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Internet Engineering Task Force (IETF)                      R. Geib, Ed.Request for Comments: 6576                              Deutsche TelekomBCP: 176                                                       A. MortonCategory: Best Current Practice                                AT&T LabsISSN: 2070-1721                                                R. Fardid                                                    Cariden Technologies                                                            A. Steinmitz                                                        Deutsche Telekom                                                              March 2012IP Performance Metrics (IPPM) Standard Advancement TestingAbstract   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 statistical methods.  The goal is an evaluation of   the metric RFC itself to determine whether its definitions are clear   and unambiguous to implementors and therefore a candidate for   advancement on the IETF Standards Track.  This document is an   Internet Best Current Practice.Status of This Memo   This memo documents an Internet Best Current Practice.   This document is a product of the Internet Engineering Task Force   (IETF).  It represents the consensus of the IETF community.  It has   received public review and has been approved for publication by the   Internet Engineering Steering Group (IESG).  Further information on   BCPs is available inSection 2 of RFC 5741.   Information about the current status of this document, any errata,   and how to provide feedback on it may be obtained athttp://www.rfc-editor.org/info/rfc6576.Geib, et al.              Best Current Practice                 [Page 1]

RFC 6576            IPPM Standard Advancement Testing         March 2012Copyright Notice   Copyright (c) 2012 IETF Trust and the persons identified as the   document authors.  All rights reserved.   This document is subject toBCP 78 and the IETF Trust's Legal   Provisions Relating to IETF Documents   (http://trustee.ietf.org/license-info) in effect on the date of   publication of this document.  Please review these documents   carefully, as they describe your rights and restrictions with respect   to this document.  Code Components extracted from this document must   include Simplified BSD License text as described in Section 4.e of   the Trust Legal Provisions and are provided without warranty as   described in the Simplified BSD License.Table of Contents1. Introduction ....................................................31.1. Requirements Language ......................................52. Basic Idea ......................................................53. Verification of Conformance to a Metric Specification ...........7      3.1. Tests of an Individual Implementation against a Metric           Specification ..............................................8      3.2. Test Setup Resulting in Identical Live Network           Testing Conditions .........................................9      3.3. Tests of Two or More Different Implementations           against a Metric Specification ............................153.4. Clock Synchronization .....................................163.5. Recommended Metric Verification Measurement Process .......17      3.6. Proposal to Determine an Equivalence Threshold for           Each Metric Evaluated .....................................204. Acknowledgements ...............................................215. Contributors ...................................................216. Security Considerations ........................................217. References .....................................................217.1. Normative References ......................................217.2. Informative References ....................................23Appendix A.  An Example on a One-Way Delay Metric Validation ......24A.1.  Compliance to Metric Specification Requirements ...........24A.2.  Examples Related to Statistical Tests for One-Way Delay ...25Appendix B.  Anderson-Darling K-sample Reference and 2 Sample                C++ Code .............................................27Appendix C.  Glossary .............................................36Geib, et al.              Best Current Practice                 [Page 2]

RFC 6576            IPPM Standard Advancement Testing         March 20121.  Introduction   The Internet Standards Process as updated byRFC 6410 [RFC6410]   specifies that widespread deployment and use is sufficient to show   interoperability as a condition for advancement to Internet Standard.   The previous requirement of interoperability tests prior to advancing   an RFC to the Standard maturity level specified inRFC 2026 [RFC2026]   andRFC 5657 [RFC5657] has been removed.  While the modified   requirement is applicable to protocols, wide deployment of different   measurement systems does not prove that the implementations measure   metrics in a standard way.Section 5.3 of RFC 5657 [RFC5657]   explicitly mentions the special case of Standards that are not "on-   the-wire" protocols.  While this special case is not explicitly   mentioned byRFC 6410 [RFC6410], the four criteria inSection 2.2 of   RFC 6410 [RFC6410] are augmented by this document for RFCs that   specify performance metrics.  This document takes the position that   flexible metric definitions can be proven to be clear and unambiguous   through tests that compare the results from independent   implementations.  It describes tests that infer whether metric   specifications are sufficient using a definition of metric   "interoperability": measuring equivalent results (in a statistical   sense) under the same network conditions.  The document expands on   this problem and its solution.   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, using the One-Way Delay Metric.   In the case of metric specifications, the conditions that satisfy the   "interoperability" requirement are less obvious, and there is a need   for IETF agreement on practices to judge metric specification   "interoperability" in the context of the IETF Standards Process.   This memo provides methods that 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].Geib, et al.              Best Current Practice                 [Page 3]

RFC 6576            IPPM Standard Advancement Testing         March 2012   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 protocol   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 that 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 this   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   requirement.   Conclusions on equivalence are reached by two measures.   First, implementations are compared against individual metric   specifications to make sure that differences in implementation are   minimized 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 statistical   methods, the equivalence of the results is verified.  To illustrateGeib, et al.              Best Current Practice                 [Page 4]

RFC 6576            IPPM Standard Advancement Testing         March 2012   application of the process and methods defined here, evaluation of   the One-Way Delay Metric [RFC2679] is provided inAppendix A.  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.   [TESTPLAN] can serve as a template for a metric RFC report that   accompanies the protocol action request to the Area Director,   including a description of the test setup, procedures, results for   each implementation, and conclusions.1.1.  Requirements Language   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this   document are to be interpreted as described inRFC 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 RECOMMENDED to use identical metric options for any test   proposed here (an exception would be if a variable parameter of the   metric definition is not configurable in one or more   implementations).  Calibrations specified by metric standards SHOULD   be performed to further identify (and possibly reduce) potential   sources of error in the test setup.   The IPPM Framework [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 areGeib, et al.              Best Current Practice                 [Page 5]

RFC 6576            IPPM Standard Advancement Testing         March 2012   expected to lead to small deviations in results only.  To   characterize statistical equivalence in the case of small deviations,   [RFC2330] and [RFC2679] suggest to apply a 95% confidence interval.   QuotingRFC 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      [RFC2330] for a discussion on self-consistency.   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 sample size must be large enough to minimize its influence on      the consistency of the test results.  This consideration may be      especially important if two implementations measure with different      average packet transmission rates.   o  The implementation with the lowest average packet transmission      rate determines the smallest temporal interval for which samples      can be compared.   o  Repeat comparisons with several independent metric samples to      avoid random indications of compatibility (or the lack of it).   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.Geib, et al.              Best Current Practice                 [Page 6]

RFC 6576            IPPM Standard Advancement Testing         March 2012   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 that 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,      measure across the Internet, and include a single impairment      generator to impact all measurement flows in a non-discriminatory      way.   The first two approaches work, but involve higher expenses than the   others (due to travel and/or shipping plus installation).  For the   third option, ensuring two identically configured impairment   generators requires well-defined test cases and possibly identical   hardware and software.Geib, et al.              Best Current Practice                 [Page 7]

RFC 6576            IPPM Standard Advancement Testing         March 2012   As documented in a test report [TESTPLAN], the last option was   required to prove compatibility of two delay metric implementations.   An impairment generator is probably required when testing   compatibility of most other metrics, and it is therefore RECOMMENDED   to include an impairment generator in metric test setups.3.1.  Tests of an Individual Implementation against a Metric      Specification   A metric implementation is compliant with a metric specification if   it supports the requirements classified as "MUST" and "REQUIRED" in   the related metric specification.  An implementation that implements   all requirements is fully compliant with the specification, and the   degree of compliance SHOULD be noted in the conclusions of the   report.   Further, supported options of a metric implementation SHOULD be   documented in sufficient detail to evaluate whether the specification   was correctly interpreted.  The documentation of chosen options   should minimize (and recognize) differences in the test setup if two   metric implementations are compared.  Further, this documentation is   used to validate or clarify the wording of the metric specification   option, to remove options that saw no implementation or that are   badly specified from the metric specification.  This documentation   SHOULD be included for all implementation-relevant specifications of   a metric picked for a comparison, even those that are not explicitly   marked as "MUST" or "REQUIRED" in the RFC text.  This applies for the   following sections of all metric specifications:   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 Synchronization-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      Metric.Geib, et al.              Best Current Practice                 [Page 8]

RFC 6576            IPPM Standard Advancement Testing         March 2012   [RFC2330] and [RFC2679] emphasize precision as an aim of IPPM metric   implementations.  A single IPPM-conforming implementation should   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 suggested for the metric test is   the Anderson-Darling K sample test (ADK sample test, K stands for the   number of samples to be compared) [ADK].  Please note thatRFC 2330   andRFC 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 a confidence level of 95%.  The conditions   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 set of parameters with the smallest   deviation 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.   The test conditions to be documented for a passed metric test   include:   o  The metric resolution at which a test was passed (e.g., the      resolution of timestamps).   o  The parameters modified by an impairment generator.   o  The impairment generator parameter settings.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 probeGeib, et al.              Best Current Practice                 [Page 9]

RFC 6576            IPPM Standard Advancement Testing         March 2012   flows results in repeated collection of data.  If both measures are   combined, Wide Area Network (WAN) 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, e.g., by   causing a high CPU load or by causing timestamp imprecision due to   unwanted queuing while transmitting or receiving test packets.   Tunneling multiple flows destined for a single physical port of a   network element allows transmission of all packets 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 a single outer IP origin and      destination address as well as origin and destination port numbers      that are identical for all packets.   o  An easily accessible tunneling protocol allows for carrying 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 setup and      operation to avoid disturbances or influence on the test results.   o  The tunneling protocol should not incur any extra cost for those      interested in setting up a metric test.   An illustration of a test setup with two layer 2 tunnels and two   flows between two linecards of one implementation is given in   Figure 1.Geib, et al.              Best Current Practice                [Page 10]

RFC 6576            IPPM Standard Advancement Testing         March 2012           Implementation                   ,---.       +--------+                               +~~~~~~~~~~~/     \~~~~~~| Remote |            +------->-----F2->-|          /       \     |->---+  |            | +---------+      | Tunnel 1(         )    |     |  |            | | transmit|-F1->-|         (         )    |->+  |  |            | | LC1     |      +~~~~~~~~~|         |~~~~|  |  |  |            | | receive |-<--+           (         )    | F1  F2 |            | +---------+    |           |Internet |    |  |  |  |            *-------<-----+  F2          |         |    |  |  |  |              +---------+ |  | +~~~~~~~~~|         |~~~~|  |  |  |              | transmit|-*  *-|         |         |    |--+<-*  |              | LC2     |      | Tunnel 2(         )    |  |     |              | receive |-<-F1-|          \       /     |<-*     |              +---------+      +~~~~~~~~~~~\     /~~~~~~| Router |                                            `-+-'       +--------+     For simplicity, only two linecards of one implementation and two                      flows F between them are shown.      Figure 1: Illustration of a Test Setup with Two Layer 2 Tunnels   Figure 2 shows the network elements required to set up layer 2   tunnels as shown by Figure 1.            Implementation            +-----+                   ,---.            | LC1 |                  /     \            +-----+                 /       \              +------+               |        +-------+  (         )  +-------+  |Remote|            +--------+  |       |  |         |  |       |  |      |            |Ethernet|  | Tunnel|  |Internet |  | Tunnel|  |      |            |Switch  |--| Head  |--|         |--| Head  |--|      |            +--------+  | Router|  |         |  | Router|  |      |               |        |       |  (         )  |       |  |Router|            +-----+     +-------+   \       /   +-------+  +------+            | LC2 |                  \     /            +-----+                   `-+-'   Figure 2: Illustration of a Hardware Setup to Realize the Test Setup        Illustrated by Figure 1 with Layer 2 Tunnels or PseudowiresGeib, et al.              Best Current Practice                [Page 11]

RFC 6576            IPPM Standard Advancement Testing         March 2012   The test setup successfully used during a delay metric test   [TESTPLAN] is given as an example in Figure 3.  Note that the shown   setup allows a metric test between two remote sites.           +----+  +----+                                +----+  +----+           |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 3: Example of Test Setup Successfully Used during a Delay                                Metic Test   In Figure 3, LC10 identifies measurement clients / linecards.  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.   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   Virtual LANs (VLANs) are applied and the measurement streams are   carried in different VLANs, the IP tunnel or pseudowires respectively   are setup in physical port mode to avoid setup of pseudowires per   VLAN (which may see different paths due to ECMP routing); see   [RFC4448].  The remote router and the Ethernet switch shown in   Figure 3 have to support 802.1Q in this setup.   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]).Geib, et al.              Best Current Practice                [Page 12]

RFC 6576            IPPM Standard Advancement Testing         March 2012   An Ethernet port mode IP tunnel carrying several 802.1Q VLANs each   containing measurement traffic of a single measurement system was   successfully applied when testing compatibility of two metric   implementations [TESTPLAN].  Ethernet over Layer 2 Tunneling Protocol   Version 3 (L2TPv3) [RFC4719] was picked for this test.   The following headers may have to be accounted for when calculating   total packet length, if VLANs and Ethernet over L2TPv3 tunnels are   applied:   o  Ethernet 802.1Q: 22 bytes.   o  L2TPv3 Header: 4-16 bytes for L2TPv3 data messages over IP; 16-28      bytes for L2TPv3 data messages over UDP.   o  IPv4 Header (outer IP header): 20 bytes.   o  MPLS Labels may be added by a carrier.  Each MPLS Label has a      length of 4 bytes.  At the time of this writing, between 1 and 4      Labels seems to be a fair guess of what's expected.   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 unsuitable: 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].  At the time of   this 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 setup, as such implementations may   cause incalculable delay shifts.   Ethernet pseudowires may also be set up on MPLS networks [RFC4448].   While there is no technical issue with this solution, MPLS interfaces   are mostly found in the network provider domain.  Hence, not all of   the above criteria for selecting a tunneling protocol are met.   Note that setting up a metric test environment is not a plug-and-play   issue.  Skilled networking engineers should be consulted and involved   if a setup between remote sites is preferred.   Passing or failing an ADK test with 2 samples could be a random   result (note that [RFC2330] defines a sample as a set of singleton   metric values produced by a measurement stream, and we continue to   use this terminology here).  The error margin of a statistical test   is higher if the number of samples it is based on is low (the number   of samples taken influences the so-called "degree of freedom" of aGeib, et al.              Best Current Practice                [Page 13]

RFC 6576            IPPM Standard Advancement Testing         March 2012   statistical test, and a higher degree of freedom produces more   reliable results).  To pass an ADK with higher probability, the   number of samples collected per implementation under identical   networking conditions SHOULD be greater than 2.  Hardware and load   constraints may enforce an upper limit on the number of simultaneous   measurement streams.  The ADK test allows one to combine different   samples (see Section 9 of [ADK]) and then to run a 2-sample test   between combined samples.  At least 4 samples per implementation   captured under identical networking conditions is RECOMMENDED when   comparing different metric implementations by a statistical test.   It is RECOMMENDED that tests be carried out by establishing N   different parallel measurement flows.  Two or three linecards per   implementation serving to send or receive measurement flows should be   sufficient to create 4 or more parallel measurement flows.  Other   options are to separate flows by DiffServ marks (without deploying   any Quality of Service (QoS) in the inner or outer tunnel) or to use   a single Constant Bitrate (CBR) flow and evaluate whether every n-th   singleton belongs to a specific measurement flow.  Note that a   practical test indeed showed that ADK passed with 4 samples even if a   2-sample test failed [TESTPLAN].   Some additional guidelines to calculate and compare samples to   perform a metric test are:   o  Comparing different probes of a common underlying distribution in      terms of metrics characterizing a communication network requires      respecting the temporal nature for which the assumption of a      common underlying distribution may hold.  Any singletons or      samples to be compared must be captured within the same time      interval.   o  If statistical events like rates are used to characterize measured      metrics of a time interval, a minimum of 5 singletons of a      relevant metric should be picked to ensure a minimum confidence      into the reported value.  The error margin of the determined rate      depends on the number of singletons (refer to statistical      textbooks on student's t-test).  As an example, any packet loss      measurement interval to be compared with the results of another      implementation contains at least five lost packets to have some      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 smallGeib, et al.              Best Current Practice                [Page 14]

RFC 6576            IPPM Standard Advancement Testing         March 2012      differences in distributions fairly well and will fail for a high      number of compared results (RFC 2330 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-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      Specification   [RFC2330] expects that "a methodology for a given metric exhibits   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 specifications, however, allow for implementor options to   the largest possible degree.  It cannot be expected that two   implementors allow 100% identical options in their implementations.   Testers SHOULD pick the same metric measurement 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 metric implementation options, the individual options   picked for every compared metric implementation should be documented   as specified inSection 3.5.  If the cause of the failure is a lack   of specification clarity or multiple legitimate interpretations of   the definition text, the text should be modified and the resulting   memo proposed for consensus and (possible) advancement to Internet   Standard.   The same statistical test as applicable to quantify precision of a   single metric implementation must be used to compare metric result   equivalence for different implementations.  To documentGeib, et al.              Best Current Practice                [Page 15]

RFC 6576            IPPM Standard Advancement Testing         March 2012   compatibility, the smallest measurement resolution at which the   compared implementations passed the ADK sample test must be   documented.   For different implementations of the same metric, "variations in   conditions" are reasonably expected.  The ADK test comparing samples   of the different implementations may result in a lower precision than   the test for precision in the same-implementation comparison.3.4.  Clock Synchronization   Clock synchronization effects require special attention.  Accuracy of   one-way active delay measurements for any metric implementation   depends on clock synchronization between the source and destination   of tests.  Ideally, one-way active delay measurement [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 and distort sample one-way values and their   interval statistics.  Discarding sample one-way delay values for any   implementation is recommended when one of the following reliability   conditions is met:   o  Delay is measured and is finite in one direction but not the      other.   o  Absolute value of the difference between the sum of one-way      measurements in both directions and the round-trip measurement is      greater than X% of the latter value.   Examination of the second condition requires round-trip time (RTT)   measurement for reference, e.g., based on TWAMP [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 requires further   study.Geib, et al.              Best Current Practice                [Page 16]

RFC 6576            IPPM Standard Advancement Testing         March 2012   An IPPM-compliant metric implementation of an RFC that requires   synchronized clocks is expected to provide precise measurement   results.   IF an implementation publishes a specification of its precision, such   as "a precision of 1 ms (+/- 500 us) with a confidence of 95%", then   the specification should be met over a useful measurement duration.   For example, if the metric is measured along an Internet path that is   stable and not 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   Internet Standard status is clearly written, that there are a   sufficient number of verified equivalent implementations, and that   options that have been implemented are documented.   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 is 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 as   specified in this document.   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 Internet Standard.   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,Geib, et al.              Best Current Practice                [Page 17]

RFC 6576            IPPM Standard Advancement Testing         March 2012   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 to Internet Standard, as described here (similar   to the reports 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 4.      ,---.     /     \    ( 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   |                   +-------+                                +----------+       Figure 4: Illustration of the Metric Standardization Process   Any recommendation for the advancement of a metric specification MUST   be accompanied by an implementation report.  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 participants have the clearest context in   their minds regarding the different subtleties that can arise.Geib, et al.              Best Current Practice                [Page 18]

RFC 6576            IPPM Standard Advancement Testing         March 2012   In particular, the implementation report MUST include the following   at minimum:   o  The metric compared and the RFC specifying it.  This includes      statements as required bySection 3.1 ("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), Differentiated Services Code Point      (DSCP), and any other measurement stream properties that could      result in deviating results.  Deviations in results can also be      caused if chosen IP addresses and ports of different      implementations 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 bySection 3.3 ("Tests of Two or More      Different Implementations against a Metric Specification") of this      document.   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 inSection 3.2 ("Test Setup Resulting in Identical Live   Network Testing Conditions".   If a different test setup 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:Geib, et al.              Best Current Practice                [Page 19]

RFC 6576            IPPM Standard Advancement Testing         March 2012   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 the 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 countermeasure is to connect the      measurement equipment to be compared by a NAT device or establish      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.  Proposal to Determine an Equivalence Threshold for Each Metric      Evaluated   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 is 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   implementation.   Comparative results for the same implementation represent a bound on   cross-implementation equivalence.  This should be particularly useful   when the metric does *not* produce 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 one-way delay and   should be likewise applicable to distributions of delay variation.Geib, et al.              Best Current Practice                [Page 20]

RFC 6576            IPPM Standard Advancement Testing         March 2012Appendix B discusses two possible ways to perform the ADK analysis:   the R statistical language [Rtool] with ADK package [Radk] and C++   code.   Conclusion: 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 implementations.   Thus, when 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 draft version of this document;   he suggested statistical tests and the evaluation of time series   information.  Matthias Wieser's thesis on a metric test resulted in   new input for this document.  Henk Uijterwaal and Lars Eggert have   encouraged and helped to organize this work.  Mike Hamilton, Scott   Bradner, David Mcdysan, and Emile Stephan commented on this document.   Carol Davids reviewed a version of the document before it became a WG   item.5.  Contributors   Scott Bradner, Vern Paxson, and Allison Mankin drafted [METRICTEST],   and major parts of it are included in this document.6.  Security Considerations   This memo does not raise any specific security issues.7.  References7.1.  Normative References   [RFC2003]      Perkins, C., "IP Encapsulation within IP",RFC 2003,                  October 1996.   [RFC2119]      Bradner, S., "Key words for use in RFCs to Indicate                  Requirement Levels",BCP 14,RFC 2119, March 1997.Geib, et al.              Best Current Practice                [Page 21]

RFC 6576            IPPM Standard Advancement Testing         March 2012   [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.   [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.   [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.   [RFC6410]      Housley, R., Crocker, D., and E. Burger, "Reducing the                  Standards Track to Two Maturity Levels",BCP 9,RFC 6410, October 2011.Geib, et al.              Best Current Practice                [Page 22]

RFC 6576            IPPM Standard Advancement Testing         March 20127.2.  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-Duffield]  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.   [METRICTEST]   Bradner, S. and V. Paxson, "Advancement of metrics                  specifications on the IETF Standards Track", Work                  in Progress, August 2007.   [RFC2026]      Bradner, S., "The Internet Standards Process --                  Revision 3",BCP 9,RFC 2026, October 1996.   [RFC4459]      Savola, P., "MTU and Fragmentation Issues with In-the-                  Network Tunneling",RFC 4459, April 2006.   [RFC5357]      Hedayat, K., Krzanowski, R., Morton, A., Yum, K., and                  J. Babiarz, "A Two-Way Active Measurement Protocol                  (TWAMP)",RFC 5357, October 2008.   [Radk]         Scholz, F., "adk: Anderson-Darling K-Sample Test and                  Combinations of Such Tests.  R package version 1.0",                  2008.   [Rtool]        R Development Core Team, "R: A language and                  environment for statistical computing.  R Foundation                  for Statistical Computing, Vienna, Austria.  ISBN                  3-900051-07-0", 2011, <http://www.R-project.org/>.   [TESTPLAN]     Ciavattone, L., Geib, R., Morton, A., and M. Wieser,                  "Test Plan and Results for AdvancingRFC 2679 on the                  Standards Track", Work in Progress, March 2012.Geib, et al.              Best Current Practice                [Page 23]

RFC 6576            IPPM Standard Advancement Testing         March 2012Appendix A.  An Example on a One-Way Delay Metric Validation   The text of this appendix is not binding.  It is an example of what   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 Sections3.5 (3rd   bullet point) and 3.8.2 of [RFC2679].   (1)  Configure a path with 1-second 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-second 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   that may be present in an implementation.  SeeSection 3.7.2 of   [RFC2679] andSection 10.2 of [RFC2330].   (1)  Configure a path with X ms one-way constant delay and ideally        include 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).Geib, et al.              Best Current Practice                [Page 24]

RFC 6576            IPPM Standard Advancement Testing         March 2012   (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        stationary.   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   that may be present in an implementation.  This test is intended to   evaluate measurements in Sections3 and4 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 inSection 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   result of 1 ms.  The same test may fail if timestamps with a   resolution of 100 microseconds are evaluated.  The implementation 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 that sample delay values are calculated for each system   for identical 6-minute intervals for the duration of the whole test.Geib, et al.              Best Current Practice                [Page 25]

RFC 6576            IPPM Standard Advancement Testing         March 2012   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, e.g., 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.Geib, et al.              Best Current Practice                [Page 26]

RFC 6576            IPPM Standard Advancement Testing         March 2012   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 the 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 test   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 K-sample Reference and 2 Sample C++ Code   There are many statistical tools available, and this appendix   describes two that are familiar to the authors.   The "R tool" is a language and command-line environment for   statistical computing and plotting [Rtool].  With the optional "adk"   package installed [Radk], it can perform individual and combined   sample ADK computations.  The user must consult the package   documentation and the original paper [ADK] to interpret the results,   but this is as it should be.   The C++ code below will perform an AD2-sample comparison when   compiled and presented with two column vectors in a file (using white   space as separation).  This version contains modifications made by   Wes Eddy in Sept 2011 to use the vectors and run as a stand-alone   module.  The status of the comparison can be checked on the command   line with "$ echo $?" or the last line can be replaced with a printf   statement for adk_result instead.  /*      Copyright (c) 2012 IETF Trust and the persons identified      as authors of the code.  All rights reserved.      Redistribution and use in source and binary forms, with      or without modification, is permitted pursuant to, and subject      to the license terms contained in, the Simplified BSD License      set forth inSection 4.c of the IETF Trust's Legal Provisions      Relating to IETF Documents (http://trustee.ietf.org/license-info).Geib, et al.              Best Current Practice                [Page 27]

RFC 6576            IPPM Standard Advancement Testing         March 2012  */  /* 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:  *http://www.itl.nist.gov/div898/software/dataplot.html/  * June 2001. */ #include <iostream> #include <fstream> #include <vector> #include <sstream> using namespace std; int main() {    vector<double> vec1, vec2;    double adk_result;    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,               old_eq_line1;    static double adk_criterium = 1.993;    /* vec1 and vec2 to be initialized with sample 1 and     * sample 2 values in ascending order */    while (!cin.eof()) {       double f1, f2;       cin >> f1;       cin >> f2;       vec1.push_back(f1);       vec2.push_back(f2);Geib, et al.              Best Current Practice                [Page 28]

RFC 6576            IPPM Standard Advancement Testing         March 2012    }    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 requiredGeib, et al.              Best Current Practice                [Page 29]

RFC 6576            IPPM Standard Advancement Testing         March 2012     * 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++;                    }            }            else            {            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] )                    {                    val_eq_z_samp2++;                    }    /* the smaller of the two actual data values is picked     * as the next zj.     */        if(z > z_aux)Geib, et al.              Best Current Practice                [Page 30]

RFC 6576            IPPM Standard Advancement Testing         March 2012                    {                    z = z_aux;                    next_z_sample2 = true;                    }             else                    {                    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;                    }                }            }           else              {            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 number of               * values in the combined sample equal to zj               * (that's hj/2).               */                  H_j = val_st_z_samp1 + val_st_z_samp2Geib, et al.              Best Current Practice                [Page 31]

RFC 6576            IPPM Standard Advancement Testing         March 2012                         + hj / 2;              /* F1j is the number of values in the 1st sample               * that are less than zj plus one half the number               * of values in this sample that 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               * that are less than zj plus one half the number               * of values in this sample that 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 zj of 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, i.e., zj+1               * are addressed.               */                val_eq_z_samp1++;              /* next the lines of the next values z, i.e.,               * zj+1 are addressed               */                  val_eq_z_samp2++;                  }           else                  {              /* 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)                            {Geib, et al.              Best Current Practice                [Page 32]

RFC 6576            IPPM Standard Advancement Testing         March 2012              /* 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 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 that               * are less than zj plus one half the number of values in               * this sample that 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 that               * are less than zj plus one half the number of values in               * this sample that 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, i.e., zj+1 is               * addressed.  Here, only sample 2 must be addressed.               */                    val_eq_z_samp2++;                                    if (val_eq_z_samp1 == 0)                                    {                                    val_eq_z_samp1 = stop_loop1;                                    }                            }Geib, et al.              Best Current Practice                [Page 33]

RFC 6576            IPPM Standard Advancement Testing         March 2012    /* the smaller z value was contained in sample 2;     * hence, this value is the zj to base the following     * calculations on.     */                  else                  {    /* 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 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 that     * are less than zj plus; in this case, these are within     * sample 1 only one half the number of values in this     * sample that 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 that     * are less than zj plus one half the number of values     * in this sample that 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;Geib, et al.              Best Current Practice                [Page 34]

RFC 6576            IPPM Standard Advancement Testing         March 2012    /* next the line of the next value z, i.e., zj+1 is     * addressed.  Here, only sample 1 must be addressed.     */                  val_eq_z_samp1++;                  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     */            j++;            }    // 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     */    return adk_result <= adk_criterium; }Geib, et al.              Best Current Practice                [Page 35]

RFC 6576            IPPM Standard Advancement Testing         March 2012Appendix C.  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 to 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.                                  |   +-------------+-----------------------------------------------------+Geib, et al.              Best Current Practice                [Page 36]

RFC 6576            IPPM Standard Advancement Testing         March 2012Authors' Addresses   Ruediger Geib (editor)   Deutsche Telekom   Heinrich Hertz Str. 3-7   Darmstadt  64295   Germany   Phone: +49 6151 58 12747   EMail: Ruediger.Geib@telekom.de   Al Morton   AT&T Labs   200 Laurel Avenue South   Middletown, NJ  07748   USA   Phone: +1 732 420 1571   Fax:   +1 732 368 1192   EMail: acmorton@att.com   URI:http://home.comcast.net/~acmacm/   Reza Fardid   Cariden Technologies   888 Villa Street, Suite 500   Mountain View, CA  94041   USA   Phone:   EMail: rfardid@cariden.com   Alexander Steinmitz   Deutsche Telekom   Memmelsdorfer Str. 209b   Bamberg  96052   Germany   Phone:   EMail: Alexander.Steinmitz@telekom.deGeib, et al.              Best Current Practice                [Page 37]