report: further edits of methodology throughput sections

Change-Id: I571d1a47743eb31ee10caf3f3336ac7437daf878
Signed-off-by: Maciek Konstantynowicz <mkonstan@cisco.com>

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-.. _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