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diff --git a/docs/report/introduction/methodology.rst b/docs/report/introduction/methodology.rst index 483cbb7295..ff5714c259 100644 --- a/docs/report/introduction/methodology.rst +++ b/docs/report/introduction/methodology.rst @@ -35,8 +35,286 @@ Ethernet): All rates are reported from external Traffic Generator perspective. -Description of MLRsearch algorithm is provided in -:ref:`mlrsearch_algorithm`. +.. _mlrsearch_algorithm: + +MLRsearch Algorithm +------------------- + +Multiple Loss Rate search (MLRsearch) is a 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. + +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*). Maximum Receive Rate MRR ------------------------ @@ -391,3 +669,8 @@ The initial tests are designed as follows: - Connection close after set test duration time. - Resulting flow sequence: >Syn, <Syn-Ack, >Ack, >Req[1], <Rep[1], .., >Req[n], <Rep[n], >Fin, <Fin, >Ack. + +.. _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 |