Benchmarking Methodology Working Group                         G. Lencse
Internet-Draft                               Szechenyi Istvan University
Intended status: Informational                                  K. Shima
Expires: 1 January 2023                         IIJ Innovation Institute
                                                            30 June 2022


  Benchmarking Methodology for Stateful NATxy Gateways using RFC 4814
                       Pseudorandom Port Numbers
               draft-lencse-bmwg-benchmarking-stateful-04

Abstract

   RFC 2544 has defined a benchmarking methodology for network
   interconnect devices.  RFC 5180 addressed IPv6 specificities and it
   also provided a technology update, but excluded IPv6 transition
   technologies.  RFC 8219 addressed IPv6 transition technologies,
   including stateful NAT64.  However, none of them discussed how to
   apply RFC 4814 pseudorandom port numbers to any stateful NATxy
   (NAT44, NAT64, NAT66) technologies.  We discuss why using
   pseudorandom port numbers with stateful NATxy gateways is a difficult
   problem.  We recommend a solution limiting the port number ranges and
   using two phases: the preliminary phase and the real test phase.  We
   show how the classic performance measurement procedures (e.g.
   throughput, frame loss rate, latency, etc.) can be carried out.  We
   also define new performance metrics and measurement procedures for
   maximum connection establishment rate, connection tear down rate and
   connection tracking table capacity measurements.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on 1 January 2023.






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Copyright Notice

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   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   Please review these documents carefully, as they describe your rights
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   provided without warranty as described in the Revised BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
   2.  Pseudorandom Port Numbers and Stateful Translation  . . . . .   3
   3.  Test Setup and Terminology  . . . . . . . . . . . . . . . . .   4
   4.  Recommended Benchmarking Method . . . . . . . . . . . . . . .   5
     4.1.  Restricted Port Number Ranges . . . . . . . . . . . . . .   6
     4.2.  Preliminary Test Phase  . . . . . . . . . . . . . . . . .   6
     4.3.  Consideration of the Cases of Stateful Operation  . . . .   7
     4.4.  Control of the Connection Tracking Table Entries  . . . .   8
     4.5.  Measurement of the Maximum Connection Establishment
            Rate . . . . . . . . . . . . . . . . . . . . . . . . . .   9
     4.6.  Validation of Connection Establishment  . . . . . . . . .  10
     4.7.  Real Test Phase . . . . . . . . . . . . . . . . . . . . .  11
     4.8.  Measurement of the Connection Tear Down Rate  . . . . . .  12
     4.9.  Measurement of the Connection Tracking Table Capacity . .  13
     4.10. Writing and Reading Order of the State Table  . . . . . .  18
   5.  Implementation and Experience . . . . . . . . . . . . . . . .  18
   6.  Limitations of using UDP as Transport Layer Protocol  . . . .  18
   7.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  19
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  19
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  19
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  19
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  19
     10.2.  Informative References . . . . . . . . . . . . . . . . .  20
   Appendix A.  Change Log . . . . . . . . . . . . . . . . . . . . .  21
     A.1.  00  . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
     A.2.  01  . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
     A.3.  02  . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
     A.4.  03  . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
     A.5.  04  . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  22




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1.  Introduction

   [RFC2544] has defined a comprehensive benchmarking methodology for
   network interconnect devices, which is still in use.  It was mainly
   IP version independent, but it used IPv4 in its examples.  [RFC5180]
   addressed IPv6 specificities and also added technology updates, but
   declared IPv6 transition technologies out of its scope.  [RFC8219]
   addressed the IPv6 transition technologies, including stateful NAT64.
   It has reused several benchmarking procedures from [RFC2544] (e.g.
   throughput, frame loss rate), it has redefined the latency
   measurement, and added further ones, e.g. the PDV (packet delay
   variation) measurement.

   However, none of them discussed, how to apply [RFC4814] pseudorandom
   port numbers, when benchmarking stateful NATxy (NAT44, NAT64, NAT66)
   gateways.  We are not aware of any other RFCs that address this
   question.

   First, we discuss why using pseudorandom port numbers with stateful
   NATxy gateways is a hard problem.

   Then we recommend a solution.

1.1.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

2.  Pseudorandom Port Numbers and Stateful Translation

   In its appendix, [RFC2544] has defined a frame format for test frames
   including specific source and destination port numbers.  [RFC4814]
   recommends to use pseudorandom and uniformly distributed values for
   both source and destination port numbers.  However, stateful NATxy
   (NAT44, NAT64, NAT66) solutions use the port numbers to identify
   connections.  The usage of pseudorandom port numbers causes different
   problems depending on the direction.

   *  As for the private to public direction, pseudorandom source and
      destination port numbers could be used, however, this approach
      would be a denial of service attack against the stateful NATxy
      gateway, because it would exhaust its connection tracking table
      capacity.  To that end, let us see some calculations using the
      recommendations of RFC 4814:




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      -  The recommended source port range is: 1024-65535, thus its size
         is: 64512.

      -  The recommended destination port range is: 1-49151, thus its
         size is: 49151.

      -  The number of source and destination port number combinations
         is: 3,170,829,312.

      We note that section 12 of [RFC2544] also requires testing with
      256 destination networks, which further increases the number of
      connection tracking table entries.

   *  As for the public to private direction, the stateful DUT (Device
      Under Test) would drop any packets that do not belong to an
      existing connection, therefore, the direct usage of pseudorandom
      port numbers from the above-mentioned ranges is not feasible.

3.  Test Setup and Terminology

   Our methodology works with any IP version.  We use IPv4 in the Test
   Setup shown in Figure 1 to facilitate its easy understanding based on
   the well-known stateful NAT44 (also called NAPT: Network Address and
   Port Translation) solution.


                 +--------------------------------------+
        10.0.0.2 |Initiator                    Responder| 198.19.0.2
   +-------------|                Tester                |<------------+
   | private IPv4|                         [state table]| public IPv4 |
   |             +--------------------------------------+             |
   |                                                                  |
   |             +--------------------------------------+             |
   |    10.0.0.1 |                 DUT:                 | 198.19.0.1  |
   +------------>|        Sateful NATxy gateway         |-------------+
     private IPv4|     [connection tracking table]      | public IPv4
                 +--------------------------------------+


       Figure 1: Test Setup for benchmarking stateful NATxy gateways


   As for transport layer protocol, [RFC2544] recommended testing with
   UDP, and it was kept also in [RFC8219].  For the general
   recommendation, we also keep UDP, thus the port numbers in the
   following text are to be understood as UDP port numbers.  We discuss
   the limitation of this approach in Section 6.




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   We define the most important elements of our proposed benchmarking
   system as follows.

   *  Connection tracking table: The stateful NATxy gateway uses a
      connection tracking table to be able to perform the stateful
      translation in the public to private direction.  Its size, policy
      and content are unknown for the Tester.

   *  Four tuple: The four numbers that identify a connection are source
      IP address, source port number, destination IP address,
      destination port number.

   *  State table: The Responder of the Tester extracts the four tuple
      from each received test frame and stores it in its state table.
      Recommendation is given for writing and reading order of the state
      table in Section 4.10.

   *  Initiator: The port of the Tester that may initiate a connection
      through the stateful DUT in the private to public direction.
      Theoretically, it can use any source and destination port numbers
      from the ranges recommended by [RFC4814]: if the used four tuple
      does not belong to an existing connection, the DUT will register a
      new connection into its connection tracking table.

   *  Responder: The port of the Tester that may not initiate a
      connection through the stateful DUT in the public to private
      direction.  It may send only frames that belong to an existing
      connection.  To that end, it uses four tuples that have been
      previously extracted from the received test frames and stored in
      its state table.

   *  Preliminary test phase: Test frames are sent only by the Initiator
      to the Responder through the DUT to fill both the connection
      tracking table of the DUT and the state table of the Responder.
      This is a newly introduced operation phase for stateful NATxy
      benchmarking.  The necessity of this phase is explained in
      Section 4.2.

   *  Real test phase: The actual test (e.g. throughput, latency, etc.)
      is performed in this phase after the completion of the preliminary
      test phase.  Test frames are sent as required (e.g. bidirectional
      test or unidirectional test in any of the two directions).

4.  Recommended Benchmarking Method







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4.1.  Restricted Port Number Ranges

   The Initiator SHOULD use restricted ranges for source and destination
   port numbers to avoid the denial of service attack like event against
   the connection tracking table of the DUT described in Section 2.  The
   size of the source port number range SHOULD be larger (e.g. in the
   order of a few times ten thousand), whereas the size of the
   destination port number range SHOULD be smaller (may vary from a few
   to several hundreds or thousands as needed).  The rationale is that
   source and destination port numbers that can be observed in the
   Internet traffic are not symmetrical.  Whereas source port numbers
   may be random, there are a few very popular destination port numbers
   (e.g. 443, 80, etc., see [IIR2020]) and others hardly occur.  And we
   have found that their role is also asymmetric in the Linux kernel
   routing hash function [LEN2020].

   The product of the sizes of the two ranges can be used as a
   parameter.  The performance of the stateful NATxy gateway MAY be
   examined as a function of this parameter.

4.2.  Preliminary Test Phase

   The preliminary phase serves two purposes:

   1.  The connection tracking table of the DUT is filled.  It is
       important, because its maximum connection establishment rate may
       be lower than its maximum frame forwarding rate (that is
       throughput).

   2.  The state table of the Responder is filled with valid four
       tuples.  It is a precondition for the Responder to be able to
       transmit frames that belong to connections exist in the
       connection tracking table of the DUT.

   Whereas the above two things are always necessary before the real
   test phase, the preliminary phase can be used without the real test
   phase.  It is done so, when the maximum connection establishment rate
   is measured (as described in Section 4.5).

   A preliminary test phase MUST be performed before all tests performed
   in the real test phase.  In this phase, the following things happen:

   1.  The Initiator sends test frames to the Responder through the DUT
       at a specific frame rate.

   2.  The DUT performs the stateful translation of the test frames and
       it also stores the new combinations in its connection tracking
       table.



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   3.  The Responder receives the translated test frames and updates its
       state table with the received four tuples.  The responder
       transmits no test frames during the preliminary phase.

   When the preliminary test phase is performed in preparation to the
   real test phase, the applied frame rate and the duration of the
   preliminary phase SHOULD be carefully selected so that:

   *  The applied frame rate be safely lower than the maximum connection
      establishment rate.

   *  Enough four tuples be stored in the state table of the Responder
      so that it can generate frames with the proper distribution of the
      four tuples.

   Please refer to Section 4.4 for further conditions regarding timeout
   and port number combinations.

4.3.  Consideration of the Cases of Stateful Operation

   We consider the most important Events that may happen during the
   operation of a stateful NATxy gateway, and the Actions of the gateway
   as follows.

   1.  EVENT: A packet not belonging to an existing connection arrives
       in the private to public direction.  ACTION: A new connection is
       registered into the connection tracking table and the packet is
       translated and forwarded.

   2.  EVENT: A packet not belonging to an existing connection arrives
       in the public to private direction.  ACTION: The packet is
       discarded.

   3.  EVENT: A packet belonging to an existing connection arrives (in
       any dicection).  ACTION: The packet is translated and forwarded
       and the timeout counter of the corresponding connection tracking
       table entry is reset.

   4.  EVENT: A connection tracking table entry times out.  ACTION: The
       entry is deleted from the connection tracking table.

   Due to "black box" testing, the Tester is not able to directly
   examine (or delete) the entries of the connection tracking table.
   But the entires can be and MUST be controlled by setting an
   appropriate timeout value and carefully selecting the port numbers of
   the packets (as described in Section 4.4) to be able to produce
   meaningful and repeatable measurement results.




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   We aim to support the measurement of the following performance
   characteristics of a stateful NATxy gateway:

   1.  maximum connection establishment rate

   2.  all "classic" performance metrics like throughput, frame loss
       rate, latency, etc.

   3.  connection tear down rate

   4.  connection tracking table capacity

4.4.  Control of the Connection Tracking Table Entries

   It is necessary to control the connection tracking table entries of
   the DUT in order to achieve clear conditions for the measurements.
   We can simply achieve the following two extreme situations:

   1.  All frames create a new entry in the connection tracking table of
       the DUT and no old entries are deleted during the test.  This is
       required for measuring the maximum connection establishment rate.

   2.  No new entries are created in the connection tracking table of
       the DUT and no old ones are deleted during the test.  This is
       ideal for the real test phase measurements, like throughput,
       latency, etc.

   From this point we use the following three assumptions:

   1.  A single source address destination address pair is used for all
       tests.  We make this assumption for simplicity.  Of course, we
       are aware that [RFC2544] requires testing also with 256 different
       destination networks.

   2.  The connection tracking table of the stateful NATxy is large
       enough to store all connections defined by the different source
       port number destination port number combinations.

   3.  Each experiment is started with an empty connection tracking
       table.  (It can be ensured by deleting its content before the
       experiment.)

   The first extreme situation can be achieved by

   *  using different source port number destination port number
      combinations for every single test frame in the preliminary phase
      and




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   *  setting the UDP timeout of the NATxy gateway to a value higher
      than the length of the preliminary phase.

   The second extreme situation can be achieved by

   *  enumerating all the possible source port number destination port
      number combinations in the preliminary phase and

   *  setting the UDP timeout of the NATxy gateway to a value higher
      than the length of the preliminary phase plus the gap between the
      two phases plus the length of the real test phase.

   [RFC4814] REQUIRES pseudorandom port numbers, which we believe is a
   good approximation of the distribution of the source port numbers a
   NATxy gateway on the Internet may face with.

   We note that although the enumeration of all possible source port
   number destination port number combinations is not a requirement for
   the first extreme situation and the usage of different source port
   number destination port number combinations is not a requirement for
   the second extreme situation, pseudorandom enumeration of source port
   number destination port number combinations is a good solution in
   both cases.  It may be computing efficiently generated by preparing a
   random permutation of the previously enumerated all possible source
   port number destination port number combinations using Dustenfeld's
   random shuffle algorithm [DUST1964].

   Important warning: in normal (non-NAT) router testing, the port
   number selection algorithm, whether it is pseudo-random or enumerated
   in increasing (or decreasing) order does not affect final results.
   However, our experience with iptables shows that if the connection
   tracking table is filled using port number enumeration in increasing
   order, then the maximum connection establishment rate of iptables
   degrades significantly compared to its performance using pseudorandom
   port numbers [LEN2021].

   The enumeration of the source port number destination port number
   combinations in increasing or decreasing order (or in any other
   specific order) MAY be used as an additional measurement.

4.5.  Measurement of the Maximum Connection Establishment Rate

   The maximum connection establishment rate is an important
   characteristic of the stateful NATxy gateway and its determination is
   necessary for the safe execution of the preliminary test phase
   (without frame loss) before the real test phase.





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   The measurement procedure of the maximum connection establishment
   rate is very similar to the throughput measurement procedure defined
   in [RFC2544].

   Procedure: The Initiator sends a specific number of test frames using
   all different source port number destination port number combinations
   at a specific rate through the DUT.  The Responder counts the frames
   that are successfully translated by the DUT.  If the count of offered
   frames is equal to the count of received frames, the rate of the
   offered stream is raised and the test is rerun.  If fewer frames are
   received than were transmitted, the rate of the offered stream is
   reduced and the test is rerun.

   The maximum connection establishment rate is the fastest rate at
   which the count of test frames successfully translated by the DUT is
   equal to the number of test frames sent to it by the Initiator.

   Notes:

   1.  In practice, we RECOMMEND the usage of binary search.

   2.  As for the successful translation, the Responder MAY check that
       the source IP address is different than the original source IP
       address set by the Initiator.  However, it is still not a
       guarantee for the establishment of the connection in the DUT.
       Therefore we RECOMMEND the usage of the validation of the
       connection establishment defined in Section 4.6.

4.6.  Validation of Connection Establishment

   Due to "black box" testing, the entries of the connection tracking
   table of the DUT may not be directly examined, but the presence of
   the connections can be checked easily by sending frames from the
   Responder to the Initiator in the Real Test Phase using all four
   tuples stored in the state table of the Tester (at a low enough frame
   rate).  The arrival of all test frames indicates that the connections
   are really present.

   Procedure: When all the desired N number of test frames were sent by
   the Initiator to the Receiver at frame rate R in the Preliminary
   Phase for the maximum connection establishment rate measurement, and
   the Receiver has successfully received all the N frames, the
   establishment of the connections is checked in the Real Test Phase as
   follows:

   *  The Responder sends test frames to the Initiator at frame rate:
      r=R*alpha, for the duration of N/r using a different four tuple
      from its state table for each test frame.



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   *  The Initiator counts the received frames, and if all N frames are
      arrived then the frame rate of the maximum connection
      establishment rate is raised, otherwise lowered (as well as in the
      case if test frames were missing in the preliminary phase).

   Notes:

   *  The alpha is a kind of "safety factor", its aim is to make sure
      that the frame rate used for the validation is not too high, and
      test may fail only in the case if at least one connection is not
      present in the connection tracking table of the DUT.  (So alpha
      should be typically less than 1, e.g.  0.8 or 0.5.)

   *  The duration of N/r and the frame rate of r means that N frames
      are sent for validation.

   *  The order of four tuple selection is arbitrary provided that all
      four tuples MUST be used.

   *  Please refer to Section 4.9 for a short analysis of the operation
      of the measurement and what problems may occur.

4.7.  Real Test Phase

   As for the traffic direction, there are three possible cases during
   the real test phase:

   *  bidirectional traffic: The Initiator sends test frames to the
      Responder and the Responder sends test frames to the Initiator.

   *  unidirectional traffic from the Initiator to the Responder: The
      Initiator sends test frames to the Responder but the Responder
      does not send test frames to the Initiator.

   *  unidirectional traffic from the Responder to the Initiator: The
      Responder sends test frames to the Initiator but the Initiator
      does not send test frames to the Responder.

   If the Initiator sends test frames, then it uses pseudorandom source
   port numbers and destination port numbers from the restricted port
   number ranges.  The responder receives the test frames, updates its
   state table and processes the test frames as required by the given
   measurement procedure (e.g. only counts them for throughput test,
   handles timestamps for latency or PDV tests, etc.).







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   If the Responder sends test frames, then it uses the four tuples from
   its state table.  The reading order of the state table may follow
   different policies (discussed in Section 4.10).  The Initiator
   receives the test frames, and processes them as required by the given
   measurement procedure.

   As for the actual measurement procedures, we RECOMMEND to use the
   updated ones from Section 7 of [RFC8219].

4.8.  Measurement of the Connection Tear Down Rate

   Connection tear down can cause significant load for the NATxy
   gateway.  The connection tear down performance can be measured as
   follows:

   1.  Load a certain number of connections (N) into the connection
       tracking table of the DUT (in the same way as done to measure the
       maximum connection establishment rate).

   2.  Record TimestampA.

   3.  Delete the content of the connection tracking table of the DUT.

   4.  Record TimestampB.

   The connection tear down rate can be computed as:

   connection tear down rate = N / ( TimestampB - TimestampA)

   The connection tear down rate SHOULD be measured for various values
   of N.

   We assume that the content of the connection tracking table may be
   deleted by an out-of-band control mechanism specific to the given
   NATxy gateway implementation.  (E.g. by removing the appropriate
   kernel module under Linux.)

   We are aware that the performance of removing the entire content of
   the connection tracking table at one time may be different from
   removing all the entries one by one.











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4.9.  Measurement of the Connection Tracking Table Capacity

   The connection tracking table capacity is an important metric of
   stateful NATxy gateways.  Its measurement is not easy, because an
   elementary step of a validated maximum connection establishment rate
   measurement (defined in Section 4.6) may have only a few distinct
   observable outcomes, but some of them they may have different root
   causes:

   1.  During the preliminary phase, the number of test frames received
       by the Responder is less than the number of test frames sent by
       the Initiator.  It may have different root causes, including:

       1.  The R frame sending rate was higher than the maximum
           connection establishment rate.  (Note that now the maximum
           connection establishment rate is considered unknown, because
           we can not measure the maximum connection establishment
           without our assumption 2 in Section 4.4!)  This root cause
           may be eliminated by lowering the R rate and re-executing the
           test.  (This step may be performed multiple times, while
           R>0.)

       2.  The capacity of the connection tracking table of the DUT has
           been exhausted.  (And either the DUT does not want to delete
           connections or the deletion of the connections makes it
           slower.  This case is not investigated further in the
           preliminary phase.)

   2.  During the preliminary phase, the number of test frames received
       by the Responder equals the number of test frames sent by the
       Initiator.  In this case the connections are validated in the
       Real Test Phase.  The validation may have two kinds of observable
       results:

       1.  The number of validation frames received by the Initiator
           equals the number of validation frames sent by the Responder.
           (It proves that the capacity of the connection tracking table
           of the DUT is enough and both R and r were chosen properly.)

       2.  The number of validation frames received by the Initiator is
           less than the number of validation frames sent by the
           Responder.  This phenomenon may have various root causes:









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           1.  The capacity of the connection tracking table of the DUT
               has been exhausted.  (It does not matter, whether some
               existing connections are discarded and new ones are
               stored, or the new connections are discarded.  Some
               connections are lost anyway, and it makes validation
               fail.)

           2.  The R frame sending rate used by the Initiator was too
               high in the Preliminary Phase and thus some connections
               were not established, even though all test frames arrived
               to the Responder.  This root cause may be eliminated by
               lowering the R rate and re-executing the test.  (This
               step may be performed multiple times, while R>0.)

           3.  The r frame sending rate used by the Responder was too
               high in the Real Test Phase and thus some test frames did
               not arrive to the Initiator, even though all connections
               were present in the connection tracking table of the DUT.
               This root cause may be eliminated by lowering the r rate
               and re-executing the test.  (This step may be performed
               multiple times, while r>0.)

           And here is the problem: as the above three root causes are
           indistinguishable, it is not easy to decide, whether R or r
           should be decreased.

   We have some experience with benchmarking stateful NATxy gateways.
   When we tested iptables with very high number of connections, the
   256GB RAM of the DUT was exhausted and it stopped responding.  Such a
   situation may make the connection tracking table capacity
   measurements rather inconvenient.  We include this possibility in our
   recommended measurement procedure, but we do not address the
   detection and elimination of such a situation.  (E.g. how the
   algorithm can reset the DUT.)

   For the connection tracking table size measurement, fist we need a
   safe number: C0.  It is a precondition, that C0 number of connections
   can surely be stored in the connection tracking table of the DUT.
   Using C0, one can determine the maximum connection establishment rate
   using C0 number of connections.  It is done with a binary search
   using validation.  The result is: R0.  The values C0 and R0 will
   serve as "safe" starting values for the following two searches.

   First, we perform an exponential search to find the order of
   magnitude of the connection tracking table capacity.  The search
   stops if the DUT collapses OR the maximum connection establishment
   rate severely drops (e.g. to its one tenth) due to doubling the
   number of connections.



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   Then, the result of the exponential search gives the order of
   magnitude of the size of the connection tracking table.  Before
   disclosing the possible algorithms to determine the size of the
   connection tracking table, we consider a three possible replacement
   policies of the NATxy gateway:

   1.  The gateway does not delete any live connections until their
       timeout expires.

   2.  The gateway replaces the live connections according to LRU (least
       recently used) policy.

   3.  The gateway does a garbage collection, when its connection
       tracking table is full and a frame with a new four tuple arrives.
       During the garbage collection, it deletes the K least recently
       used connections, where K greater than 1.

   Now, we examine, what happens and how many validation frames arrive
   in the there cases.  Let the size of the connection tracking table be
   S, and the number of preliminary frames be N, where S is less than N.

   1.  The connections defined by the first S test frames are registered
       into the connection tracking table of the DUT, and the last N-S
       connections are lost.  (It is a another question if the last N-S
       test frames are translated and forwarded in the preliminary or
       simply dropped.)  During validation, the validation frames with
       four tuples corresponding to the first S test frames will arrive
       to the Initiator, and the other N-S validation frames will be
       lost.

   2.  All connections are registered into the connection tracking table
       of the DUT, but the first N-S connections are replaced (and thus
       lost).  During validation, the validation frames with four tuples
       corresponding to the last S test frames will arrive to the
       Initiator, and the other N-S validation frames will be lost.

   3.  Depending on the values of K, S and N, maybe less than S
       connections will survive.  In the worst case, only S-K+1
       validation frames arrive, even though, the size of the connection
       tracking table is S.

   If we know that the stateful NATxy gateway uses the first or second
   replacement policy, and we also know that both R and r rates are low
   enough, then the final step of determining the size of the connection
   tracking table is simple.  If Responder sent N validation frames and
   the Initator received N' of them, then the size of the connection
   tracking table is N'.




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   In the general case, we perform a binary search to find the exact
   value of the connection tracking table capacity within E error.  The
   search chooses the lower half of the interval if the DUT collapses OR
   the maximum connection establishment rate severely drops (e.g. to its
   half) otherwise it chooses the higher half.  The search stops if the
   size of the interval is less than the E error.

   The algorithms for the general case are defined using C like
   pseudocode in Figure 2.  In practice, this algorithm may be made more
   efficient in a way that the binary search for the maximum connection
   establishment rate stops, if an elementary test fails at a rate under
   RS*beta or RS*gamma during the external search or during the final
   binary search for the capacity of the connection tracking table,
   respectively.  (This saves a lot a execution time by eliminating the
   long lasting tests at low rates.)




































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 // The binary_search_for_maximum_connection_establishment_rate(c,r)
 // function performs a binary search for the maximum connection
 // establishment rate in the [0, r] interval using c number of
 // connections.

 // This is an exponential search for finding the order of magnitude
 // of the connection tracking table capacity
 // Variables:
 //   C0 and R0 are beginning safe values for connection tracking table
        size and connection establishment rate, respectively
 //   CS and RS are their currently used safe values
 //   CT and RT are their values for current examination
 //   beta is a factor expressing unacceptable drop of R (e.g. beta=0.1)
 R0=binary_search_for_maximum_connection_establishment_rate(C0,maxrate);
 for ( CS=C0, RS=R0;  1; CS=CT, RS=RT )
 {
   CT=2*CS;
   RT=binary_search_for_maximum_connection_establishment_rate(CT,RS);
   if ( DUT_collapsed || RT < RS*beta )
     break;
 }
 // here the size of the connection tracking table is between CS and CT

 // This the final binary search for finding the connection tracking
 // table capacity within E error
 // Variables:
 //   CS and RS are the safe values for connection tracking table size
 //     and connection establishment rate, respectively
 //   C and R are the values for current examination
 //   gamma is a factor expressing unacceptable drop of R
 //     (e.g. gamma=0.5)
 for ( D=CT-CS;  D>E; D=CT-CS )
 {
   C=(CS+CT)/2;
   R=binary_search_for_maximum_connection_establishment_rate(C,RS);
   if ( DUT_collapsed || R < RS*gamma)
     CT=C; // take the lower half of the interval
   else
     CS=C,RS=R; // take the upper half of the interval
 }
 // here the size of the connection tracking table is CS within E error

    Figure 2: Measurement of the Connection Tracking Table Capacity








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4.10.  Writing and Reading Order of the State Table

   As for writing policy of the state table of the Responder, we
   RECOMMEND round robin, because it ensures that its entries are
   automatically kept fresh and consistent with that of the connection
   tracking table of the DUT.

   The Responder can read its state table in various orders, for
   example:

   *  pseudorandom

   *  round robin

   We RECOMMEND pseudorandom to follow the spirit of [RFC4814].  Round
   robin may be used as a computationally cheaper alternative.

5.  Implementation and Experience

   The "stateful" branch of siitperf [SIITPERF] is an implementation of
   this concept.  It is documented in this (open access) paper
   [LEN2022].

   Our experience with this methodology using siitperf for measuring the
   scalability of the iptables stateful NAT44 and Jool stateful NAT64
   implementations is described in
   [I-D.lencse-v6ops-transition-scalability].

6.  Limitations of using UDP as Transport Layer Protocol

   Stateful NATxy solutions handle TCP and UDP differently, e.g.
   iptables uses 30s timeout for UDP and 60s timeout for TCP.  Thus
   benchmarking results produced using UDP do not necessarily
   characterize the performance of a NATxy gateway well enough, when
   they are used for forwarding Internet traffic.  As for the given
   example, timeout values of the DUT may be adjusted, but it requires
   extra consideration.

   Other differences in handling UDP or TCP are also possible.  Thus we
   recommend that further investigations are to be performed in this
   field.

   As a mitigation of this problem, we recommend that testing with
   protocols usig TCP (like HTTP and HTTPS) can be performed as
   described in [I-D.ietf-bmwg-ngfw-performance].  This approach also
   solves the potential problem of protocol helpers may be present in
   the stateful DUT.




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7.  Acknowledgements

   The authors would like to thank Al Morton, Sarah Banks, Edwin
   Cordeiro, Lukasz Bromirski and Sandor Repas for their comments.

8.  IANA Considerations

   This document does not make any request to IANA.

9.  Security Considerations

   We have no further security considerations beyond that of [RFC8219].
   Perhaps they should be cited here so that they be applied not only
   for the benchmarking of IPv6 transition technologies, but also for
   the benchmarking of stateful NATxy gateways.

10.  References

10.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC2544]  Bradner, S. and J. McQuaid, "Benchmarking Methodology for
              Network Interconnect Devices", RFC 2544,
              DOI 10.17487/RFC2544, March 1999,
              <https://www.rfc-editor.org/info/rfc2544>.

   [RFC4814]  Newman, D. and T. Player, "Hash and Stuffing: Overlooked
              Factors in Network Device Benchmarking", RFC 4814,
              DOI 10.17487/RFC4814, March 2007,
              <https://www.rfc-editor.org/info/rfc4814>.

   [RFC5180]  Popoviciu, C., Hamza, A., Van de Velde, G., and D.
              Dugatkin, "IPv6 Benchmarking Methodology for Network
              Interconnect Devices", RFC 5180, DOI 10.17487/RFC5180, May
              2008, <https://www.rfc-editor.org/info/rfc5180>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC8219]  Georgescu, M., Pislaru, L., and G. Lencse, "Benchmarking
              Methodology for IPv6 Transition Technologies", RFC 8219,
              DOI 10.17487/RFC8219, August 2017,
              <https://www.rfc-editor.org/info/rfc8219>.



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10.2.  Informative References

   [DUST1964] Durstenfeld, R., "Algorithm 235: Random
              permutation",  Communications of the ACM, vol. 7, no. 7,
              p.420., DOI 10.1145/364520.364540, July 1964,
              <https://dl.acm.org/doi/10.1145/364520.364540>.

   [I-D.ietf-bmwg-ngfw-performance]
              Balarajah, B., Rossenhoevel, C., and B. Monkman,
              "Benchmarking Methodology for Network Security Device
              Performance", Work in Progress, Internet-Draft, draft-
              ietf-bmwg-ngfw-performance-13, 12 January 2022,
              <https://www.ietf.org/archive/id/draft-ietf-bmwg-ngfw-
              performance-13.txt>.

   [I-D.lencse-v6ops-transition-scalability]
              Lencse, G., "Scalability of IPv6 Transition Technologies
              for IPv4aaS", Work in Progress, Internet-Draft, draft-
              lencse-v6ops-transition-scalability-02, 7 March 2022,
              <https://www.ietf.org/archive/id/draft-lencse-v6ops-
              transition-scalability-02.txt>.

   [IIR2020]  Kurahashi, T., Matsuzaki, Y., Sasaki, T., Saito, T., and
              F. Tsutsuji, "Periodic observation report: Internet trends
              as seen from IIJ infrastructure - 2020",  Internet
              Infrastructure Review, vol. 49, December 2020,
              <https://www.iij.ad.jp/en/dev/iir/pdf/
              iir_vol49_report_EN.pdf>.

   [LEN2020]  Lencse, G., "Adding RFC 4814 Random Port Feature to
              Siitperf: Design, Implementation and Performance
              Estimation",  International Journal of Advances in
              Telecommunications, Electrotechnics, Signals and Systems,
              vol 9, no 3, pp. 18-26., DOI 10.11601/ijates.v9i3.291,
              2020, <http://www.hit.bme.hu/~lencse/
              publications/291-1113-1-PB.pdf>.

   [LEN2021]  Lencse, G., "Design and Implementation of a Software
              Tester for Benchmarking Stateful NAT64 Gateways: Theory
              and Practice of Extending Siitperf for Stateful
              Tests",  it was under review in Computer
              Communications,  then it was significantly rewritten,
              2021, <http://www.hit.bme.hu/~lencse/publications/SFNAT64-
              tester-for-review.pdf>.

   [LEN2022]  Lencse, G., "Design and Implementation of a Software
              Tester for Benchmarking Stateful NAT64xy Gateways: Theory
              and Practice of Extending Siitperf for Stateful



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              Tests",  Computer Communications, vol. 172, no. 1, pp.
              75-88, August 1, 2022, DOI 10.1016/j.comcom.2022.05.028,
              2022, <http://www.hit.bme.hu/~lencse/publications/ECC-
              2022-SFNAT64xy-Tester-published.pdf>.

   [SIITPERF] Lencse, G., "Siitperf: An RFC 8219 compliant SIIT
              (stateless NAT64) tester written in C++ using
              DPDK",  source code,  available from GitHub, 2019-2022,
              <https://github.com/lencsegabor/siitperf>.

Appendix A.  Change Log

A.1.  00

   Initial version.

A.2.  01

   Updates based on the comments received on the BMWG mailing list and
   minor corrections.

A.3.  02

   Section 4.4 was completely re-written.  As a consequence, the
   occurrences of the now undefined "mostly different" source port
   number destination port number combinations were deleted from
   Section 4.5, too.

A.4.  03

   Added Section 4.3 about the consideration of the cases of stateful
   operation.

   Consistency checking.  Removal of some parts obsoleted by the
   previous re-writing of Section 4.4.

   Added Section 4.8 about the method for measuring connection tear down
   rate.

   Updates for Section 5 about the implementation and experience.

A.5.  04

   Update of the abstract.

   Added Section 4.6 about validation of connection establishment.





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   Added Section 4.9 about the method for measuring connection tracking
   table capacity.

   Consistency checking and corrections.

Authors' Addresses

   Gabor Lencse
   Szechenyi Istvan University
   Gyor
   Egyetem ter 1.
   H-9026
   Hungary
   Email: lencse@sze.hu


   Keiichi Shima
   IIJ Innovation Institute
   Iidabashi Grand Bloom, 2-10-2 Fujimi, Tokyo
   102-0071
   Japan
   Email: keiichi@iijlab.net





























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