path: root/docs/report/introduction/methodology_mlrsearch_tests.rst

.. _mlrsearch_algorithm:

MLRsearch Tests
---------------

Multiple Loss Rate search (MLRsearch) tests use new search algorithm
implemented in FD.io CSIT project. MLRsearch discovers multiple packet
throughput rates in a single search, with each rate associated with a
distinct Packet Loss Ratio (PLR) criteria. MLRsearch is being
standardized in IETF with `draft-vpolak-mkonstan-mlrsearch-XX
<https://tools.ietf.org/html/draft-vpolak-mkonstan-mlrsearch-00>`_.

Two throughput measurements used in FD.io CSIT are Non-Drop Rate (NDR,
with zero packet loss, PLR=0) and Partial Drop Rate (PDR, with packet
loss rate not greater than the configured non-zero PLR). MLRsearch
discovers NDR and PDR in a single pass reducing required execution time
compared to separate binary searches for NDR and PDR. 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 standard NDR/PDR binary search,
while guaranteeing the same or similar results.

If needed, MLRsearch can be easily adopted to discover more throughput rates
with different pre-defined PLRs.

.. Note:: All throughput rates are *always* bi-directional
   aggregates of two equal (symmetric) uni-directional packet rates
   received and reported by an external traffic generator.

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.

- *Initial phase*:

  - Uses link rate as a starting transmit rate and discovers the Maximum
    Receive Rate (MRR) used as an input to the first intermediate phase.

- *Intermediate phases*:

  - Start with initial trial duration (in the first phase) and converge
    geometrically towards the final trial duration (in the final phase).
  - Track two values for NDR and two for PDR.

    - The values are called (NDR or PDR) lower_bound and upper_bound.
    - Each value comes from a specific trial measurement
      (most recent for that transmit rate),
      and as such the value is associated with that measurement's duration and
      loss.
    - A bound can be invalid, for example if NDR lower_bound
      has been measured with nonzero loss.
    - Invalid bounds are not real boundaries for the searched value,
      but are needed to track interval widths.
    - Valid bounds are real boundaries for the searched value.
    - Each non-initial phase ends with all bounds valid.

  - Start with a large (lower_bound, upper_bound) interval width and
    geometrically converge towards the width goal (measurement resolution)
    of the phase. Each phase halves the previous width goal.
  - Use internal and external searches:

    - External search - measures at transmit rates outside the (lower_bound,
      upper_bound) interval. Activated when a bound is invalid,
      to search for a new valid bound by doubling the interval width.
      It is a variant of `exponential search`_.
    - Internal search - `binary search`_, measures at transmit rates within the
      (lower_bound, upper_bound) valid interval, halving the interval width.

- *Final phase* is 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 main benefits of MLRsearch vs. binary search include:

- In general MLRsearch is likely to execute more search trials overall, but
  less trials at a set final duration.
- In well behaving cases it greatly reduces (>50%) the overall duration
  compared to a single PDR (or NDR) binary search 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.

Search Implementation
~~~~~~~~~~~~~~~~~~~~~

Following is a brief description of the current MLRsearch
implementation in FD.io CSIT.

Input Parameters
````````````````

#. *maximum_transmit_rate* - maximum packet transmit rate to be used by
   external traffic generator, limited by either the actual Ethernet
   link rate or traffic generator NIC model capabilities. Sample
   defaults: 2 * 14.88 Mpps for 64B 10GE link rate,
   2 * 18.75 Mpps for 64B 40GE NIC maximum rate.
#. *minimum_transmit_rate* - minimum packet transmit rate to be used for
   measurements. MLRsearch fails if lower transmit rate needs to be
   used to meet search criteria. Default: 2 * 10 kpps (could be higher).
#. *final_trial_duration* - required trial duration for final rate
   measurements. Default: 30 sec.
#. *initial_trial_duration* - trial duration for initial MLRsearch phase.
   Default: 1 sec.
#. *final_relative_width* - required measurement resolution expressed as
   (lower_bound, upper_bound) interval width relative to upper_bound.
   Default: 0.5%.
#. *packet_loss_ratio* - maximum acceptable PLR search criteria for
   PDR measurements. Default: 0.5%.
#. *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.
   Default (2). (Value chosen based on limited experimentation to date.
   More experimentation needed to arrive to clearer guidelines.)

Initial Phase
`````````````

1. First trial measures at maximum rate and discovers MRR.

   a. *in*: trial_duration = initial_trial_duration.
   b. *in*: offered_transmit_rate = maximum_transmit_rate.
   c. *do*: single trial.
   d. *out*: measured loss ratio.
   e. *out*: mrr = measured receive rate.

2. Second trial measures at MRR and discovers MRR2.

   a. *in*: trial_duration = initial_trial_duration.
   b. *in*: offered_transmit_rate = MRR.
   c. *do*: single trial.
   d. *out*: measured loss ratio.
   e. *out*: mrr2 = measured receive rate.

3. Third trial measures at MRR2.

   a. *in*: trial_duration = initial_trial_duration.
   b. *in*: offered_transmit_rate = MRR2.
   c. *do*: single trial.
   d. *out*: measured loss ratio.

Non-initial Phases
``````````````````

1. Main loop:

   a. *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_strial_duration and final_trial_duration.
   b. *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.
   c. *in*: ndr_interval, pdr_interval from the previous main loop iteration
      or the previous phase.
      If the previous phase is the initial phase, both intervals have
      lower_bound = MRR2, uper_bound = MRR.
      Note that the initial phase is likely to create intervals with invalid
      bounds.
   d. *do*: According to the procedure described in point 2,
      either exit the phase (by jumping to 1.g.),
      or prepare new transmit rate to measure with.
   e. *do*: Perform the trial measurement at the new transmit rate
      and trial_duration, compute its loss ratio.
   f. *do*: Update the bounds of both intervals, based on the new measurement.
      The actual update rules are numerous, as NDR external search
      can affect PDR interval and vice versa, but the result
      agrees with rules of both internal and external search.
      For example, any new measurement below an invalid lower_bound
      becomes the new lower_bound, while the old measurement
      (previously acting as the invalid lower_bound)
      becomes a new and valid upper_bound.
      Go to next iteration (1.c.), taking the updated intervals as new input.
   g. *out*: current ndr_interval and pdr_interval.
      In the final phase this is also considered
      to be the result of the whole search.
      For other phases, the next phase loop is started
      with the current results as an input.

2. New transmit rate (or exit) calculation (for 1.d.):

   - If there is an invalid bound then prepare for external search:

     - *If* the most recent measurement at NDR lower_bound transmit rate
       had the loss higher than zero, then
       the new transmit rate is NDR lower_bound
       decreased by two NDR interval widths.
     - Else, *if* the most recent measurement at PDR lower_bound
       transmit rate had the loss higher than PLR, then
       the new transmit rate is PDR lower_bound
       decreased by two PDR interval widths.
     - Else, *if* the most recent measurement at NDR upper_bound
       transmit rate had no loss, then
       the new transmit rate is NDR upper_bound
       increased by two NDR interval widths.
     - Else, *if* the most recent measurement at PDR upper_bound
       transmit rate had the loss lower or equal to PLR, then
       the new transmit rate is PDR upper_bound
       increased by two PDR interval widths.
   - If interval width is higher than the current phase goal:

     - Else, *if* NDR interval does not meet the current phase width goal,
       prepare for internal search. The new transmit rate is
       (NDR lower bound + NDR upper bound) / 2.
     - Else, *if* PDR interval does not meet the current phase width goal,
       prepare for internal search. The new transmit rate is
       (PDR lower bound + PDR upper bound) / 2.
   - Else, *if* some bound has still only been measured at a lower duration,
     prepare to re-measure at the current duration (and the same transmit
     rate). The order of priorities is:

     - NDR lower_bound,
     - PDR lower_bound,
     - NDR upper_bound,
     - PDR upper_bound.
   - *Else*, do not prepare any new rate, to exit the phase.
     This ensures that at the end of each non-initial phase
     all intervals are valid, narrow enough, and measured
     at current phase trial duration.

Implementation Deviations
~~~~~~~~~~~~~~~~~~~~~~~~~

This document so far has been describing a simplified version of MLRsearch
algorithm. The full algorithm as implemented 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. *Optimistic maximum rate.*
   The increased rate is never higher than the maximum rate.
   Upper bound at that rate is always considered valid.
3. *Pessimistic minimum rate.*
   The decreased rate is never lower than the minimum rate.
   If a lower bound at that rate is invalid,
   a phase stops refining the interval further (until it gets re-measured).
4. *Conservative interval updates.*
   Measurements above current upper bound never update a valid upper bound,
   even if drop ratio is low.
   Measurements below current lower bound always update any lower bound
   if drop ratio is high.
5. *Ensure sufficient interval width.*
   Narrow intervals make external search take more time to find a valid bound.
   If the new transmit increased or decreased rate would result in width
   less than the current goal, increase/decrease more.
   This can happen if the measurement for the other interval
   makes the current interval too narrow.
   Similarly, take care the measurements in the initial phase
   create wide enough interval.
6. *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*).

.. _binary search: https://en.wikipedia.org/wiki/Binary_search
.. _exponential search: https://en.wikipedia.org/wiki/Exponential_search
.. _estimation of standard deviation: https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
.. _simplified error propagation formula: https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification