CSIT-1420: Split methodology section to more files

Change-Id: I861e578434abdf72244d684fca8cfd66e1db9c28
Signed-off-by: Tibor Frank <tifrank@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