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+---
+title: Multiple Loss Ratio Search for Packet Throughput (MLRsearch)
+# abbrev: MLRsearch
+docname: draft-vpolak-mkonstan-bmwg-mlrsearch-01
+date: 2019-03-27
+
+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
+#  - sortrefs
+#  - symrefs
+  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
+        role: editor
+        email: vrpolak@cisco.com
+
+normative:
+  RFC2544:
+  RFC8174:
+
+informative:
+
+
+--- abstract
+
+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 and
+define a common (standard?) way to evaluate NFV packet throughput
+performance that takes into account varying characteristics of NFV
+systems under test.
+
+--- middle
+
+# Terminology
+
+* NDR - Non-Drop Rate, a packet throughput metric with Packet Loss Ratio
+  equal zero (a zero packet loss), expressed in packets-per-second
+  (pps). NDR packet throughput has an associated metric oftentimes
+  referred to as NDR bandwidth expressed in bits-per-second (bps), and
+  calculated as a product of:
+  * NDR packet rate for specific packet (frame) size, and
+  * Packet (L2 frame size) size in bits plus any associated L1 overhead.
+* PLR - Packet Loss Ratio, a packet loss metric calculated as a ratio of
+  (packets_transmitted - packets_received) to packets_transmitted, over
+  the test trial duration.
+* PDR - Partial-Drop Rate, a packet throughput metric with Packet Loss
+  Ratio greater than zero (a non-zero packet loss), expressed in
+  packets-per-second (pps). PDR packet throughput has an associated
+  metric oftentimes referred to as PDR bandwidth expressed in bits-per-
+  second (bps), and calculated as a product of:
+  * PDR packet rate for specific packet (frame) size, and
+  * Packet (L2 frame size) size in bits plus any associated L1 overhead.
+
+# MLRsearch Background
+
+Multiple Loss Rate search (MLRsearch) is a packet throughput search
+algorithm suitable for deterministic (as opposed to probabilistic)
+systems. MLRsearch discovers multiple packet throughput rates in a
+single search, each rate associated with a distinct Packet Loss Ratio
+(PLR) criteria.
+
+Two popular names for particular PLR criteria are Non-Drop Rate (NDR,
+with PLR=0, zero packet loss) and Partial Drop Rate (PDR, with PLR>0,
+non-zero packet loss). MLRsearch discovers NDR and PDR in a single
+search 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.
+(TODO: Specify "standard" in the previous sentence.)
+
+If needed, MLRsearch can be easily adopted to discover more throughput
+rates with different pre-defined PLRs.
+
+Unless otherwise noted, all throughput rates are *always* bi-directional
+aggregates of two equal (symmetric) uni-directional packet rates
+received and reported by an external traffic generator.
+
+# 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.
+* 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
+  * 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.
+
+# Sample Implementation
+
+Following is a brief description of a sample MLRsearch implementation
+based on the open-source code running in FD.io CSIT project as part of a
+Continuous Integration / Continuous Development (CI/CD) framework.
+
+## Input Parameters
+
+1. **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.
+2. **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).
+3. **final_trial_duration** - required trial duration for final rate
+   measurements. Default: 30 sec.
+4. **initial_trial_duration** - trial duration for initial MLRsearch phase.
+   Default: 1 sec.
+5. **final_relative_width** - required measurement resolution expressed as
+   (lower_bound, upper_bound) interval width relative to upper_bound.
+   Default: 0.5%.
+6. **packet_loss_ratio** - maximum acceptable PLR search criteria for
+   PDR measurements. Default: 0.5%.
+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.
+   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.
+   * *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.
+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.
+3. Third trial measures at MRR2.
+   * *in*: trial_duration = initial_trial_duration.
+   * *in*: offered_transmit_rate = MRR2.
+   * *do*: single trial.
+   * *out*: measured loss ratio.
+
+## Non-initial phases
+
+1. Main loop:
+   * *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.
+   * *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.
+   * *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.
+   * *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.
+   * *do*: Perform the trial measurement at the new transmit rate
+     and trial_duration, compute its loss ratio.
+   * *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.
+   * *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.
+
+# Known Implementations
+
+The only known working implementation of MLRsearch is in Linux Foundation
+FD.io CSIT project. https://wiki.fd.io/view/CSIT. https://git.fd.io/csit/.
+
+## FD.io CSIT 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*).
+
+# IANA Considerations
+
+..
+
+# Security Considerations
+
+..
+
+# Acknowledgements
+
+..
+
+--- back