4 Multiple Loss Rate search (MLRsearch) is a new search algorithm
5 implemented in FD.io CSIT project. MLRsearch discovers multiple packet
6 throughput rates in a single search, with each rate associated with a
7 distinct Packet Loss Ratio (PLR) criteria.
9 Two throughput measurements used in FD.io CSIT are Non-Drop Rate (NDR,
10 with zero packet loss, PLR=0) and Partial Drop Rate (PDR, with packet
11 loss rate not greater than the configured non-zero PLR). MLRsearch
12 discovers NDR and PDR in a single pass reducing required execution time
13 compared to separate binary searches for NDR and PDR. MLRsearch reduces
14 execution time even further by relying on shorter trial durations
15 of intermediate steps, with only the final measurements
16 conducted at the specified final trial duration.
17 This results in the shorter overall search
18 execution time when compared to a standard NDR/PDR binary search,
19 while guaranteeing the same or similar results.
21 If needed, MLRsearch can be easily adopted to discover more throughput rates
22 with different pre-defined PLRs.
24 .. Note:: All throughput rates are *always* bi-directional
25 aggregates of two equal (symmetric) uni-directional packet rates
26 received and reported by an external traffic generator.
31 The main properties of MLRsearch:
33 - MLRsearch is a duration aware multi-phase multi-rate search algorithm.
35 - Initial phase determines promising starting interval for the search.
36 - Intermediate phases progress towards defined final search criteria.
37 - Final phase executes measurements according to the final search
42 - Uses link rate as a starting transmit rate and discovers the Maximum
43 Receive Rate (MRR) used as an input to the first intermediate phase.
45 - *Intermediate phases*:
47 - Start with initial trial duration (in the first phase) and converge
48 geometrically towards the final trial duration (in the final phase).
49 - Track two values for NDR and two for PDR.
51 - The values are called (NDR or PDR) lower_bound and upper_bound.
52 - Each value comes from a specific trial measurement
53 (most recent for that transmit rate),
54 and as such the value is associated with that measurement's duration and loss.
55 - A bound can be invalid, for example if NDR lower_bound
56 has been measured with nonzero loss.
57 - Invalid bounds are not real boundaries for the searched value,
58 but are needed to track interval widths.
59 - Valid bounds are real boundaries for the searched value.
60 - Each non-initial phase ends with all bounds valid.
62 - Start with a large (lower_bound, upper_bound) interval width and
63 geometrically converge towards the width goal (measurement resolution)
64 of the phase. Each phase halves the previous width goal.
65 - Use internal and external searches:
67 - External search - measures at transmit rates outside the (lower_bound,
68 upper_bound) interval. Activated when a bound is invalid,
69 to search for a new valid bound by doubling the interval width.
70 It is a variant of `exponential search`_.
71 - Internal search - `binary search`_, measures at transmit rates within the
72 (lower_bound, upper_bound) valid interval, halving the interval width.
74 - *Final phase* is executed with the final test trial duration, and the final
75 width goal that determines resolution of the overall search.
76 Intermediate phases together with the final phase are called non-initial phases.
78 The main benefits of MLRsearch vs. binary search include:
80 - In general MLRsearch is likely to execute more search trials overall, but
81 less trials at a set final duration.
82 - In well behaving cases it greatly reduces (>50%) the overall duration
83 compared to a single PDR (or NDR) binary search duration,
84 while finding multiple drop rates.
85 - In all cases MLRsearch yields the same or similar results to binary search.
86 - Note: both binary search and MLRsearch are susceptible to reporting
87 non-repeatable results across multiple runs for very bad behaving
92 - Worst case MLRsearch can take longer than a binary search e.g. in case of
93 drastic changes in behaviour for trials at varying durations.
98 Following is a brief description of the current MLRsearch
99 implementation in FD.io CSIT.
104 #. *maximum_transmit_rate* - maximum packet transmit rate to be used by
105 external traffic generator, limited by either the actual Ethernet
106 link rate or traffic generator NIC model capabilities. Sample
107 defaults: 2 * 14.88 Mpps for 64B 10GE link rate,
108 2 * 18.75 Mpps for 64B 40GE NIC maximum rate.
109 #. *minimum_transmit_rate* - minimum packet transmit rate to be used for
110 measurements. MLRsearch fails if lower transmit rate needs to be
111 used to meet search criteria. Default: 2 * 10 kpps (could be higher).
112 #. *final_trial_duration* - required trial duration for final rate
113 measurements. Default: 30 sec.
114 #. *initial_trial_duration* - trial duration for initial MLRsearch phase.
116 #. *final_relative_width* - required measurement resolution expressed as
117 (lower_bound, upper_bound) interval width relative to upper_bound.
119 #. *packet_loss_ratio* - maximum acceptable PLR search criteria for
120 PDR measurements. Default: 0.5%.
121 #. *number_of_intermediate_phases* - number of phases between the initial
122 phase and the final phase. Impacts the overall MLRsearch duration.
123 Less phases are required for well behaving cases, more phases
124 may be needed to reduce the overall search duration for worse behaving cases.
125 Default (2). (Value chosen based on limited experimentation to date.
126 More experimentation needed to arrive to clearer guidelines.)
131 1. First trial measures at maximum rate and discovers MRR.
133 a. *in*: trial_duration = initial_trial_duration.
134 b. *in*: offered_transmit_rate = maximum_transmit_rate.
135 c. *do*: single trial.
136 d. *out*: measured loss ratio.
137 e. *out*: mrr = measured receive rate.
139 2. Second trial measures at MRR and discovers MRR2.
141 a. *in*: trial_duration = initial_trial_duration.
142 b. *in*: offered_transmit_rate = MRR.
143 c. *do*: single trial.
144 d. *out*: measured loss ratio.
145 e. *out*: mrr2 = measured receive rate.
147 3. Third trial measures at MRR2.
149 a. *in*: trial_duration = initial_trial_duration.
150 b. *in*: offered_transmit_rate = MRR2.
151 c. *do*: single trial.
152 d. *out*: measured loss ratio.
159 a. *in*: trial_duration for the current phase.
160 Set to initial_trial_duration for the first intermediate phase;
161 to final_trial_duration for the final phase;
162 or to the element of interpolating geometric sequence
163 for other intermediate phases.
164 For example with two intermediate phases, trial_duration
165 of the second intermediate phase is the geometric average
166 of initial_strial_duration and final_trial_duration.
167 b. *in*: relative_width_goal for the current phase.
168 Set to final_relative_width for the final phase;
169 doubled for each preceding phase.
170 For example with two intermediate phases,
171 the first intermediate phase uses quadruple of final_relative_width
172 and the second intermediate phase uses double of final_relative_width.
173 c. *in*: ndr_interval, pdr_interval from the previous main loop iteration
174 or the previous phase.
175 If the previous phase is the initial phase, both intervals have
176 lower_bound = MRR2, uper_bound = MRR.
177 Note that the initial phase is likely to create intervals with invalid bounds.
178 d. *do*: According to the procedure described in point 2,
179 either exit the phase (by jumping to 1.g.),
180 or prepare new transmit rate to measure with.
181 e. *do*: Perform the trial measurement at the new transmit rate
182 and trial_duration, compute its loss ratio.
183 f. *do*: Update the bounds of both intervals, based on the new measurement.
184 The actual update rules are numerous, as NDR external search
185 can affect PDR interval and vice versa, but the result
186 agrees with rules of both internal and external search.
187 For example, any new measurement below an invalid lower_bound
188 becomes the new lower_bound, while the old measurement
189 (previously acting as the invalid lower_bound)
190 becomes a new and valid upper_bound.
191 Go to next iteration (1.c.), taking the updated intervals as new input.
192 g. *out*: current ndr_interval and pdr_interval.
193 In the final phase this is also considered
194 to be the result of the whole search.
195 For other phases, the next phase loop is started
196 with the current results as an input.
198 2. New transmit rate (or exit) calculation (for 1.d.):
200 - If there is an invalid bound then prepare for external search:
202 - *If* the most recent measurement at NDR lower_bound transmit rate
203 had the loss higher than zero, then
204 the new transmit rate is NDR lower_bound
205 decreased by two NDR interval widths.
206 - Else, *if* the most recent measurement at PDR lower_bound
207 transmit rate had the loss higher than PLR, then
208 the new transmit rate is PDR lower_bound
209 decreased by two PDR interval widths.
210 - Else, *if* the most recent measurement at NDR upper_bound
211 transmit rate had no loss, then
212 the new transmit rate is NDR upper_bound
213 increased by two NDR interval widths.
214 - Else, *if* the most recent measurement at PDR upper_bound
215 transmit rate had the loss lower or equal to PLR, then
216 the new transmit rate is PDR upper_bound
217 increased by two PDR interval widths.
218 - If interval width is higher than the current phase goal:
220 - Else, *if* NDR interval does not meet the current phase width goal,
221 prepare for internal search. The new transmit rate is
222 (NDR lower bound + NDR upper bound) / 2.
223 - Else, *if* PDR interval does not meet the current phase width goal,
224 prepare for internal search. The new transmit rate is
225 (PDR lower bound + PDR upper bound) / 2.
226 - Else, *if* some bound has still only been measured at a lower duration,
227 prepare to re-measure at the current duration (and the same transmit rate).
228 The order of priorities is:
234 - *Else*, do not prepare any new rate, to exit the phase.
235 This ensures that at the end of each non-initial phase
236 all intervals are valid, narrow enough, and measured
237 at current phase trial duration.
239 Implementation Deviations
240 -------------------------
242 This document so far has been describing a simplified version of MLRsearch algorithm.
243 The full algorithm as implemented contains additional logic,
244 which makes some of the details (but not general ideas) above incorrect.
245 Here is a short description of the additional logic as a list of principles,
246 explaining their main differences from (or additions to) the simplified description,
247 but without detailing their mutual interaction.
249 1. *Logarithmic transmit rate.*
250 In order to better fit the relative width goal,
251 the interval doubling and halving is done differently.
252 For example, the middle of 2 and 8 is 4, not 5.
253 2. *Optimistic maximum rate.*
254 The increased rate is never higher than the maximum rate.
255 Upper bound at that rate is always considered valid.
256 3. *Pessimistic minimum rate.*
257 The decreased rate is never lower than the minimum rate.
258 If a lower bound at that rate is invalid,
259 a phase stops refining the interval further (until it gets re-measured).
260 4. *Conservative interval updates.*
261 Measurements above current upper bound never update a valid upper bound,
262 even if drop ratio is low.
263 Measurements below current lower bound always update any lower bound
264 if drop ratio is high.
265 5. *Ensure sufficient interval width.*
266 Narrow intervals make external search take more time to find a valid bound.
267 If the new transmit increased or decreased rate would result in width
268 less than the current goal, increase/decrease more.
269 This can happen if the measurement for the other interval
270 makes the current interval too narrow.
271 Similarly, take care the measurements in the initial phase
272 create wide enough interval.
273 6. *Timeout for bad cases.*
274 The worst case for MLRsearch is when each phase converges to intervals
275 way different than the results of the previous phase.
276 Rather than suffer total search time several times larger
277 than pure binary search, the implemented tests fail themselves
278 when the search takes too long (given by argument *timeout*).
280 .. _binary search: https://en.wikipedia.org/wiki/Binary_search
281 .. _exponential search: https://en.wikipedia.org/wiki/Exponential_search
282 .. _estimation of standard deviation: https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
283 .. _simplified error propagation formula: https://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplification