Measure one-way delay with 2 or more implementations, using
        identical waiting time thresholds for loss set at 2 seconds.

   (3)  Configure the path with 3 sec one-way delay.

   (4)  Repeat measurements.

   (5)  Observe that the increase measured in step 4 caused all packets
        to be declared lost, and that all packets that arrive
        successfully in step 2 are assigned a valid one-way delay.

   One-way Delay, First-bit to Last bit, RFC 2679

   This test determines if implementations register the same relative
   increase in delay from one measurement to another under different
   delay conditions.  This test tends to cancel the sources of error
   which may be present in an implementation.  See Section 3.7.2 of
   RFC2679, and Section 10.2 of RFC2330.

   (1)  Configure a path with X ms one-way constant delay, and ideally
        including a low-speed link.

   (2)  Measure one-way delay with 2 or more implementations, using
        identical options and equal size small packets (e.g., 100 octet
        IP payload).

   (3)  Maintain the same path with X ms one-way delay.

   (4)  Measure one-way delay with 2 or more implementations, using
        identical options and equal size large packets (e.g., 1500 octet
        IP payload).

   (5)  Observe that the increase measured in steps 2 and 4 is
        equivalent to the increase in ms expected due to the larger
        serialization time for each implementation.  Most of the
        measurement errors in each system should cancel, if they are

   One-way Delay, RFC 2679

   This test determines if implementations register the same relative
   increase in delay from one measurement to another under different
   delay conditions.  This test tends to cancel the sources of error
   which may be present in an implementation.  This test is intended to
   evaluate measurments in sections 3 and 4 of RFC2679.

   (1)  Configure a path with X ms one-way constant delay.

   (2)  Measure one-way delay with 2 or more implementations, using
        identical options.

   (3)  Configure the path with X+Y ms one-way delay.

   (4)  Repeat measurements.

   (5)  Observe that the increase measured in steps 2 and 4 is ~Y ms for
        each implementation.  Most of the measurement errors in each
        system should cancel, if they are stationary.

   Error Calibration, RFC 2679

   This is a simple check to determine if an implementation reports the
   error calibration as required in Section 4.8 of RFC2679.  Note that
   the context (Type-P) must also be reported.

A.2.  Examples related to statistical tests for One-way Delay

   A one way delay measurement may pass an ADK test with a timestamp
   resultion of 1 ms.  The same test may fail, if timestamps with a
   resolution of 100 microseconds are eavluated.  The implementation
   then is then conforming to the metric specification up to a timestamp
   resolution of 1 ms.

   Let's assume another one way delay measurement comparison between
   implementation 1, probing with a frequency of 2 probes per second and
   implementation 2 probing at a rate of 2 probes every 3 minutes.  To
   ensure reasonable confidence in results, sample metrics are
   calculated from at least 5 singletons per compared time interval.
   This means, sample delay values are calculated for each system for
   identical 6 minute intervals for the whole test duration.  Per 6
   minute interval, the sample metric is calculated from 720 singletons
   for implementation 1 and from 6 singletons for implementation 2.
   Note, that if outliers are not filtered, moving averages are an
   option for an evaluation too.  The minimum move of an averaging
   interval is three minutes in this example.

   The data in table 1 may result from measuring One-Way Delay with
   implementation 1 (see column Implemnt_1) and implementation 2 (see
   column implemnt_2).  Each data point in the table represents a
   (rounded) average of the sampled delay values per interval.  The
   resolution of the clock is one micro-second.  The difference in the
   delay values may result eg. from different probe packet sizes.

         | Implemnt_1 | Implemnt_2 | Implemnt_2 - Delta_Averages |
         |    5000    |    6549    |             4997            |
         |    5008    |    6555    |             5003            |
         |    5012    |    6564    |             5012            |
         |    5015    |    6565    |             5013            |
         |    5019    |    6568    |             5016            |
         |    5022    |    6570    |             5018            |
         |    5024    |    6573    |             5021            |
         |    5026    |    6575    |             5023            |
         |    5027    |    6577    |             5025            |
         |    5029    |    6580    |             5028            |
         |    5030    |    6585    |             5033            |
         |    5032    |    6586    |             5034            |
         |    5034    |    6587    |             5035            |
         |    5036    |    6588    |             5036            |
         |    5038    |    6589    |             5037            |
         |    5039    |    6591    |             5039            |
         |    5041    |    6592    |             5040            |
         |    5043    |    6599    |             5047            |
         |    5046    |    6606    |             5054            |
         |    5054    |    6612    |             5060            |

                                  Table 1

   Average values of sample metrics captured during identical time
   intervals are compared.  This excludes random differences caused by
   differing probing intervals or differing temporal distance of
   singletons resulting from their Poisson distributed sending times.

   In the example, 20 values have been picked (note that at least 100
   values are recommended for a single run of a real test).  Data must
   be ordered by ascending rank.  The data of Implemnt_1 and Implemnt_2
   as shown in the first two columns of table 1 clearly fails an ADK
   test with 95% confidence.

   The results of Implemnt_2 are now reduced by difference of the
   averages of column 2 (rounded to 6581 us) and column 1 (rounded to
   5029 us), which is 1552 us.  The result may be found in column 3 of
   table 1.  Comparing column 1 and column 3 of the table by an ADK test
   shows, that the data contained in these columns passes an ADK tests
   with 95% confidence.

   >>> Comment: Extensive averaging was used in this example, because of
   the vastly different sampling frequencies.  As a result, the
   distributions compared do not exactly align with a metric in
   [RFC2679], but illustrate the ADK process adequately.

Appendix B.  Anderson-Darling 2 sample C++ code

             /* Routines for computing the Anderson-Darling 2 sample
              * test statistic.
              * Implemented based on the description in
              * "Anderson-Darling K Sample Test" Heckert, Alan and
              * Filliben, James, editors, Dataplot Reference Manual,
              * Chapter 15 Auxiliary, NIST, 2004.
              * Official Reference by 2010
              * Heckert, N. A. (2001). Dataplot website at the
              * National Institute of Standards and Technology:
              * June 2001.

             #include <iostream>
             #include <fstream>
             #include <vector>
             #include <sstream>

             using namespace std;

             vector<double> vec1, vec2;
             double adk_result;
             double adk_criterium = 1.993;

             /* vec1 and vec2 to be initialised with sample 1 and
              * sample 2 values in ascending order.

             /* example for iterating the vectors
              * for(vector<double>::iterator it = vec1->begin();
              * it != vec1->end(); it++
              * {
              * cout << *it << endl;
              * }

             static int k, val_st_z_samp1, val_st_z_samp2,
                        val_eq_z_samp1, val_eq_z_samp2,
                            j, n_total, n_sample1, n_sample2, L,
                        max_number_samples, line, maxnumber_z;
             static int column_1, column_2;
             static double adk, n_value, z, sum_adk_samp1,
                    sum_adk_samp2, z_aux;
             static double H_j, F1j, hj, F2j, denom_1_aux, denom_2_aux;
             static bool next_z_sample2, equal_z_both_samples;
             static int stop_loop1, stop_loop2, stop_loop3,old_eq_line2,

             static double adk_criterium = 1.993;

             k = 2;
             n_sample1 = vec1->size() - 1;
             n_sample2 = vec2->size() - 1;

             // -1 because vec[0] is a dummy value

             n_total = n_sample1 + n_sample2;

             /* value equal to the line with a value = zj in sample 1.
              * Here j=1, so the line is 1.

             val_eq_z_samp1 = 1;

             /* value equal to the line with a value = zj in sample 2.
              * Here j=1, so the line is 1.

             val_eq_z_samp2 = 1;

             /* value equal to the last line with a value < zj
              * in sample 1. Here j=1, so the line is 0.

             val_st_z_samp1 = 0;

             /* value equal to the last line with a value < zj
              * in sample 1. Here j=1, so the line is 0.

             val_st_z_samp2 = 0;

             sum_adk_samp1 = 0;
             sum_adk_samp2 = 0;
             j = 1;

             // as mentioned above, j=1

             equal_z_both_samples = false;
             next_z_sample2 = false;

             //assuming the next z to be of sample 1

             stop_loop1 = n_sample1 + 1;

             // + 1 because vec[0] is a dummy, see n_sample1 declaration

             stop_loop2 = n_sample2 + 1;
             stop_loop3 = n_total + 1;

             /* The required z values are calculated until all values
              * of both samples have been taken into account. See the
              * lines above for the stoploop values. Construct required
              * to avoid a mathematical operation in the While condition

              while (((stop_loop1 > val_eq_z_samp1)
                    || (stop_loop2 > val_eq_z_samp2)) && stop_loop3 > j)
                if(val_eq_z_samp1 < n_sample1+1)

             /* here, a preliminary zj value is set.
              * See below how to calculate the actual zj.

                      z = (*vec1)[val_eq_z_samp1];

             /* this while sequence calculates the number of values
              * equal to z.
                     while ((val_eq_z_samp1+1 < n_sample1)
                             && z == (*vec1)[val_eq_z_samp1+1] )
                     val_eq_z_samp1 = 0;
                     val_st_z_samp1 = n_sample1;

             // this should be val_eq_z_samp1 - 1 = n_sample1

             if(val_eq_z_samp2 < n_sample2+1)
                     z_aux = (*vec2)[val_eq_z_samp2];;

             /* this while sequence calculates the number of values
              * equal to z_aux

                     while ((val_eq_z_samp2+1 < n_sample2)
                             && z_aux == (*vec2)[val_eq_z_samp2+1] )

             /* the smaller of the two actual data values is picked
              * as the next zj.

                 if(z > z_aux)
                             z = z_aux;
                             next_z_sample2 = true;
                             if (z == z_aux)
                             equal_z_both_samples = true;

             /* This is the case, if the last value of column1 is
              * smaller than the remaining values of column2.
                             if (val_eq_z_samp1 == 0)
                             z = z_aux;
                             next_z_sample2 = true;
                     val_eq_z_samp2 = 0;
                     val_st_z_samp2 = n_sample2;

             // this should be val_eq_z_samp2 - 1 = n_sample2


             /* in the following, sum j = 1 to L is calculated for
              * sample 1 and sample 2.

                    if (equal_z_both_samples)

             /* hj is the number of values in the combined sample
              * equal to zj
                           hj = val_eq_z_samp1 - val_st_z_samp1
                        + val_eq_z_samp2 - val_st_z_samp2;

             /* H_j is the number of values in the combined sample
              * smaller than zj plus one half the the number of
              * values in the combined sample equal to zj
              * (that's hj/2).

                           H_j = val_st_z_samp1 + val_st_z_samp2
                                 + hj / 2;

             /* F1j is the number of values in the 1st sample
              * which are less than zj plus one half the number
              * of values in this sample which are equal to zj.

                           F1j = val_st_z_samp1 + (double)
                     (val_eq_z_samp1 - val_st_z_samp1) / 2;

             /* F2j is the number of values in the 1st sample
              * which are less than zj     plus one half the number
              * of values in this sample which are equal to zj.

                           F2j = val_st_z_samp2 + (double)
                    (val_eq_z_samp2 - val_st_z_samp2) / 2;

             /* set the line of values equal to zj to the
              * actual line of the last value picked for zj.
                           val_st_z_samp1 = val_eq_z_samp1;

             /* Set the line of values equal to zj to the actual
              * line of the last value picked for zjof each
              * sample. This is required as data smaller than zj
              * is accounted differently than values equal to zj.

                   val_st_z_samp2 = val_eq_z_samp2;

             /* next the lines of the next values z, ie. zj+1
              * are addressed.


             /* next the lines of the next values z, ie.
              * zj+1 are addressed


             /* the smaller z value was contained in sample 2,
              * hence this value is the zj to base the following
              * calculations on.
                           if (next_z_sample2)

             /* hj is the number of values in the combined
              * sample equal to zj, in this case these are
              * within sample 2 only.
                           hj = val_eq_z_samp2 - val_st_z_samp2;

             /* H_j is the number of values in the combined sample
              * smaller than zj plus one half the the number of
              * values in the combined sample equal to zj
              * (that's hj/2).

                               H_j = val_st_z_samp1 + val_st_z_samp2
                             + hj / 2;

             /* F1j is the number of values in the 1st sample which
              * are less than zj plus one half the number of values in
              * this sample which are equal to zj.
              * As val_eq_z_samp2 < val_eq_z_samp1, these are the
              * val_st_z_samp1 only.
                           F1j = val_st_z_samp1;

             /* F2j is the number of values in the 1st sample which
              * are less than zj plus one half the number of values in
              * this sample which are equal to zj. The latter are from
              * sample 2 only in this case.

                   F2j = val_st_z_samp2 + (double)
                        (val_eq_z_samp2 - val_st_z_samp2) / 2;

             /* Set the line of values equal to zj to the actual line
              * of the last value picked for zj of sample 2 only in
              * this case.
                               val_st_z_samp2 = val_eq_z_samp2;

             /* next the line of the next value z, ie. zj+1 is
              * addressed. Here, only sample 2 must be addressed.

                                   if (val_eq_z_samp1 == 0)
                                   val_eq_z_samp1 = stop_loop1;

             /* the smaller z value was contained in sample 2,
              * hence this value is the zj to base the following
              * calculations on.


             /* hj is the number of values in the combined
              * sample equal to zj, in this case these are
              * within sample 1 only.
                           hj = val_eq_z_samp1 - val_st_z_samp1;

             /* H_j is the number of values in the combined
              * sample smaller than zj plus one half the the number
              * of values in the combined sample equal to zj
              * (that's hj/2).

                   H_j = val_st_z_samp1 + val_st_z_samp2
                         + hj / 2;

             /* F1j is the number of values in the 1st sample which
              * are less than zj plus, in this case these are within
              * sample 1 only one half the number of values in this
              * sample which are equal to zj. The latter are from
              * sample 1 only in this case.

                   F1j = val_st_z_samp1 + (double)
                        (val_eq_z_samp1 - val_st_z_samp1) / 2;

             /* F2j is the number of values in the 1st sample which
              * are less than zj plus one half the number of values
              * in this sample which are equal to zj. As
              * val_eq_z_samp1 < val_eq_z_samp2, these are the
              * val_st_z_samp2 only.

                           F2j = val_st_z_samp2;

             /* Set the line of values equal to zj to the actual line
              * of the last value picked for zj of sample 1 only in
              * this case

                   val_st_z_samp1 = val_eq_z_samp1;

             /* next the line of the next value z, ie. zj+1 is
              * addressed. Here, only sample 1 must be addressed.

                           if (val_eq_z_samp2 == 0)
                                   val_eq_z_samp2 = stop_loop2;

                     denom_1_aux = n_total * F1j - n_sample1 * H_j;
                     denom_2_aux = n_total * F2j - n_sample2 * H_j;

                     sum_adk_samp1 = sum_adk_samp1 + hj
                             * (denom_1_aux * denom_1_aux) /
                                                (H_j * (n_total - H_j)
                             - n_total * hj / 4);
                     sum_adk_samp2 = sum_adk_samp2 + hj
                             * (denom_2_aux * denom_2_aux) /
                                                 (H_j * (n_total - H_j)
                             - n_total * hj / 4);

                     next_z_sample2 = false;
                     equal_z_both_samples = false;

             /* index to count the z. It is only required to prevent
              * the while slope to execute endless

             // calculating the adk value is the final step.

             adk_result = (double) (n_total - 1) / (n_total
                     * n_total * (k - 1))
                     * (sum_adk_samp1 / n_sample1
                     + sum_adk_samp2 / n_sample2);

             /* if(adk_result <= adk_criterium)
              * adk_2_sample test is passed

                                 Figure 4

Appendix C.  A tunneling set up for remote metric implementation testing

   Parties interested in testing metric compliance is most convenient if
   all involved parties can stay in their local test laboratories.
   Figure 4 shows a test configuration which may enable remote metric
   compliance testing.

           +----+  +----+                                +----+  +----+
           |LC10|  |LC11|           ,---.                |LC20|  |LC21|
           +----+  +----+          /     \    +-------+  +----+  +----+
             | V10  | V11         /       \   | Tunnel|   | V20   |  V21
             |      |            (         )  | Head  |   |       |
            +--------+  +------+ |         |  | Router|__+----------+
            |Ethernet|  |Tunnel| |Internet |  +---B---+  |Ethernet  |
            |Switch  |--|Head  |-|         |      |      |Switch    |
            +-+--+---+  |Router| |         |  +---+---+  +--+--+----+
              |__|      +--A---+ (         )--|Option.|     |__|
                                  \       /   |Impair.|
            Bridge                 \     /    |Gener. |     Bridge
            V20 to V21              `-+-?     +-------+     V10 to V11

                                 Figure 5

   LC10 identify measurement clients /line cards.  V10 and the others
   denote VLANs.  All VLANs are using the same tunnel from A to B and in
   the reverse direction.  The remote site VLANs are U-bridged at the
   local site Ethernet switch.  The measurement packets of site 1 travel
   tunnel A->B first, are U-bridged at site 2 and travel tunnel B->A
   second.  Measurement packets of site 2 travel tunnel B->A first, are
   U-bridged at site 1 and travel tunnel A->B second.  So all
   measurement packets pass the same tunnel segments, but in different
   segment order.  An experiment to prove or reject the above test set
   up shown in figure 4 has been agreed but not yet scheduled between
   Deutsche Telekom and RIPE.

   Figure 4 includes an optional impairment generator.  If this
   impairment generator is inserted in the IP path between the tunnel
   head end routers, it equally impacts all measurement packets and
   flows.  Thus trouble with ensuring identical test set up by
   configuring two separated impairment generators identically is
   avoided (which was another proposal allowing remote metric compliance

Appendix D.  Glossary

   | ADK         | Anderson-Darling K-Sample test, a test used to      |
   |             | check whether two samples have the same statistical |
   |             | distribution.                                       |
   | ECMP        | Equal Cost Multipath, a load balancing mechanism    |
   |             | evaluating MPLS labels stacks, IP addresses and     |
   |             | ports.                                              |
   | EDF         | The "Empirical Distribution Function" of a set of   |
   |             | scalar measurements is a function F(x) which for    |
   |             | any x gives the fractional proportion of the total  |
   |             | measurements that were smaller than or equal as x.  |
   | Metric      | A measured quantity related to the performance and  |
   |             | reliability of the Internet, expressed by a value.  |
   |             | This could be a singleton (single value), a sample  |
   |             | of single values or a statistic based on a sample   |
   |             | of singletons.                                      |
   | OWAMP       | One-way Active Measurement Protocol, a protocol for |
   |             | communication between IPPM measurement systems      |
   |             | specified by IPPM.                                  |
   | OWD         | One-Way Delay, a performance metric specified by    |
   |             | IPPM.                                               |
   | Sample      | A sample metric is derived from a given singleton   |
   | metric      | metric by evaluating a number of distinct instances |
   |             | together.                                           |
   | Singleton   | A singleton metric is, in a sense, one atomic       |
   | metric      | measurement of this metric.                         |
   | Statistical | A 'statistical' metric is derived from a given      |
   | metric      | sample metric by computing some statistic of the    |
   |             | values defined by the singleton metric on the       |
   |             | sample.                                             |
   | TWAMP       | Two-way Active Measurement Protocol, a protocol for |
   |             | communication between IPPM measurement systems      |
   |             | specified by IPPM.                                  |

                                  Table 2

Authors' Addresses

   Ruediger Geib (editor)
   Deutsche Telekom
   Heinrich Hertz Str. 3-7
   Darmstadt,   64295

   Phone: +49 6151 628 2747

   Al Morton
   AT&T Labs
   200 Laurel Avenue South
   Middletown, NJ  07748

   Phone: +1 732 420 1571
   Fax:   +1 732 368 1192

   Reza Fardid
   Cariden Technologies
   888 Villa Street, Suite 500
   Mountain View, CA  94041


   Alexander Steinmitz
   HS Fulda
   Marquardstr. 35
   Fulda,   36039