path: root/docs/ietf/draft-ietf-bmwg-mlrsearch-02.md

---
title: Multiple Loss Ratio Search for Packet Throughput (MLRsearch)
abbrev: Multiple Loss Ratio Search
docname: draft-ietf-bmwg-mlrsearch-02
date: 2022-03-07

ipr: trust200902
area: ops
wg: Benchmarking Working Group
kw: Internet-Draft
cat: info

coding: us-ascii
pi:    # can use array (if all yes) or hash here
  toc: yes
  sortrefs:   # defaults to yes
  symrefs: yes

author:
      -
        ins: M. Konstantynowicz
        name: Maciek Konstantynowicz
        org: Cisco Systems
        role: editor
        email: mkonstan@cisco.com
      -
        ins: V. Polak
        name: Vratko Polak
        org: Cisco Systems
        email: vrpolak@cisco.com

normative:
  RFC2544:

informative:
  FDio-CSIT-MLRsearch:
    target: https://s3-docs.fd.io/csit/rls2110/report/introduction/methodology_data_plane_throughput/methodology_data_plane_throughput.html#mlrsearch-tests
    title: "FD.io CSIT Test Methodology - MLRsearch"
    date: 2021-11
  PyPI-MLRsearch:
    target: https://pypi.org/project/MLRsearch/0.4.0/
    title: "MLRsearch 0.4.0, Python Package Index"
    date: 2021-04

--- abstract

TODO: Update after all sections are ready.

This document proposes changes to [RFC2544], specifically to packet
throughput search methodology, by defining a new search algorithm
referred to as Multiple Loss Ratio search (MLRsearch for short). Instead
of relying on binary search with pre-set starting offered load, it
proposes a novel approach discovering the starting point in the initial
phase, and then searching for packet throughput based on defined packet
loss ratio (PLR) input criteria and defined final trial duration time.
One of the key design principles behind MLRsearch is minimizing the
total test duration and searching for multiple packet throughput rates
(each with a corresponding PLR) concurrently, instead of doing it
sequentially.

The main motivation behind MLRsearch is the new set of challenges and
requirements posed by NFV (Network Function Virtualization),
specifically software based implementations of NFV data planes. Using
[RFC2544] in the experience of the authors yields often not repetitive
and not replicable end results due to a large number of factors that are
out of scope for this draft. MLRsearch aims to address this challenge
in a simple way of getting the same result sooner, so more repetitions
can be done to describe the replicability.

--- middle

{::comment}
    As we use kramdown to convert from markdown,
    we use this way of marking comments not to be visible in rendered draft.
    https://stackoverflow.com/a/42323390
    If other engine is used, convert to this way:
    https://stackoverflow.com/a/20885980
{:/comment}

# Terminology

TODO: Update after most other sections are updated.

{::comment}
    The following is probably not needed (or defined elsewhere).

    * Frame size: size of an Ethernet Layer-2 frame on the wire, including
      any VLAN tags (dot1q, dot1ad) and Ethernet FCS, but excluding Ethernet
      preamble and inter-frame gap. Measured in bytes (octets).
    * Packet size: same as frame size, both terms used interchangeably.
    * Device Under Test (DUT): In software networking, "device" denotes a
      specific piece of software tasked with packet processing. Such device
      is surrounded with other software components (such as operating system
      kernel). It is not possible to run devices without also running the
      other components, and hardware resources are shared between both. For
      purposes of testing, the whole set of hardware and software components
      is called "system under test" (SUT). As SUT is the part of the whole
      test setup performance of which can be measured by [RFC2544] methods,
      this document uses SUT instead of [RFC2544] DUT. Device under test
      (DUT) can be re-introduced when analysing test results using whitebox
      techniques, but this document sticks to blackbox testing.
    * System Under Test (SUT): System under test (SUT) is a part of the
      whole test setup whose performance is to be benchmarked. The complete
      test setup contains other parts, whose performance is either already
      established, or not affecting the benchmarking result.
    * Bi-directional throughput tests: involve packets/frames flowing in
      both transmit and receive directions over every tested interface of
      SUT/DUT. Packet flow metrics are measured per direction, and can be
      reported as aggregate for both directions and/or separately
      for each measured direction. In most cases bi-directional tests
      use the same (symmetric) load in both directions.
    * Uni-directional throughput tests: involve packets/frames flowing in
      only one direction, i.e. either transmit or receive direction, over
      every tested interface of SUT/DUT. Packet flow metrics are measured
      and are reported for measured direction.
    * Packet Throughput Rate: maximum packet offered load DUT/SUT forwards
      within the specified Packet Loss Ratio (PLR). In many cases the rate
      depends on the frame size processed by DUT/SUT. Hence packet
      throughput rate MUST be quoted with specific frame size as received by
      DUT/SUT during the measurement. For bi-directional tests, packet
      throughput rate should be reported as aggregate for both directions.
      Measured in packets-per-second (pps) or frames-per-second (fps),
      equivalent metrics.
    * Bandwidth Throughput Rate: a secondary metric calculated from packet
      throughput rate using formula: bw_rate = pkt_rate * (frame_size +
      L1_overhead) * 8, where L1_overhead for Ethernet includes preamble (8
      octets) and inter-frame gap (12 octets). For bi-directional tests,
      bandwidth throughput rate should be reported as aggregate for both
      directions. Expressed in bits-per-second (bps).
    * TODO do we need this as it is identical to RFC2544 Throughput?
      Non Drop Rate (NDR): maximum packet/bandwidth throughput rate sustained
      by DUT/SUT at PLR equal zero (zero packet loss) specific to tested
      frame size(s). MUST be quoted with specific packet size as received by
      DUT/SUT during the measurement. Packet NDR measured in
      packets-per-second (or fps), bandwidth NDR expressed in
      bits-per-second (bps).
    * TODO if needed, reformulate to make it clear there can be multiple rates
      for multiple (non-zero) loss ratios.
      : Partial Drop Rate (PDR): maximum packet/bandwidth throughput rate
      sustained by DUT/SUT at PLR greater than zero (non-zero packet loss)
      specific to tested frame size(s). MUST be quoted with specific packet
      size as received by DUT/SUT during the measurement. Packet PDR
      measured in packets-per-second (or fps), bandwidth PDR expressed in
      bits-per-second (bps).
    * TODO: Refer to FRMOL instead.
      Maximum Receive Rate (MRR): packet/bandwidth rate regardless of PLR
      sustained by DUT/SUT under specified Maximum Transmit Rate (MTR)
      packet load offered by traffic generator. MUST be quoted with both
      specific packet size and MTR as received by DUT/SUT during the
      measurement. Packet MRR measured in packets-per-second (or fps),
      bandwidth MRR expressed in bits-per-second (bps).
    * TODO just keep using "trial measurement"?
      Trial: a single measurement step. See [RFC2544] section 23.
    * TODO already defined in RFC2544:
      Trial duration: amount of time over which packets are transmitted
      in a single measurement step.
{:/comment}
{::comment}
{:/comment}

* TODO: The current text uses Throughput for the zero loss ratio load.
  Is the capital T needed/useful?
* DUT and SUT: see the definitions in https://gerrit.fd.io/r/c/csit/+/35545
* Traffic Generator (TG) and Traffic Analyzer (TA): see
  https://datatracker.ietf.org/doc/html/rfc6894#section-4
  TODO: Maybe there is an earlier RFC?
* Overall search time: the time it takes to find all required loads within
  their precision goals, starting from zero trials measured at given
  DUT configuration and traffic profile.
* TODO: traffic profile?
* Intended load: https://datatracker.ietf.org/doc/html/rfc2285#section-3.5.1
* Offered load: https://datatracker.ietf.org/doc/html/rfc2285#section-3.5.2
* Maximum offered load (MOL): see
  https://datatracker.ietf.org/doc/html/rfc2285#section-3.5.3
* Forwarding rate at maximum offered load (FRMOL)
  https://datatracker.ietf.org/doc/html/rfc2285#section-3.6.2
* Trial Loss Count: the number of frames transmitted
  minus the number of frames received. Negative count is possible,
  e.g. when SUT duplicates some frames.
* Trial Loss Ratio: ratio of frames received relative to frames
  transmitted over the trial duration.
  For bi-directional throughput tests, the aggregate ratio is calculated,
  based on the aggregate number of frames transmitted and received.
  If the trial loss count is negative, its absolute value MUST be used
  to keep compliance with RFC2544.
* Safe load: any value, such that trial measurement at this (or lower)
  intended load is correcrly handled by both TG and TA, regardless of SUT behavior.
  Frequently, it is not known what the safe load is.
* Max load (TODO rename?): Maximal intended load to be used during search.
  Benchmarking team decides which value is low enough
  to guarantee values reported by TG and TA are reliable.
  It has to be a safe load, but it can be lower than a safe load estimate
  for added safety.
  See the subsection on unreliable test equipment below.
  This value MUST NOT be higher than MOL, which itself MUST NOT
  be higher than Maximum Frame Rate
  https://datatracker.ietf.org/doc/html/rfc2544#section-20
* Min load: Minimal intended load to be used during search.
  Benchmarking team decides which value is high enough
  to guarantee the trial measurement results are valid.
  E.g. considerable overall search time can be saved by declaring SUT
  faulty if min load trial shows too high loss rate.
  Zero frames per second is a valid min load value
* Effective loss ratio: a corrected value of trial loss ratio
  chosen to avoid difficulties if SUT exhibits decreasing loss ratio
  with increasing load. It is the maximum of trial loss ratios
  measured at the same duration on all loads smaller than (and including)
  the current one.
* Target loss ratio: a loss ratio value acting as an input for the search.
  The search is finding tight enough lower and upper bounds in intended load,
  so that the measurement at the lower bound has smaller or equal
  trial loss ratio, and upper bound has strictly larger trial loss ratio.
  For the tightest upper bound, the effective loss ratio is the same as
  trial loss ratio at that upper bound load.
  For the tightest lower bound, the effective loss ratio can be higher
  than the trial loss ratio at that lower bound, but still not larger
  than the target loss ratio.
* TODO: Search algorithm.
* TODO: Precision goal.
* TODO: Define a "benchmarking group".
* TODO: Upper and lower bound.
* TODO: Valid and invalid bound?
* TODO: Interval and interval width?

TODO: Mention NIC/PCI bandwidth/pps limits can be lower than bandwidth of medium.

# Intentions of this document

{::comment}
    Instead of talking about DUTs being non-deterministic
    and vendors "gaming" in order to get better Throughput results,
    Maciek and Vratko currently prefer to talk about result repeatability.
{:/comment}

The intention of this document is to provide recommendations for:
* optimizing search for multiple target loss ratios at once,
* speeding up the overall search time,
* improve search results repeatability and comparability.

No part of RFC2544 is intended to be obsoleted by this document.

{::comment}
    This document may contain examples which contradict RFC2544 requirements
    and suggestions.
    That is not an ecouragement for benchmarking groups
    to stop being compliant with RFC2544.
{:/comment}

# RFC2544

## Throughput search

It is useful to restate the key requirements of RFC2544
using the new terminology (see section Terminology).

The following sections of RFC2544 are of interest for this document.

* https://datatracker.ietf.org/doc/html/rfc2544#section-20
  Mentions the max load SHOULD not be larget than the theoretical
  maximum rate for the frame size on the media.

* https://datatracker.ietf.org/doc/html/rfc2544#section-23
  Lists the actions to be done for each trial measurement,
  it also mentions loss rate as an example of trial measurement results.
  This document uses loss count instead, as that is the quantity
  that is easier for the current test equipment to measure,
  e.g. it is not affected by the real traffic duration.
  TODO: Time uncertainty again.

* https://datatracker.ietf.org/doc/html/rfc2544#section-24
  Mentions "full length trials" leading to the Throughput found,
  as opposed to shorter trial durations, allowed in an attempt
  to "minimize the length of search procedure".
  This document talks about "final trial duration" and aims to
  "optimize overal search time".

* https://datatracker.ietf.org/doc/html/rfc2544#section-26.1
  with https://www.rfc-editor.org/errata/eid422
  finaly states requirements for the search procedure.
  It boils down to "increase intended load upon zero trial loss
  and decrease intended load upon non-zero trial loss".

No additional constraints are placed on the load selection,
and there is no mention of an exit condition, e.g. when there is enough
trial measurements to proclaim the largest load with zero trial loss
(and final trial duration) to be the Throughput found.

{::comment}
    The following section is probably not useful enough.

    ## Generalized search

    Note that the Throughput search can be restated as a "conditional
    load search" with a specific condition.

    "increase intended load upon trial result satisfying the condition
    and decrease intended load upon trial result not satisfying the condition"
    where the Throughput condition is "trial loss count is zero".

    This works for any condition that can be evaluated from a single
    trial measurement result, and is likely to be true at low loads
    and false at high loads.

    MLRsearch can incorporate multiple different conditions,
    as long as there is total ligical ordering between them
    (e.g. if a condition for a target loss ratio is not satisfied,
    it is also not satisfied for any other codition which uses
    larger target loss ratio).

    TODO: How to call a "load associated with this particular condition"?
{:/comment}

{::comment}

    TODO: Not sure if this subsection is needed an where.

    ## Simple bisection

    There is one obvious and simple search algorithm which conforms
    to throughput search requirements: simple bijection.

    Input: target precision, in frames per second.

    Procedure:

    1. Chose min load to be zero.
       1. No need to measure, loss count has to be zero.
       2. Use the zero load as the current lower bound.
    2. Chose max load to be the max value allowed by bandwidth of the medium.
       1. Perform a trial measurement (at the full length duration) at max load.
       2. If there is zero trial loss count, return max load as Throughput.
       3. Use max load as the current upper bound.
    3. Repeat until the difference between lower bound and upper bound is
       smaller or equal to the precision goal.
       1. If it is not larget, return the current lower bound as Throughput.
       2. Else: Chose new load as the arithmetic average of lower and upper bound.
       3. Perform a trial measurement (at the full length duration) at this load.
       4. If the trial loss rate is zero, consider the load as new lower bound.
       5. Else consider the load as the new upper bound.
       6. Jump back to the repeat at 3.

    Another possible stop condition is the overal search time so far,
    but that is not really a different condition, as the time for search to reach
    the precision goal is just a function of precision goal, trial duration
    and the difference between max and min load.

    While this algorithm can be accomodated to search for multiple
    target loss ratios "at the same time (see somewhere below),
    it is still missing multiple improvement which give MLRsearch
    considerably better overal search time in practice.

{:/comment}

# Problems

## Repeatability and Comparability

RFC2544 does not suggest to repeat Throughput search,
{::comment}probably because the full set of tests already takes long{:/comment}
and from just one Throughput value, it cannot be determined
how repeatable that value is (how likely it is for a repeated Throughput search
to end up with a value less then the precision goal away from the first value).

Depending on SUT behavior, different benchmark groups
can report significantly different Througput values,
even when using identical SUT and test equipment,
just because of minor differences in their search algorithm
(e.g. different max load value).

While repeatability can be addressed by repeating the search several times,
the differences in the comparability scenario may be systematic,
e.g. seeming like a bias in one or both benchmark groups.

MLRsearch algorithm does not really help with the repeatability problem.
This document RECOMMENDS to repeat a selection of "important" tests
ten times, so users can ascertain the repeatability of the results.

TODO: How to report? Average and standard deviation?

Following MLRsearch algorithm leaves less freedom for the benchmark groups
to encounter the comparability problem,
alghough more research is needed to determine the effect
of MLRsearch's tweakable parameters.

{::comment}
    Possibly, the old DUTs were quite sharply consistent in their performance,
    and/or precision goals were quite large in order to save overal search time.

    With software DUTs and with time-efficient search algorithms,
    nowadays the repeatability of Throughput can be quite low,
    as in standard deviation of repeated Througput results
    is considerably higher than the precision goal.
{:/comment}

{::comment}
    TODO: Unify with PLRsearch draft.
    TODO: No-loss region, random region, lossy region.
    TODO: Tweaks with respect to non-zero loss ratio goal.
    TODO: Duration dependence?

    Both RFC2544 and MLRsearch return Throughput somewhere inside the random region,
    or at most the precision goal below it.
{:/comment}

{::comment}
    TODO: Make sure this is covered elsewhere, then delete.

    ## Search repeatability

    The goal of RFC1242 and RFC2544 is to limit how vendors benchmark their DUTs,
    in order to force them to report values that have higher chance
    to be confirmed by independent benchmarking groups following the same RFCs.

    This works well for deterministic DUTs.

    But for non-deterministic DUTs, the RFC2544 Throughput value
    is only guaranteed to fall somewhere below the lossy region (TODO define).
    It is possible to arrive at a value positioned likely high in the random region
    at the cost of increased overall search duration,
    simply by lowering the load by very small amounts (instead of exact halving)
    upon lossy trial and increasing by large amounts upon lossless trial.

    Prescribing an exact search algorithm (bisection or MLRsearch or other)
    will force vendors to report less "gamey" Throughput values.
{:/comment}

{::comment}
    ## Extensions

    The following two sections are probably out of scope,
    as they does not affect MLRsearch design choices.

    ### Direct and inverse measurements

    TODO expand: Direct measurement is single trial measurement,
    with predescribed inputs and outputs turned directly into the quality of interest
    Examples:
    Latency https://datatracker.ietf.org/doc/html/rfc2544#section-26.2
    is a single direct measurement.
    Frame loss rate https://datatracker.ietf.org/doc/html/rfc2544#section-26.3
    is a sequence of direct measurements.

    TODO expand: Indirect measurement aims to solve an "inverse function problem",
    meaning (a part of) trial measurement output is prescribed, and the quantity
    of interest is (derived from) the input parameters of trial measurement
    that achieves the prescribed output.
    In general this is a hard problem, but if the unknown input parameter
    is just one-dimensional quantity, algorithms such as bisection
    do converge regardless of outputs seen.
    We call any such algorithm examining one-dimensional input as "search".
    Of course, some exit condition is needed for the search to end.
    In case of Throughput, bisection algorithm tracks both upper bound
    and lower bound, with lower bound at the end of search is the quantity
    satisfying the definition of Throughput.

    ### Metrics other than frames

    TODO expand: Small TCP transaction can succeed even if some frames are lost.

    TODO expand: It is possible for loss ratio to use different metric than load.
    E.g. pps loss ratio when traffic profile uses higher level transactions per second.

    ### TODO: Stateful DUT

    ### TODO: Stateful traffic
{:/comment}

## Non-Zero Target Loss Ratios

https://datatracker.ietf.org/doc/html/rfc1242#section-3.17
defines Throughput as:
    The maximum rate at which none of the offered frames
    are dropped by the device.

and then it says:
    Since even the loss of one frame in a
    data stream can cause significant delays while
    waiting for the higher level protocols to time out,
    it is useful to know the actual maximum data
    rate that the device can support.

{::comment}

    While this may still be true for some protocols,
    research has been performed...

    TODO: Add this link properly: https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-Y.1541-201112-I!!PDF-E&type=items
    TODO: List values from that document, from 10^-3 to 4*10^-6.

    ...on other protocols and use cases,
    resulting in some small but non-zero loss ratios being considered
    as acceptable. Unfortunately, the acceptable value depends on use case
    and properties such as TCP window size and round trip time,
    so no single value of target loss rate (other than zero)
    is considered to be universally applicable.

{:/comment}

New "software DUTs" (traffic forwarding programs running on
commercial-off-the-shelf compute server hardware) frequently exhibit quite
low repeatability of Throughput results per above definition.

This is due to, in general, throughput rates of software DUTs (programs)
being sensitive to server resource allocation by OS during runtime,
as well as any interrupts or blocking of software threads involved
in packet processing.

To deal with this, this document recommends discovery of multiple throughput rates of interest for software DUTs that run on general purpose COTS servers (with x86, AArch64 Instruction Set Architectures):
* throughput rate with target of zero packet loss ratio.
* at least one throughput rate with target of non-zero packet loss ratio.


In our experience, the higher the target loss ratio is,
the better is the repeatability of the corresponding load found.

TODO: Define a good name for a load corresponding to a specific non-zero
target loss ration, while keeping Throughput for the load corresponding
to zero target loss ratio.

This document RECOMMENDS the benchmark groups to search for corresponding loads
to at least one non-zero target loss ratio.
This document does not suggest any particular non-zero target loss ratio value
to search the corresponding load for.

{::comment}
    What is worse, some benchmark groups (which groups?; citation needed)
    started reporting loads that achieved only "approximate zero loss",
    while still calling that a Throughput (and thus becoming non-compliant
    with RFC2544).
{:/comment}

# Solution ideas

This document gives several independent ideas on how to lower the (average)
overall search time, while remaining unconditionally compliant with RFC2544
(and adding some of extensions).

This document also specifies one particular way to combine all the ideas
into a single search algorithm class (single logic with few tweakable parameters).

Little to no research has been done into the question of which combination
of ideas achieves the best compromise with respect to overal search time,
high repeatability and high comparability.

TODO: How important it is to discuss particular implementation choices,
especially when motivated by non-deterministic SUT behavior?

## Short duration trials

https://datatracker.ietf.org/doc/html/rfc2544#section-24
already mentions the possibity of using shorter duration
for trials that are not part of "final determination".

Obviously, the upper and lower bound from a smaller duration trial
can be used as the initial upper and lower bound for the final determination.

MLRsearch makes it clear a re-measurement is always needed
(new trial measurement with the same load but longer duration).
It also specifes what to do if the longer trial is no longer a valid bound
(TODO define?), e.g. start an external search.
Additionaly one halving can be saved during the shorter duration search.

## FRMOL as reasonable start

TODO expand: Overal search ends with "final determination" search,
preceded by "shorter duration search" preceded by "bound initialization",
where the bounds can be considerably different from min and max load.

For SUTs with high repeatability, the FRMOL is usually a good approximation
of Throughput. But for less repeatable SUTs, forwarding rate (TODO define)
is frequently a bad approximation to Throughput, therefore halving
and other robust-to-worst-case approaches have to be used.
Still, forwarding rate at FRMOL load can be a good initial bound.

## Non-zero loss ratios

See the "Popularity of non-zero target loss ratios" section above.

TODO: Define "trial measurement result classification criteria",
or keep reusing long phrases without definitions?

A search for a load corresponding to a non-zero target loss rate
is very similar to a search for Throughput,
just the criterion when to increase or decrease the intended load
for the next trial measurement uses the comparison of trial loss ratio
to the target loss ratio (instead of comparing loss count to zero)
Any search algorithm that works for Throughput can be easily used also for
non-zero target loss rates, perhaps with small modifications
in places where the measured forwarding rate is used.

Note that it is possible to search for multiple loss ratio goals if needed.

## Concurrent ratio search

A single trial measurement result can act as an upper bound for a lower
target loss ratio, and as a lower bound for a higher target loss ratio
at the same time. This is an example of how
it can be advantageous to search for all loss ratio goals "at once",
or at least "reuse" trial measurement result done so far.

Even when a search algorithm is fully deterministic in load selection
while focusing on a single loss ratio and trial duration,
the choice of iteration order between target loss ratios and trial durations
can affect the obtained results in subtle ways.
MLRsearch offers one particular ordering.

{::comment}
    It is not clear if the current ordering is "best",
    it is not even clear how to measure how good an ordering is.
    We would need several models for bad SUT behaviors,
    bug-free implementations of different orderings,
    simulator to show the distribution of rates found,
    distribution of overall durations,
    and a criterion of which rate distribution is "bad"
    and whether it is worth the time saved.
{:/comment}
{::comment}
{:/comment}

## Load selection heuristics and shortcuts

Aside of the two heuristics already mentioned (FRMOL based initial bounds
and saving one halving when increasing trial duration),
there are other tricks that can save some overall search time
at the cost of keeping the difference between final lower and upper bound
intentionally large (but still within the precision goal).

TODO: Refer implementation subsections on:
* Uneven splits.
* Rounding the interval width up.
* Using old invalid bounds for interval width guessing.

The impact on overall duration is probably small,
and the effect on result distribution maybe even smaller.
TODO: Is the two-liner above useful at all?

# Non-compliance with RFC2544

It is possible to achieve even faster search times by abandoning
some requirements and suggestions of RFC2544,
mainly by reducing the wait times at start and end of trial.

Such results are therefore no longer compliant with RFC2544
(or at least not unconditionally),
but they may still be useful for internal usage, or for comparing
results of different DUTs achieved with an identical non-compliant algorithm.

TODO: Refer to the subsection with CSIT customizations.

# Additional Requirements

RFC2544 can be understood as having a number of implicit requirements.
They are made explicit in this section
(as requirements for this document, not for RFC2544).

Recommendations on how to properly address the implicit requirements
are out of scope of this document.

{::comment}

    Although some (insufficient) ideas are proposed.

{:/comment}

## TODO: Search Stop Criteria

TODO: Mention the timeout parameter?

{::comment}

    TODO: highlight importance of results consistency
    for SUT performance trending and anomaly detection.

{:/comment}

## Reliability of Test Equipment

Both TG and TA MUST be able to handle correctly
every intended load used during the search.

On TG side, the difference between Intended Load and Offered Load
MUST be small.

TODO: How small? Difference of one packet may not be measurable
due to time uncertainties.

{::comment}

    Maciek: 1 packet out of 10M, that's 10**-7 accuracy.

    Vratko: For example, TRex uses several "worker" threads, each doing its own
    rounding on how many packets to send, separately per each traffic stream.
    For high loads and durations, the observed number of frames transmitted
    can differ from the expected (fractional) value by tens of frames.

{:/comment}

TODO expand: time uncertainty.

To ensure that, max load (see Terminology) has to be set to low enough value.
Benchmark groups MAY list the max load value used,
especially if the Throughput value is equal (or close) to the max load.

{::comment}

    The following is probably out of scope of this document,
    but can be useful when put into a separate document.

    TODO expand: If it results in smaller Throughput reported,
    it is not a big issue. Treat similarly to bandwidth and PPS limits of NICs.

    TODO expand: TA dropping packets when loaded only lowers Throughput,
    so not an issue.

    TODO expand: TG sending less packets but stopping at target duration
    is also fine, as long as the forwarding rate is used as Throughput value,
    not the higher intended load.

    TODO expand: Duration stretching is not fine.
    Neither "check for actual duration" nor "start+sleep+stop"
    are reliable solutions due to time overheads and uncertainty
    of TG starting/stopping traffic (and TA stopping counting packets).

{:/comment}

Solutions (even problem formulations) for the following open problems
are outside of the scope of this document:
* Detecting when the test equipment operates above its safe load.
* Finding a large but safe load value.
* Correcting any result affected by max load value not being a safe load.

{::comment}

    TODO: Mention 90% of self-test as an idea:
    https://datatracker.ietf.org/doc/html/rfc8219#section-9.2.1

    This is pointing to DNS testing, nothing to do with throughput,
    so how is it relevant here?

{:/comment}

{::comment}

    Part of discussion on BMWG mailing list (with small edits):

    This is a hard issue.
    The algorithm as described has no way of knowing
    which part of the whole system is limiting the performance.

    It could be SUT only (no problem, testing SUT as expected),
    it could be TG only (can be mitigated by TG self-test
    and using small enough loads).

    But it could also be an interaction between DUT and TG.
    Imagine a TG (the Traffic Analyzer part) which is only able
    to handle incoming traffic up to some rate,
    but passes the self-test as the Generator part has maximal rate
    not larger than that. But what if SUT turns that steady rate
    into long-enough bursts of a higher rate (with delays between bursts
    large enough, so average forwarding rate matches the load).
    This way TA will see some packets as missing (when its buffers
    fill up), even though SUT has processed them correctly.

{:/comment}

### Very late frames

{::comment}

    In CSIT we are aggressive at skipping all wait times around trial,
    but few of DUTs have large enough buffers.
    Or there is another reason why we are seeing negative loss counts.

{:/comment}


RFC2544 requires quite conservative time delays
see https://datatracker.ietf.org/doc/html/rfc2544#section-23
to prevent frames buffered in one trial measurement
to be counted as received in a subsequent trial measurement.

However, for some SUTs it may still be possible to buffer enough frames,
so they are still sending them (perhaps in bursts)
when the next trial measurement starts.
Sometimes, this can be detected as a negative trial loss count, e.g. TA receiving
more frames than TG has sent during this trial measurement. Frame duplication
is another way of causing the negative trial loss count.

https://datatracker.ietf.org/doc/html/rfc2544#section-10
recommends to use sequence numbers in frame payloads,
but generating and verifying them requires test equipment resources,
which may be not plenty enough to suport at high loads.
(Using low enough max load would work, but frequently that would be
smaller than SUT's sctual Throughput.)

RFC2544 does not offer any solution to the negative loss problem,
except implicitly treating negative trial loss counts
the same way as positive trial loss counts.

This document also does not offer any practical solution.

Instead, this document SUGGESTS the search algorithm to take any precaution
necessary to avoid very late frames.

This document also REQUIRES any detected duplicate frames to be counted
as additional lost frames.
This document also REQUIRES, any negative trial loss ratio
to be treated as positive trial loss ratio of the same absolute value.

{::comment}

    !!! Make sure this is covered elsewere, at least in better comments. !!!

    ## TODO: Bad behavior of SUT

    (Highest load with always zero loss can be quite far from lowest load
    with always nonzero loss.)
    (Non-determinism: warm up, periodic "stalls", perf decrease over time, ...)

    Big buffers:
    http://www.hit.bme.hu/~lencse/publications/ECC-2017-B-M-DNS64-revised.pdf
    See page 8 and search for the word "gaming".

{:/comment}

!!! Nothing below is up-to-date with draft v02. !!!

# MLRsearch Background

TODO: Old section, probably obsoleted by preceding section(s).

Multiple Loss Ratio search (MLRsearch) is a packet throughput search
algorithm suitable for deterministic systems (as opposed to
probabilistic systems). MLRsearch discovers multiple packet throughput
rates in a single search, each rate is associated with a distinct
Packet Loss Ratio (PLR) criterion.

For cases when multiple rates need to be found, this property makes
MLRsearch more efficient in terms of time execution, compared to
traditional throughput search algorithms that discover a single packet
rate per defined search criteria (e.g. a binary search specified by
[RFC2544]). MLRsearch reduces execution time even further by relying on
shorter trial durations of intermediate steps, with only the final
measurements conducted at the specified final trial duration. This
results in the shorter overall search execution time when compared to a
traditional binary search, while guaranteeing the same results for
deterministic systems.

In practice, two rates with distinct PLRs are commonly used for packet
throughput measurements of NFV systems: Non Drop Rate (NDR) with PLR=0
and Partial Drop Rate (PDR) with PLR>0. The rest of this document
describes MLRsearch with NDR and PDR pair as an example.

Similarly to other throughput search approaches like binary search,
MLRsearch is effective for SUTs/DUTs with PLR curve that is
non-decreasing with growing offered load. It may not be as
effective for SUTs/DUTs with abnormal PLR curves, although
it will always converge to some value.

MLRsearch relies on traffic generator to qualify the received packet
stream as error-free, and invalidate the results if any disqualifying
errors are present e.g. out-of-sequence frames.

MLRsearch can be applied to both uni-directional and bi-directional
throughput tests.

For bi-directional tests, MLRsearch rates and ratios are aggregates of
both directions, based on the following assumptions:

* Traffic transmitted by traffic generator and received by SUT/DUT
  has the same packet rate in each direction,
  in other words the offered load is symmetric.
* SUT/DUT packet processing capacity is the same in both directions,
  resulting in the same packet loss under load.

MLRsearch can be applied even without those assumptions,
but in that case the aggregate loss ratio is less useful as a metric.

MLRsearch can be used for network transactions consisting of more than
just one packet, or anything else that has intended load as input
and loss ratio as output (duration as input is optional).
This text uses mostly packet-centric language.

# MLRsearch Overview

The main properties of MLRsearch:

* MLRsearch is a duration aware multi-phase multi-rate search algorithm:
  * Initial Phase determines promising starting interval for the search.
  * Intermediate Phases progress towards defined final search criteria.
  * Final Phase executes measurements according to the final search
    criteria.
  * Final search criteria are defined by following inputs:
    * Target PLRs (e.g. 0.0 and 0.005 when searching for NDR and PDR).
    * Final trial duration.
    * Measurement resolution.
* Initial Phase:
  * Measure MRR over initial trial duration.
  * Measured MRR is used as an input to the first intermediate phase.
* Multiple Intermediate Phases:
  * Trial duration:
    * Start with initial trial duration in the first intermediate phase.
    * Converge geometrically towards the final trial duration.
  * Track all previous trial measurement results:
    * Duration, offered load and loss ratio are tracked.
    * Effective loss ratios are tracked.
      * While in practice, real loss ratios can decrease with increasing load,
        effective loss ratios never decrease. This is achieved by sorting
        results by load, and using the effective loss ratio of the previous load
        if the current loss ratio is smaller than that.
    * The algorithm queries the results to find best lower and upper bounds.
      * Effective loss ratios are always used.
    * The phase ends if all target loss ratios have tight enough bounds.
  * Search:
    * Iterate over target loss ratios in increasing order.
    * If both upper and lower bound are in measurement results for this duration,
      apply bisect until the bounds are tight enough,
      and continue with next loss ratio.
    * If a bound is missing for this duration, but there exists a bound
      from the previous duration (compatible with the other bound
      at this duration), re-measure at the current duration.
    * If a bound in one direction (upper or lower) is missing for this duration,
      and the previous duration does not have a compatible bound,
      compute the current "interval size" from the second tightest bound
      in the other direction (lower or upper respectively)
      for the current duration, and choose next offered load for external search.
    * The logic guarantees that a measurement is never repeated with both
      duration and offered load being the same.
    * The logic guarantees that measurements for higher target loss ratio
      iterations (still within the same phase duration) do not affect validity
      and tightness of bounds for previous target loss ratio iterations
      (at the same duration).
  * Use of internal and external searches:
    * External search:
      * It is a variant of "exponential search".
      * The "interval size" is multiplied by a configurable constant
        (powers of two work well with the subsequent internal search).
    * Internal search:
      * A variant of binary search that measures at offered load between
        the previously found bounds.
      * The interval does not need to be split into exact halves,
        if other split can get to the target width goal faster.
        * The idea is to avoid returning interval narrower than the current
          width goal. See sample implementation details, below.
* Final Phase:
  * Executed with the final test trial duration, and the final width
    goal that determines resolution of the overall search.
* Intermediate Phases together with the Final Phase are called
  Non-Initial Phases.
* The returned bounds stay within prescribed min_rate and max_rate.
  * When returning min_rate or max_rate, the returned bounds may be invalid.
    * E.g. upper bound at max_rate may come from a measurement
      with loss ratio still not higher than the target loss ratio.

The main benefits of MLRsearch vs. binary search include:

* In general, MLRsearch is likely to execute more trials overall, but
  likely less trials at a set final trial duration.
* In well behaving cases, e.g. when results do not depend on trial
  duration, it greatly reduces (>50%) the overall duration compared to a
  single PDR (or NDR) binary search over duration, while finding
  multiple drop rates.
* In all cases MLRsearch yields the same or similar results to binary
  search.
* Note: both binary search and MLRsearch are susceptible to reporting
  non-repeatable results across multiple runs for very bad behaving
  cases.

Caveats:

* Worst case MLRsearch can take longer than a binary search, e.g. in case of
  drastic changes in behaviour for trials at varying durations.
  * Re-measurement at higher duration can trigger a long external search.
    That never happens in binary search, which uses the final duration
    from the start.

# Sample Implementation

Following is a brief description of a sample MLRsearch implementation,
which is a simplified version of the existing implementation.

## Input Parameters

1. **max_rate** - Maximum Transmit Rate (MTR) of packets to
   be used by external traffic generator implementing MLRsearch,
   limited by the actual Ethernet link(s) rate, NIC model or traffic
   generator capabilities.
2. **min_rate** - minimum packet transmit rate to be used for
   measurements. MLRsearch fails if lower transmit rate needs to be
   used to meet search criteria.
3. **final_trial_duration** - required trial duration for final rate
   measurements.
4. **initial_trial_duration** - trial duration for initial MLRsearch phase.
5. **final_relative_width** - required measurement resolution expressed as
   (lower_bound, upper_bound) interval width relative to upper_bound.
6. **packet_loss_ratios** - list of maximum acceptable PLR search criteria.
7. **number_of_intermediate_phases** - number of phases between the initial
   phase and the final phase. Impacts the overall MLRsearch duration.
   Less phases are required for well behaving cases, more phases
   may be needed to reduce the overall search duration for worse behaving cases.

## Initial Phase

1. First trial measures at configured maximum transmit rate (MTR) and
   discovers maximum receive rate (MRR).
   * IN: trial_duration = initial_trial_duration.
   * IN: offered_transmit_rate = maximum_transmit_rate.
   * DO: single trial.
   * OUT: measured loss ratio.
   * OUT: MRR = measured receive rate.
   Received rate is computed as intended load multiplied by pass ratio
   (which is one minus loss ratio). This is useful when loss ratio is computed
   from a different metric than intended load. For example, intended load
   can be in transactions (multiple packets each), but loss ratio is computed
   on level of packets, not transactions.

   * Example: If MTR is 10 transactions per second, and each transaction has
     10 packets, and receive rate is 90 packets per second, then loss rate
     is 10%, and MRR is computed to be 9 transactions per second.

   If MRR is too close to MTR, MRR is set below MTR so that interval width
   is equal to the width goal of the first intermediate phase.
   If MRR is less than min_rate, min_rate is used.
2. Second trial measures at MRR and discovers MRR2.
   * IN: trial_duration = initial_trial_duration.
   * IN: offered_transmit_rate = MRR.
   * DO: single trial.
   * OUT: measured loss ratio.
   * OUT: MRR2 = measured receive rate.
   If MRR2 is less than min_rate, min_rate is used.
   If loss ratio is less or equal to the smallest target loss ratio,
   MRR2 is set to a value above MRR, so that interval width is equal
   to the width goal of the first intermediate phase.
   MRR2 could end up being equal to MTR (for example if both measurements so far
   had zero loss), which was already measured, step 3 is skipped in that case.
3. Third trial measures at MRR2.
   * IN: trial_duration = initial_trial_duration.
   * IN: offered_transmit_rate = MRR2.
   * DO: single trial.
   * OUT: measured loss ratio.
   * OUT: MRR3 = measured receive rate.
   If MRR3 is less than min_rate, min_rate is used.
   If step 3 is not skipped, the first trial measurement is forgotten.
   This is done because in practice (if MRR2 is above MRR), external search
   from MRR and MRR2 is likely to lead to a faster intermediate phase
   than a bisect between MRR2 and MTR.

## Non-Initial Phases

1. Main phase loop:
   1. IN: trial_duration for the current phase. Set to
      initial_trial_duration for the first intermediate phase; to
      final_trial_duration for the final phase; or to the element of
      interpolating geometric sequence for other intermediate phases.
      For example with two intermediate phases, trial_duration of the
      second intermediate phase is the geometric average of
      initial_trial_duration and final_trial_duration.
   2. IN: relative_width_goal for the current phase. Set to
      final_relative_width for the final phase; doubled for each
      preceding phase. For example with two intermediate phases, the
      first intermediate phase uses quadruple of final_relative_width
      and the second intermediate phase uses double of
      final_relative_width.
   3. IN: Measurement results from the previous phase (previous duration).
   4. Internal target ratio loop:
      1. IN: Target loss ratio for this iteration of ratio loop.
      2. IN: Measurement results from all previous ratio loop iterations
         of current phase (current duration).
      3. DO: According to the procedure described in point 2:
         1. either exit the phase (by jumping to 1.5),
         2. or exit loop iteration (by continuing with next target loss ratio,
            jumping to 1.4.1),
         3. or calculate new transmit rate to measure with.
      4. DO: Perform the trial measurement at the new transmit rate and
         current trial duration, compute its loss ratio.
      5. DO: Add the result and go to next iteration (1.4.1),
         including the added trial result in 1.4.2.
   5. OUT: Measurement results from this phase.
   6. OUT: In the final phase, bounds for each target loss ratio
      are extracted and returned.
      1. If a valid bound does not exist, use min_rate or max_rate.
2. New transmit rate (or exit) calculation (for point 1.4.3):
   1. If the previous duration has the best upper and lower bound,
      select the middle point as the new transmit rate.
      1. See 2.5.3. below for the exact splitting logic.
      2. This can be a no-op if interval is narrow enough already,
         in that case continue with 2.2.
      3. Discussion, assuming the middle point is selected and measured:
         1. Regardless of loss rate measured, the result becomes
            either best upper or best lower bound at current duration.
         2. So this condition is satisfied at most once per iteration.
         3. This also explains why previous phase has double width goal:
            1. We avoid one more bisection at previous phase.
            2. At most one bound (per iteration) is re-measured
               with current duration.
            3. Each re-measurement can trigger an external search.
            4. Such surprising external searches are the main hurdle
               in achieving low overall search durations.
            5. Even without 1.1, there is at most one external search
               per phase and target loss ratio.
            6. But without 1.1 there can be two re-measurements,
               each coming with a risk of triggering external search.
   2. If the previous duration has one bound best, select its transmit rate.
      In deterministic case this is the last measurement needed this iteration.
   3. If only upper bound exists in current duration results:
      1. This can only happen for the smallest target loss ratio.
      2. If the upper bound was measured at min_rate,
         exit the whole phase early (not investigating other target loss ratios).
      3. Select new transmit rate using external search:
         1. For computing previous interval size, use:
            1. second tightest bound at current duration,
            2. or tightest bound of previous duration,
               if compatible and giving a more narrow interval,
            3. or target interval width if none of the above is available.
            4. In any case increase to target interval width if smaller.
         2. Quadruple the interval width.
         3. Use min_rate if the new transmit rate is lower.
   4. If only lower bound exists in current duration results:
      1. If the lower bound was measured at max_rate,
         exit this iteration (continue with next lowest target loss ratio).
      2. Select new transmit rate using external search:
         1. For computing previous interval size, use:
            1. second tightest bound at current duration,
            2. or tightest bound of previous duration,
               if compatible and giving a more narrow interval,
            3. or target interval width if none of the above is available.
            4. In any case increase to target interval width if smaller.
         2. Quadruple the interval width.
         3. Use max_rate if the new transmit rate is higher.
   5. The only remaining option is both bounds in current duration results.
      1. This can happen in two ways, depending on how the lower bound
         was chosen.
         1. It could have been selected for the current loss ratio,
            e.g. in re-measurement (2.2) or in initial bisect (2.1).
         2. It could have been found as an upper bound for the previous smaller
            target loss ratio, in which case it might be too low.
         3. The algorithm does not track which one is the case,
            as the decision logic works well regardless.
      2. Compute "extending down" candidate transmit rate exactly as in 2.3.
      3. Compute "bisecting" candidate transmit rate:
         1. Compute the current interval width from the two bounds.
         2. Express the width as a (float) multiple of the target width goal
            for this phase.
         3. If the multiple is not higher than one, it means the width goal
            is met. Exit this iteration and continue with next higher
            target loss ratio.
         4. If the multiple is two or less, use half of that
            for new width if the lower subinterval.
         5. Round the multiple up to nearest even integer.
         6. Use half of that for new width if the lower subinterval.
         7. Example: If lower bound is 2.0 and upper bound is 5.0, and width
            goal is 1.0, the new candidate transmit rate will be 4.0.
            This can save a measurement when 4.0 has small loss.
            Selecting the average (3.5) would never save a measurement,
            giving more narrow bounds instead.
      4. If either candidate computation want to exit the iteration,
         do as bisecting candidate computation says.
      5. The remaining case is both candidates wanting to measure at some rate.
         Use the higher rate. This prefers external search down narrow enough
         interval, competing with perfectly sized lower bisect subinterval.

# FD.io CSIT Implementation

The only known working implementation of MLRsearch is in
the open-source code running in Linux Foundation
FD.io CSIT project [FDio-CSIT-MLRsearch] as part of
a Continuous Integration / Continuous Development (CI/CD) framework.

MLRsearch is also available as a Python package in [PyPI-MLRsearch].

## Additional details

This document so far has been describing a simplified version of
MLRsearch algorithm. The full algorithm as implemented in CSIT contains
additional logic, which makes some of the details (but not general
ideas) above incorrect. Here is a short description of the additional
logic as a list of principles, explaining their main differences from
(or additions to) the simplified description, but without detailing
their mutual interaction.

1. Logarithmic transmit rate.
   * In order to better fit the relative width goal, the interval
     doubling and halving is done differently.
   * For example, the middle of 2 and 8 is 4, not 5.
2. Timeout for bad cases.
   * The worst case for MLRsearch is when each phase converges to
     intervals way different than the results of the previous phase.
   * Rather than suffer total search time several times larger than pure
     binary search, the implemented tests fail themselves when the
     search takes too long (given by argument *timeout*).
3. Intended count.
   * The number of packets to send during the trial should be equal to
     the intended load multiplied by the duration.
     * Also multiplied by a coefficient, if loss ratio is calculated
       from a different metric.
       * Example: If a successful transaction uses 10 packets,
         load is given in transactions per second, but loss ratio is calculated
         from packets, so the coefficient to get intended count of packets
         is 10.
   * But in practice that does not work.
     * It could result in a fractional number of packets,
     * so it has to be rounded in a way traffic generator chooses,
     * which may depend on the number of traffic flows
       and traffic generator worker threads.
4. Attempted count. As the real number of intended packets is not known exactly,
   the computation uses the number of packets traffic generator reports as sent.
   Unless overridden by the next point.
5. Duration stretching.
   * In some cases, traffic generator may get overloaded,
     causing it to take significantly longer (than duration) to send all packets.
   * The implementation uses an explicit stop,
     * causing lower attempted count in those cases.
   * The implementation tolerates some small difference between
     attempted count and intended count.
     * 10 microseconds worth of traffic is sufficient for our tests.
   * If the difference is higher, the unsent packets are counted as lost.
     * This forces the search to avoid the regions of high duration stretching.
     * The final bounds describe the performance of not just SUT,
       but of the whole system, including the traffic generator.
6. Excess packets.
   * In some test (e.g. using TCP flows) Traffic generator reacts to packet loss
     by retransmission. Usually, such packet loss is already affecting loss ratio.
     If a test also wants to treat retransmissions due to heavily delayed packets
     also as a failure, this is once again visible as a mismatch between
     the intended count and the attempted count.
   * The CSIT implementation simply looks at absolute value of the difference,
     so it offers the same small tolerance before it starts marking a "loss".
7. For result processing, we use lower bounds and ignore upper bounds.

### FD.io CSIT Input Parameters

1. **max_rate** - Typical values: 2 * 14.88 Mpps for 64B
   10GE link rate, 2 * 18.75 Mpps for 64B 40GE NIC (specific model).
2. **min_rate** - Value: 2 * 9001 pps (we reserve 9000 pps
   for latency measurements).
3. **final_trial_duration** - Value: 30.0 seconds.
4. **initial_trial_duration** - Value: 1.0 second.
5. **final_relative_width** - Value: 0.005 (0.5%).
6. **packet_loss_ratios** - Value: 0.0, 0.005 (0.0% for NDR, 0.5% for PDR).
7. **number_of_intermediate_phases** - Value: 2.
   The value has been chosen based on limited experimentation to date.
   More experimentation needed to arrive to clearer guidelines.
8. **timeout** - Limit for the overall search duration (for one search).
   If MLRsearch oversteps this limit, it immediately declares the test failed,
   to avoid wasting even more time on a misbehaving SUT.
   Value: 600.0 (seconds).
9. **expansion_coefficient** - Width multiplier for external search.
   Value: 4.0 (interval width is quadroupled).
   Value of 2.0 is best for well-behaved SUTs, but value of 4.0 has been found
   to decrease overall search time for worse-behaved SUT configurations,
   contributing more to the overall set of different SUT configurations tested.


## Example MLRsearch Run


The following list describes a search from a real test run in CSIT
(using the default input values as above).

* Initial phase, trial duration 1.0 second.

Measurement 1, intended load 18750000.0 pps (MTR),
measured loss ratio 0.7089514628479618 (valid upper bound for both NDR and PDR).

Measurement 2, intended load 5457160.071600716 pps (MRR),
measured loss ratio 0.018650817320118702 (new tightest upper bounds).

Measurement 3, intended load 5348832.933500009 pps (slightly less than MRR2
in preparation for first intermediate phase target interval width),
measured loss ratio 0.00964383362905351 (new tightest upper bounds).

* First intermediate phase starts, trial duration still 1.0 seconds.

Measurement 4, intended load 4936605.579021453 pps (no lower bound,
performing external search downwards, for NDR),
measured loss ratio 0.0 (valid lower bound for both NDR and PDR).

Measurement 5, intended load 5138587.208637197 pps (bisecting for NDR),
measured loss ratio 0.0 (new tightest lower bounds).

Measurement 6, intended load 5242656.244044665 pps (bisecting),
measured loss ratio 0.013523745379347257 (new tightest upper bounds).

* Both intervals are narrow enough.
* Second intermediate phase starts, trial duration 5.477225575051661 seconds.

Measurement 7, intended load 5190360.904111567 pps (initial bisect for NDR),
measured loss ratio 0.0023533920869969953 (NDR upper bound, PDR lower bound).

Measurement 8, intended load 5138587.208637197 pps (re-measuring NDR lower bound),
measured loss ratio 1.2080222912800403e-06 (new tightest NDR upper bound).

* The two intervals have separate bounds from now on.

Measurement 9, intended load 4936605.381062318 pps (external NDR search down),
measured loss ratio 0.0 (new valid NDR lower bound).

Measurement 10, intended load 5036583.888432355 pps (NDR bisect),
measured loss ratio 0.0 (new tightest NDR lower bound).

Measurement 11, intended load 5087329.903232804 pps (NDR bisect),
measured loss ratio 0.0 (new tightest NDR lower bound).

* NDR interval is narrow enough, PDR interval not ready yet.

Measurement 12, intended load 5242656.244044665 pps (re-measuring PDR upper bound),
measured loss ratio 0.0101174866190136 (still valid PDR upper bound).

* Also PDR interval is narrow enough, with valid bounds for this duration.
* Final phase starts, trial duration 30.0 seconds.

Measurement 13, intended load 5112894.3238511775 pps (initial bisect for NDR),
measured loss ratio 0.0 (new tightest NDR lower bound).

Measurement 14, intended load 5138587.208637197 (re-measuring NDR upper bound),
measured loss ratio 2.030389804256833e-06 (still valid PDR upper bound).

* NDR interval is narrow enough, PDR interval not yet.

Measurement 15, intended load 5216443.04126728 pps (initial bisect for PDR),
measured loss ratio 0.005620871287975237 (new tightest PDR upper bound).

Measurement 16, intended load 5190360.904111567 (re-measuring PDR lower bound),
measured loss ratio 0.0027629971184465604 (still valid PDR lower bound).

* PDR interval is also narrow enough.
* Returning bounds:
* NDR_LOWER = 5112894.3238511775 pps; NDR_UPPER = 5138587.208637197 pps;
* PDR_LOWER = 5190360.904111567 pps; PDR_UPPER = 5216443.04126728 pps.

# IANA Considerations

No requests of IANA.

# Security Considerations

Benchmarking activities as described in this memo are limited to
technology characterization of a DUT/SUT using controlled stimuli in a
laboratory environment, with dedicated address space and the constraints
specified in the sections above.

The benchmarking network topology will be an independent test setup and
MUST NOT be connected to devices that may forward the test traffic into
a production network or misroute traffic to the test management network.

Further, benchmarking is performed on a "black-box" basis, relying
solely on measurements observable external to the DUT/SUT.

Special capabilities SHOULD NOT exist in the DUT/SUT specifically for
benchmarking purposes. Any implications for network security arising
from the DUT/SUT SHOULD be identical in the lab and in production
networks.

# Acknowledgements

Many thanks to Alec Hothan of OPNFV NFVbench project for thorough
review and numerous useful comments and suggestions.

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