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Versions: (draft-poretsky-bmwg-sip-bench-meth) 00 01 02 03 04 05 06 07 08 09 10 11 12 RFC 7502

Benchmarking Methodology Working Group                         C. Davids
Internet-Draft                          Illinois Institute of Technology
Intended status: Informational                                V. Gurbani
Expires: November 29, 2014                            Bell Laboratories,
                                                          Alcatel-Lucent
                                                             S. Poretsky
                                                    Allot Communications
                                                            May 28, 2014


Methodology for Benchmarking Session Initiation Protocol (SIP)  Devices:
                  Basic session setup and registration
                   draft-ietf-bmwg-sip-bench-meth-10

Abstract

   This document provides a methodology for benchmarking the Session
   Initiation Protocol (SIP) performance of devices.  Terminology
   related to benchmarking SIP devices is described in the companion
   terminology document.  Using these two documents, benchmarks can be
   obtained and compared for different types of devices such as SIP
   Proxy Servers, Registrars and Session Border Controllers.  The term
   "performance" in this context means the capacity of the device-under-
   test (DUT) to process SIP messages.  Media streams are used only to
   study how they impact the signaling behavior.  The intent of the two
   documents is to provide a normalized set of tests that will enable an
   objective comparison of the capacity of SIP devices.  Test setup
   parameters and a methodology are necessary because SIP allows a wide
   range of configuration and operational conditions that can influence
   performance benchmark 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
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on November 29, 2014.




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Copyright Notice

   Copyright (c) 2014 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 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.





































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Table of Contents

   1.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  4
   2.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
   3.  Benchmarking Topologies  . . . . . . . . . . . . . . . . . . .  5
   4.  Test Setup Parameters  . . . . . . . . . . . . . . . . . . . .  6
     4.1.  Selection of SIP Transport Protocol  . . . . . . . . . . .  6
     4.2.  Signaling Server . . . . . . . . . . . . . . . . . . . . .  6
     4.3.  Associated Media . . . . . . . . . . . . . . . . . . . . .  7
     4.4.  Selection of Associated Media Protocol . . . . . . . . . .  7
     4.5.  Number of Associated Media Streams per SIP Session . . . .  7
     4.6.  Session Duration . . . . . . . . . . . . . . . . . . . . .  7
     4.7.  Attempted Sessions per Second (sps)  . . . . . . . . . . .  7
     4.8.  Benchmarking algorithm . . . . . . . . . . . . . . . . . .  7
   5.  Reporting Format . . . . . . . . . . . . . . . . . . . . . . . 10
     5.1.  Test Setup Report  . . . . . . . . . . . . . . . . . . . . 10
     5.2.  Device Benchmarks for IS . . . . . . . . . . . . . . . . . 10
     5.3.  Device Benchmarks for NS . . . . . . . . . . . . . . . . . 10
   6.  Test Cases . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     6.1.  Baseline Session Establishment Rate of the test bed  . . . 11
     6.2.  Session Establishment Rate without media . . . . . . . . . 11
     6.3.  Session Establishment Rate with Media not on DUT . . . . . 11
     6.4.  Session Establishment Rate with Media on DUT . . . . . . . 12
     6.5.  Session Establishment Rate with TLS Encrypted SIP  . . . . 12
     6.6.  Session Establishment Rate with IPsec Encrypted SIP  . . . 13
     6.7.  Registration Rate  . . . . . . . . . . . . . . . . . . . . 13
     6.8.  Re-Registration Rate . . . . . . . . . . . . . . . . . . . 14
   7.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 14
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 14
   9.  Acknowledgments  . . . . . . . . . . . . . . . . . . . . . . . 14
   10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 15
     10.1. Normative References . . . . . . . . . . . . . . . . . . . 15
     10.2. Informative References . . . . . . . . . . . . . . . . . . 15
   Appendix A.  R code to simulate benchmarking algorithm . . . . . . 15
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 17
















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1.  Terminology

   In this document, the key words "MUST", "MUST NOT", "REQUIRED",
   "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT
   RECOMMENDED", "MAY", and "OPTIONAL" are to be interpreted as
   described in BCP 14, conforming to [RFC2119] and indicate requirement
   levels for compliant implementations.

   RFC 2119 defines the use of these key words to help make the intent
   of standards track documents as clear as possible.  While this
   document uses these keywords, this document is not a standards track
   document.  The term Throughput is defined in [RFC2544].

   Terms specific to SIP [RFC3261] performance benchmarking are defined
   in [I-D.sip-bench-term].


2.  Introduction

   This document describes the methodology for benchmarking Session
   Initiation Protocol (SIP) performance as described in Terminology
   document [I-D.sip-bench-term].  The methodology and terminology are
   to be used for benchmarking signaling plane performance with varying
   signaling and media load.  Media streams, when used, are used only to
   study how they impact the signaling behavior.  This document
   concentrates on benchmarking SIP session setup and SIP registrations
   only.

   The device-under-test (DUT) is a SIP server, which may be any SIP
   conforming [RFC3261] device.  Benchmarks can be obtained and compared
   for different types of devices such as a SIP proxy server, Session
   Border Controllers (SBC), SIP registrars and a SIP proxy server
   paired with a media relay.

   The test cases provide metrics for benchmarking the maximum 'SIP
   Registration Rate' and maximum 'SIP Session Establishment Rate' that
   the DUT can sustain over an extended period of time without failures
   (extended period of time is defined in the algorithm in Section 4.8).
   Some cases are included to cover encrypted SIP.  The test topologies
   that can be used are described in the Test Setup section.  Topologies
   in which the DUT handles media as well as those in which the DUT does
   not handle media are both considered.  The measurement of the
   performance characteristics of the media itself is outside the scope
   of these documents.

   SIP permits a wide range of configuration options that are explained
   in Section 4 and Section 2 of [I-D.sip-bench-term].  Benchmark values
   could possibly be impacted by Associated Media.  The selected values



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   for Session Duration and Media Streams per Session enable benchmark
   metrics to be evaluated without Associated Media.  Session
   Establishment Rate could possibly be impacted by the selected value
   for Maximum Sessions Attempted.  The benchmark for Session
   Establishment Rate is measured with a fixed value for maximum Session
   Attempts.

   SIP permits a wide range of configuration options that are explained
   in Section 4 and Section 2 of [I-D.sip-bench-term].  Benchmark
   metrics could possibly be impacted by Associated Media.  The selected
   values for Session Duration and Media Streams per Session enable
   benchmark metrics to be benchmarked without Associated Media.
   Session Setup Rate could possibly be impacted by the selected value
   for Maximum Sessions Attempted.  The benchmark for Session
   Establishment Rate is measured with a fixed value for maximum Session
   Attempts.

   Finally, the overall value of these tests is to serve as a comparison
   function between multiple SIP implementations.  One way to use these
   tests is to derive benchmarks with SIP devices from Vendor-A, derive
   a new set of benchmarks with similar SIP devices from Vendor-B and
   perform a comparison on the results of Vendor-A and Vendor-B.  This
   document does not make any claims on the interpretation of such
   results.


3.  Benchmarking Topologies

   There are two test topologies; one in which the DUT does not process
   the media (Figure 1) and the other in which it does process media
   (Figure 2).  In both cases, the tester or EA sends traffic into the
   DUT and absorbs traffic from the DUT.  The diagrams in Figure 1 and
   Figure 2 represent the logical flow of information and do not dictate
   a particular physical arrangements of the entities.

   Test organizations need to be aware that these tests generate large
   volumes of data and consequently ensure that networking devices like
   hubs, switches or routers are able to handle the generated volume.

   Figure 1 depicts a layout in which the DUT is an intermediary between
   the two interfaces of the EA.  If the test case requires the exchange
   of media, the media does not flow through the DUT but rather passes
   directly between the two endpoints.  Figure 2 shows the DUT as an
   intermediary between the two interfaces of the EA.  If the test case
   requires the exchange of media, the media flows through the DUT
   between the endpoints.





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      +--------+   Session   +--------+  Session    +--------+
      |        |   Attempt   |        |  Attempt    |        |
      |        |------------>+        |------------>+        |
      |        |             |        |             |        |
      |        |   Response  |        |  Response   |        |
      | Tester +<------------|  DUT   +<------------| Tester |
      |  (EA)  |             |        |             |  (EA)  |
      |        |             |        |             |        |
      +--------+             +--------+             +--------+
         /|\                                            /|\
          |              Media (optional)                |
          +==============================================+


            Figure 1: DUT as an intermediary, end-to-end media



      +--------+   Session   +--------+  Session    +--------+
      |        |   Attempt   |        |  Attempt    |        |
      |        |------------>+        |------------>+        |
      |        |             |        |             |        |
      |        |   Response  |        |  Response   |        |
      | Tester +<------------|  DUT   +<------------| Tester |
      |  (EA)  |             |        |             |  (EA)  |
      |        |<===========>|        |<===========>|        |
      +--------+   Media     +--------+    Media    +--------+
                 (Optional)             (Optional)


             Figure 2: DUT as an intermediary forwarding media


4.  Test Setup Parameters

4.1.  Selection of SIP Transport Protocol

   Test cases may be performed with any transport protocol supported by
   SIP.  This includes, but is not limited to, TCP, UDP, TLS and
   websockets.  The protocol used for the SIP transport protocol must be
   reported with benchmarking results.

4.2.  Signaling Server

   The Signaling Server is defined in the companion terminology
   document, ([I-D.sip-bench-term], Section 3.2.2).  The Signaling
   Server is a DUT.




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4.3.  Associated Media

   Some tests require Associated Media to be present for each SIP
   session.  The test topologies to be used when benchmarking DUT
   performance for Associated Media are shown in Figure 1 and Figure 2.

4.4.  Selection of Associated Media Protocol

   The test cases specified in this document provide SIP performance
   independent of the protocol used for the media stream.  Any media
   protocol supported by SIP may be used.  This includes, but is not
   limited to, RTP, RTSP, and SRTP.  The protocol used for Associated
   Media MUST be reported with benchmarking results.

4.5.  Number of Associated Media Streams per SIP Session

   Benchmarking results may vary with the number of media streams per
   SIP session.  When benchmarking a DUT for voice, a single media
   stream is used.  When benchmarking a DUT for voice and video, two
   media streams are used.  The number of Associated Media Streams MUST
   be reported with benchmarking results.

4.6.  Session Duration

   The value of the DUT's performance benchmarks may vary with the
   duration of SIP sessions.  Session Duration MUST be reported with
   benchmarking results.  A Session Duration of zero seconds indicates
   transmission of a BYE immediately following a successful SIP
   establishment.  Setting this parameter to the value '0' indicates
   that a BYE will be sent by the EA immediately after the EA receives a
   200 OK to the INVITE.  Setting this parameter to a time value greater
   than the duration of the test indicates that a BYE is never sent.

4.7.  Attempted Sessions per Second (sps)

   The value of the DUT's performance benchmarks may vary with the
   Session Attempt Rate offered by the tester.  Session Attempt Rate
   MUST be reported with the benchmarking results.

4.8.  Benchmarking algorithm

   In order to benchmark the test cases uniformly in Section 6, the
   algorithm described in this section should be used.  A prosaic
   description of the algorithm and a pseudo-code description are
   provided below, and a simulation written in the R statistical
   language is provided in Appendix A.

   The goal is to find the largest value, R, a SIP Session Attempt Rate,



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   measured in sessions-per-second (sps), which the DUT can process with
   zero errors over a defined, extended period.  This period is defined
   as the amount of time needed to attempt N SIP sessions, where N is a
   parameter of test, at the attempt rate, R. An iterative process is
   used to find this rate.  The algorithm corresponding to this process
   converges to R.

   If the DUT vendor provides a value for R, the tester can use this
   value.  Alternatively, in cases where the DUT vendor does not provide
   a value for R, or in cases where the tester wants to ascertain a
   vendor provided value using local media characteristics, the
   algorithm could be run by setting "r = R" and observing the value at
   convergence.

   The algorithm proceeds by initializing "r = 100"; "r" is the session
   attempt rate.  The algorithm dynamically increases and decreases "r"
   as it converges to the a maximum sps value for R. The dynamic
   increase and decrease rate is controlled by the weights "w" and "d",
   respectively.  If the DUT vendor provides a value for R, the tester
   can use that value; however, because the requirements and media
   characteristics are a function of the test environment, it is best
   that the tester reflect these requirements during testing and allow
   the algorithm to converge to R.

   The pseudo-code corresponding to the description above follows, and a
   simulation written in the R statistical language is provided in
   Appendix A.


         ; ---- Parameters of test, adjust as needed
         N  := 50000  ; Global maximum; once largest session rate has
                      ; been established, send this many requests before
                      ; calling the test a success
         m  := {...}  ; Other attributes that affect testing, such
                      ; as media streams, etc.
         r  := 100    ; Initial session attempt rate (in sessions/sec).
                      ; Adjust as needed (for example, if DUT can handle
                      ; thousands of calls in steady state, set to
                      ; appropriate value in the thousands).
         w  := 0.10   ; Traffic increase weight (0 < w <= 1.0)
         d  := max(0.10, w / 2)    ; Traffic decrease weight

         ; ---- End of parameters of test

         proc find_R

            R = max_sps(r, m, N)  ; Setup r sps, each with m media
            ; characteristics until N sessions have been set up.



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            ; Note that if a DUT vendor provides this number, the tester
            ; can use the number as a Session Attempt Rate, R, instead
            ; of invoking max_sps()

         end proc

         ; Iterative process to figure out the largest number of
         ; sps that we can achieve in order to setup n sessions.
         ; This function converges to R, the Session Attempt Rate.
         proc max_sps(r, m, n)
            s     := 0    ; session setup rate
            old_r := 0    ; old session setup rate
            h     := 0    ; Return value, R
            count := 0

            ; Note that if w is small (say, 0.10) and r is small
            ; (say, <= 9), the algorithm will not converge since it
            ; uses floor() to increment r dynamically.  It is best
            ; off to start with the defaults (w = 0.10 and
            ; r >= 10)

            while (TRUE) {
               s := send_traffic(r, m, n) ; Send r sps, with m media
               ; characteristics until n sessions established.
               if (s == n)  {
                   if (r > old_r)  {
                       old_r = r
                   }
                   else  {
                       count = count + 1
                       if (count >= 10)  {
                           # We've converged.
                           h := max(r, old_r)
                           break
                       }
                   }

                   r  := floor(r + (w * r))
               }
               else  {
                   r := floor(r - (d * r))
                   d := max(0.10, d / 2)
                   w := max(0.10, w / 2)
               }

            }
            return h
         end proc



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5.  Reporting Format

5.1.  Test Setup Report


     SIP Transport Protocol = ___________________________
     (valid values: TCP|UDP|TLS|SCTP|websockets|specify-other)
     Session Attempt Rate = _____________________________
     (session attempts/sec)
     Total Sessions Attempted = _________________________
     (total sessions to be created over duration of test)
     Media Streams Per Session =  _______________________
     (number of streams per session)
     Associated Media Protocol =  _______________________
     (RTP|RTSP|specify-other)
     Media Packet Size =  _______________________________
     (bytes)
     Establishment Threshold time =  ____________________
     (seconds)
     TLS ciphersuite used
     (for tests involving TLS) = ________________________
     (e.g., TLS_RSA_WITH_AES_128_CBC_SHA)
     IPSec profile used
     (for tests involving IPSEC) = _____________________


5.2.  Device Benchmarks for IS



     Session Establishment Rate =  ______________________
     (sessions per second)
     Is DUT acting as a media relay (yes/no) = _________


5.3.  Device Benchmarks for NS


     Registration Rate =  ____________________________
     (registrations per second)
     Re-registration Rate =  ____________________________
     (registrations per second)


6.  Test Cases






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6.1.  Baseline Session Establishment Rate of the test bed

   Objective:
      To benchmark the Session Establishment Rate of the Emulated Agent
      (EA) with zero failures.

   Procedure:
      1.  Configure the DUT in the test topology shown in Figure 1.
      2.  Set media streams per session to 0.
      3.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the baseline session establishment rate.  This rate MUST
          be recorded using any pertinent parameters as shown in the
          reporting format of Section 5.1.

   Expected Results:  This is the scenario to obtain the maximum Session
      Establishment Rate of the EA and the test bed when no DUT is
      present.  The results of this test might be used to normalize test
      results performed on different test beds or simply to better
      understand the impact of the DUT on the test bed in question.

6.2.  Session Establishment Rate without media

   Objective:
      To benchmark the Session Establishment Rate of the DUT with no
      associated media and zero failures.

   Procedure:
      1.  Configure a DUT according to the test topology shown in
          Figure 1 or Figure 2.
      2.  Set media streams per session to 0.
      3.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the session establishment rate.  This rate MUST be
          recorded using any pertinent parameters as shown in the
          reporting format of Section 5.1.

   Expected Results:  Find the Session Establishment Rate of the DUT
      when the EA is not sending media streams.

6.3.  Session Establishment Rate with Media not on DUT

   Objective:
      To benchmark the Session Establishment Rate of the DUT with zero
      failures when Associated Media is included in the benchmark test
      but the media is not running through the DUT.







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   Procedure:
      1.  Configure a DUT according to the test topology shown in
          Figure 1.
      2.  Set media streams per session to 1.
      3.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the session establishment rate with media.  This rate MUST
          be recorded using any pertinent parameters as shown in the
          reporting format of Section 5.1.

   Expected Results:  Session Establishment Rate results obtained with
      Associated Media with any number of media streams per SIP session
      are expected to be identical to the Session Establishment Rate
      results obtained without media in the case where the DUT is
      running on a platform separate from the Media Relay.

6.4.  Session Establishment Rate with Media on DUT

   Objective:
      To benchmark the Session Establishment Rate of the DUT with zero
      failures when Associated Media is included in the benchmark test
      and the media is running through the DUT.

   Procedure:
      1.  Configure a DUT according to the test topology shown in
          Figure 2.
      2.  Set media streams per session to 1.
      3.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the session establishment rate with media.  This rate MUST
          be recorded using any pertinent parameters as shown in the
          reporting format of Section 5.1.

   Expected Results:  Session Establishment Rate results obtained with
      Associated Media may be lower than those obtained without media in
      the case where the DUT and the Media Relay are running on the same
      platform.

6.5.  Session Establishment Rate with TLS Encrypted SIP

   Objective:
      To benchmark the Session Establishment Rate of the DUT with zero
      failures when using TLS encrypted SIP signaling.

   Procedure:
      1.  If the DUT is being benchmarked as a proxy or B2BUA, then
          configure the DUT in the test topology shown in Figure 1 or
          Figure 2.




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      2.  Configure the tester to enable TLS over the transport being
          used during benchmarking.  Note the ciphersuite being used for
          TLS and record it in Section 5.1.
      3.  Set media streams per session to 0 (media is not used in this
          test).
      4.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the session establishment rate with TLS encryption.

   Expected Results:  Session Establishment Rate results obtained with
      TLS Encrypted SIP may be lower than those obtained with plaintext
      SIP.

6.6.  Session Establishment Rate with IPsec Encrypted SIP

   Objective:
      To benchmark the Session Establishment Rate of the DUT with zero
      failures when using IPsec Encrypted SIP signaling.

   Procedure:
      1.  Configure a DUT according to the test topology shown in
          Figure 1 or Figure 2.
      2.  Set media streams per session to 0 (media is not used in this
          test).
      3.  Configure tester for IPSec.  Note the IPSec profile being used
          for and record it in Section 5.1.
      4.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the session establishment rate with encryption.

   Expected Results:  Session Establishment Rate results obtained with
      IPSec Encrypted SIP may be lower than those obtained with
      plaintext SIP.

6.7.  Registration Rate

   Objective:
      To benchmark the maximum registration rate the DUT can handle over
      an extended time period with zero failures.

   Procedure:
      1.  Configure a DUT according to the test topology shown in
          Figure 1 or Figure 2.
      2.  Set the registration timeout value to at least 3600 seconds.
      3.  Execute benchmarking algorithm as defined in Section 4.8 to
          get the maximum registration rate.  This rate MUST be recorded
          using any pertinent parameters as shown in the reporting
          format of Section 5.1.  For example, the use of TLS or IPSec
          during registration must be noted in the reporting format.




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   Expected Results:  Provides a maximum registration rate.

6.8.  Re-Registration Rate

   Objective:
      To benchmark the re-registration rate of the DUT with zero
      failures.

   Procedure:
      1.  Configure a DUT according to the test topology shown in
          Figure 1 or Figure 2.
      2.  First, execute test detailed in Section 6.7 to register the
          endpoints with the registrar and obtain the registration rate.
      3.  After at least 5 minutes of Step 2, but no more than 10
          minutes after Step 2 has been performed, execute Step 3 of the
          test in Section 6.7.  This will count as a re-registration
          because the SIP address of records have not yet expired.

   Expected Results:  The rate should be at least equal to but not more
      than the result of Section 6.7.


7.  IANA Considerations

   This document does not requires any IANA considerations.


8.  Security Considerations

   Documents of this type do not directly affect the security of
   Internet or corporate networks as long as benchmarking is not
   performed on devices or systems connected to production networks.
   Security threats and how to counter these in SIP and the media layer
   is discussed in RFC3261, RFC3550, and RFC3711 and various other
   drafts.  This document attempts to formalize a set of common
   methodology for benchmarking performance of SIP devices in a lab
   environment.


9.  Acknowledgments

   The authors would like to thank Keith Drage and Daryl Malas for their
   contributions to this document.  Dale Worley provided an extensive
   review that lead to improvements in the documents.  We are grateful
   to Barry Constantine for providing valuable comments during the
   document's WGLC.




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10.  References

10.1.  Normative References

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

   [RFC2544]  Bradner, S. and J. McQuaid, "Benchmarking Methodology for
              Network Interconnect Devices", RFC 2544, March 1999.

   [I-D.sip-bench-term]
              Davids, C., Gurbani, V., and S. Poretsky, "SIP Performance
              Benchmarking Terminology",
              draft-ietf-bmwg-sip-bench-term-10 (work in progress),
              May 2014.

10.2.  Informative References

   [RFC3261]  Rosenberg, J., Schulzrinne, H., Camarillo, G., Johnston,
              A., Peterson, J., Sparks, R., Handley, M., and E.
              Schooler, "SIP: Session Initiation Protocol", RFC 3261,
              June 2002.


Appendix A.  R code to simulate benchmarking algorithm


      w = 0.10
      d = max(0.10, w / 2)
      DUT_max_sps = 460     # Change as needed to set the max sps value
                            # for a DUT

      # Returns R, given r (initial session attempt rate).
      # E.g., assume that a DUT handles 460 sps in steady state
      # and you have saved this code in a file simulate.r.  Then,
      # start an R session and do the following:
      #
      # > source("simulate.r")
      # > find_R(100)
      # ... debug output omitted ...
      # [1] 458
      #
      # Thus, the max sps that the DUT can handle is 458 sps, which is
      # close to the absolute maximum of 460 sps the DUT is specified to
      # do.
      find_R <- function(r)  {
         s     = 0
         old_r = 0



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         h     = 0
         count = 0

         # Note that if w is small (say, 0.10) and r is small
         # (say, <= 9), the algorithm will not converge since it
         # uses floor() to increment r dynamically.  It is best
         # off to start with the defaults (w = 0.10 and
         # r >= 10)

         cat("r   old_r    w     d \n")
         while (TRUE)  {
            cat(r, ' ', old_r, ' ', w, ' ', d, '\n')
            s = send_traffic(r)
            if (s == TRUE)  {     # All sessions succeeded

                if (r > old_r)  {
                    old_r = r
                }
                else  {
                    count = count + 1

                    if (count >= 10)  {
                        # We've converged.
                        h = max(r, old_r)
                        break
                    }
                }

                r  = floor(r + (w * r))
            }
            else  {
                r = floor(r - (d * r))
                d = max(0.10, d / 2)
                w = max(0.10, w / 2)
            }
         }

         h
      }

      send_traffic <- function(r)  {
         n = TRUE

         if (r > DUT_max_sps)  {
             n = FALSE
         }

         n



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      }



Authors' Addresses

   Carol Davids
   Illinois Institute of Technology
   201 East Loop Road
   Wheaton, IL  60187
   USA

   Phone: +1 630 682 6024
   Email: davids@iit.edu


   Vijay K. Gurbani
   Bell Laboratories, Alcatel-Lucent
   1960 Lucent Lane
   Rm 9C-533
   Naperville, IL  60566
   USA

   Phone: +1 630 224 0216
   Email: vkg@bell-labs.com


   Scott Poretsky
   Allot Communications
   300 TradeCenter, Suite 4680
   Woburn, MA  08101
   USA

   Phone: +1 508 309 2179
   Email: sporetsky@allot.com
















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