1 # Copyright (c) 2018 Cisco and/or its affiliates.
2 # Licensed under the Apache License, Version 2.0 (the "License");
3 # you may not use this file except in compliance with the License.
4 # You may obtain a copy of the License at:
6 # http://www.apache.org/licenses/LICENSE-2.0
8 # Unless required by applicable law or agreed to in writing, software
9 # distributed under the License is distributed on an "AS IS" BASIS,
10 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
11 # See the License for the specific language governing permissions and
12 # limitations under the License.
14 """Module defining MultipleLossRatioSearch class."""
20 from AbstractSearchAlgorithm import AbstractSearchAlgorithm
21 from NdrPdrResult import NdrPdrResult
22 from ReceiveRateInterval import ReceiveRateInterval
25 class MultipleLossRatioSearch(AbstractSearchAlgorithm):
26 """Optimized binary search algorithm for finding NDR and PDR bounds.
28 Traditional binary search algorithm needs initial interval
29 (lower and upper bound), and returns final interval after bisecting
30 (until some exit condition is met).
31 The exit condition is usually related to the interval width,
32 (upper bound value minus lower bound value).
34 The optimized algorithm contains several improvements
35 aimed to reduce overall search time.
37 One improvement is searching for two intervals at once.
38 The intervals are for NDR (No Drop Rate) and PDR (Partial Drop Rate).
40 Next improvement is that the initial interval does not need to be valid.
41 Imagine initial interval (10, 11) where 11 is smaller
42 than the searched value.
43 The algorithm will try (11, 13) interval next, and if 13 is still smaller,
44 (13, 17) and so on, doubling width until the upper bound is valid.
45 The part when interval expands is called external search,
46 the part when interval is bisected is called internal search.
48 Next improvement is that trial measurements at small trial duration
49 can be used to find a reasonable interval for full trial duration search.
50 This results in more trials performed, but smaller overall duration
53 Next improvement is bisecting in logarithmic quantities,
54 so that exit criteria can be independent of measurement units.
56 Next improvement is basing the initial interval on receive rates.
58 Final improvement is exiting early if the minimal value
59 is not a valid lower bound.
61 The complete search consist of several phases,
62 each phase performing several trial measurements.
63 Initial phase creates initial interval based on receive rates
64 at maximum rate and at maximum receive rate (MRR).
65 Final phase and preceding intermediate phases are performing
66 external and internal search steps,
67 each resulting interval is the starting point for the next phase.
68 The resulting interval of final phase is the result of the whole algorithm.
70 Each non-initial phase uses its own trial duration and width goal.
71 Any non-initial phase stops searching (for NDR or PDR independently)
72 when minimum is not a valid lower bound (at current duration),
73 or all of the following is true:
74 Both bounds are valid, bound bounds are measured at the current phase
75 trial duration, interval width is less than the width goal
78 TODO: Review and update this docstring according to rst docs.
79 TODO: Support configurable number of Packet Loss Ratios.
82 class ProgressState(object):
83 """Structure containing data to be passed around in recursion."""
86 self, result, phases, duration, width_goal, packet_loss_ratio,
87 minimum_transmit_rate, maximum_transmit_rate):
88 """Convert and store the argument values.
90 :param result: Current measured NDR and PDR intervals.
91 :param phases: How many intermediate phases to perform
92 before the current one.
93 :param duration: Trial duration to use in the current phase [s].
94 :param width_goal: The goal relative width for the curreent phase.
95 :param packet_loss_ratio: PDR fraction for the current search.
96 :param minimum_transmit_rate: Minimum target transmit rate
97 for the current search [pps].
98 :param maximum_transmit_rate: Maximum target transmit rate
99 for the current search [pps].
100 :type result: NdrPdrResult
102 :type duration: float
103 :type width_goal: float
104 :type packet_loss_ratio: float
105 :type minimum_transmit_rate: float
106 :type maximum_transmit_rate: float
109 self.phases = int(phases)
110 self.duration = float(duration)
111 self.width_goal = float(width_goal)
112 self.packet_loss_ratio = float(packet_loss_ratio)
113 self.minimum_transmit_rate = float(minimum_transmit_rate)
114 self.maximum_transmit_rate = float(maximum_transmit_rate)
116 def __init__(self, measurer, final_relative_width=0.005,
117 final_trial_duration=30.0, initial_trial_duration=1.0,
118 number_of_intermediate_phases=2, timeout=600.0):
119 """Store the measurer object and additional arguments.
121 :param measurer: Rate provider to use by this search object.
122 :param final_relative_width: Final lower bound transmit rate
123 cannot be more distant that this multiple of upper bound [1].
124 :param final_trial_duration: Trial duration for the final phase [s].
125 :param initial_trial_duration: Trial duration for the initial phase
126 and also for the first intermediate phase [s].
127 :param number_of_intermediate_phases: Number of intermediate phases
128 to perform before the final phase [1].
129 :param timeout: The search will fail itself when not finished
130 before this overall time [s].
131 :type measurer: AbstractMeasurer
132 :type final_relative_width: float
133 :type final_trial_duration: float
134 :type initial_trial_duration: int
135 :type number_of_intermediate_phases: int
138 super(MultipleLossRatioSearch, self).__init__(measurer)
139 self.final_trial_duration = float(final_trial_duration)
140 self.final_relative_width = float(final_relative_width)
141 self.number_of_intermediate_phases = int(number_of_intermediate_phases)
142 self.initial_trial_duration = float(initial_trial_duration)
143 self.timeout = float(timeout)
147 def double_relative_width(relative_width):
148 """Return relative width corresponding to double logarithmic width.
150 :param relative_width: The base relative width to double.
151 :type relative_width: float
152 :returns: The relative width of double logarithmic size.
155 return 1.999 * relative_width - relative_width * relative_width
156 # The number should be 2.0, but we want to avoid rounding errors,
157 # and ensure half of double is not larger than the original value.
160 def double_step_down(relative_width, current_bound):
161 """Return rate of double logarithmic width below.
163 :param relative_width: The base relative width to double.
164 :param current_bound: The current target transmit rate to move [pps].
165 :type relative_width: float
166 :type current_bound: float
167 :returns: Transmit rate smaller by logarithmically double width [pps].
170 return current_bound * (
171 1.0 - MultipleLossRatioSearch.double_relative_width(
175 def double_step_up(relative_width, current_bound):
176 """Return rate of double logarithmic width above.
178 :param relative_width: The base relative width to double.
179 :param current_bound: The current target transmit rate to move [pps].
180 :type relative_width: float
181 :type current_bound: float
182 :returns: Transmit rate larger by logarithmically double width [pps].
185 return current_bound / (
186 1.0 - MultipleLossRatioSearch.double_relative_width(
190 def half_relative_width(relative_width):
191 """Return relative width corresponding to half logarithmic width.
193 :param relative_width: The base relative width to halve.
194 :type relative_width: float
195 :returns: The relative width of half logarithmic size.
198 return 1.0 - math.sqrt(1.0 - relative_width)
201 def half_step_up(relative_width, current_bound):
202 """Return rate of half logarithmic width above.
204 :param relative_width: The base relative width to halve.
205 :param current_bound: The current target transmit rate to move [pps].
206 :type relative_width: float
207 :type current_bound: float
208 :returns: Transmit rate larger by logarithmically half width [pps].
211 return current_bound / (
212 1.0 - MultipleLossRatioSearch.half_relative_width(relative_width))
214 def narrow_down_ndr_and_pdr(
215 self, minimum_transmit_rate, maximum_transmit_rate,
217 """Perform initial phase, create state object, proceed with next phases.
219 :param minimum_transmit_rate: Minimal target transmit rate [pps].
220 :param maximum_transmit_rate: Maximal target transmit rate [pps].
221 :param packet_loss_ratio: Fraction of packets lost, for PDR [1].
222 :type minimum_transmit_rate: float
223 :type maximum_transmit_rate: float
224 :type packet_loss_ratio: float
225 :returns: Structure containing narrowed down intervals
226 and their measurements.
228 :raises RuntimeError: If total duration is larger than timeout.
230 minimum_transmit_rate = float(minimum_transmit_rate)
231 maximum_transmit_rate = float(maximum_transmit_rate)
232 packet_loss_ratio = float(packet_loss_ratio)
233 line_measurement = self.measurer.measure(
234 self.initial_trial_duration, maximum_transmit_rate)
235 initial_width_goal = self.final_relative_width
236 for _ in range(self.number_of_intermediate_phases):
237 initial_width_goal = self.double_relative_width(initial_width_goal)
238 max_lo = maximum_transmit_rate * (1.0 - initial_width_goal)
240 minimum_transmit_rate,
241 min(max_lo, line_measurement.receive_rate))
242 mrr_measurement = self.measurer.measure(
243 self.initial_trial_duration, mrr)
244 # Attempt to get narrower width.
245 if mrr_measurement.loss_fraction > 0.0:
246 max2_lo = mrr * (1.0 - initial_width_goal)
247 mrr2 = min(max2_lo, mrr_measurement.receive_rate)
249 mrr2 = mrr / (1.0 - initial_width_goal)
250 if mrr2 > minimum_transmit_rate and mrr2 < maximum_transmit_rate:
251 line_measurement = mrr_measurement
252 mrr_measurement = self.measurer.measure(
253 self.initial_trial_duration, mrr2)
255 buf = line_measurement
256 line_measurement = mrr_measurement
257 mrr_measurement = buf
258 starting_interval = ReceiveRateInterval(
259 mrr_measurement, line_measurement)
260 starting_result = NdrPdrResult(starting_interval, starting_interval)
261 state = self.ProgressState(
262 starting_result, self.number_of_intermediate_phases,
263 self.final_trial_duration, self.final_relative_width,
264 packet_loss_ratio, minimum_transmit_rate, maximum_transmit_rate)
265 state = self.ndrpdr(state)
268 def _measure_and_update_state(self, state, transmit_rate):
269 """Perform trial measurement, update bounds, return new state.
271 :param state: State before this measurement.
272 :param transmit_rate: Target transmit rate for this measurement [pps].
273 :type state: ProgressState
274 :type transmit_rate: float
275 :returns: State after the measurement.
276 :rtype: ProgressState
278 # TODO: Implement https://stackoverflow.com/a/24683360
279 # to avoid the string manipulation if log verbosity is too low.
280 logging.info("result before update: %s", state.result)
282 "relative widths in goals: %s", state.result.width_in_goals(
283 self.final_relative_width))
284 measurement = self.measurer.measure(state.duration, transmit_rate)
285 ndr_interval = self._new_interval(
286 state.result.ndr_interval, measurement, 0.0)
287 pdr_interval = self._new_interval(
288 state.result.pdr_interval, measurement, state.packet_loss_ratio)
289 state.result = NdrPdrResult(ndr_interval, pdr_interval)
293 def _new_interval(old_interval, measurement, packet_loss_ratio):
294 """Return new interval with bounds updated according to the measurement.
296 :param old_interval: The current interval before the measurement.
297 :param measurement: The new meaqsurement to take into account.
298 :param packet_loss_ratio: Fraction for PDR (or zero for NDR).
299 :type old_interval: ReceiveRateInterval
300 :type measurement: ReceiveRateMeasurement
301 :type packet_loss_ratio: float
302 :returns: The updated interval.
303 :rtype: ReceiveRateInterval
305 old_lo, old_hi = old_interval.measured_low, old_interval.measured_high
306 # Priority zero: direct replace if the target Tr is the same.
307 if measurement.target_tr in (old_lo.target_tr, old_hi.target_tr):
308 if measurement.target_tr == old_lo.target_tr:
309 return ReceiveRateInterval(measurement, old_hi)
311 return ReceiveRateInterval(old_lo, measurement)
312 # Priority one: invalid lower bound allows only one type of update.
313 if old_lo.loss_fraction > packet_loss_ratio:
314 # We can only expand down, old bound becomes valid upper one.
315 if measurement.target_tr < old_lo.target_tr:
316 return ReceiveRateInterval(measurement, old_lo)
319 # Lower bound is now valid.
320 # Next priorities depend on target Tr.
321 if measurement.target_tr < old_lo.target_tr:
322 # Lower external measurement, relevant only
323 # if the new measurement has high loss rate.
324 if measurement.loss_fraction > packet_loss_ratio:
325 # Returning the broader interval as old_lo
326 # would be invalid upper bound.
327 return ReceiveRateInterval(measurement, old_hi)
328 elif measurement.target_tr > old_hi.target_tr:
329 # Upper external measurement, only relevant for invalid upper bound.
330 if old_hi.loss_fraction <= packet_loss_ratio:
331 # Old upper bound becomes valid new lower bound.
332 return ReceiveRateInterval(old_hi, measurement)
334 # Internal measurement, replaced boundary
335 # depends on measured loss fraction.
336 if measurement.loss_fraction > packet_loss_ratio:
337 # We have found a narrow valid interval,
338 # regardless of whether old upper bound was valid.
339 return ReceiveRateInterval(old_lo, measurement)
341 # In ideal world, we would not want to shrink interval
342 # if upper bound is not valid.
343 # In the real world, we want to shrink it for
344 # "invalid upper bound at maximal rate" case.
345 return ReceiveRateInterval(measurement, old_hi)
346 # Fallback, the interval is unchanged by the measurement.
349 def ndrpdr(self, state):
350 """Pefrom trials for this phase. Return the new state when done.
352 :param state: State before this phase.
353 :type state: ProgressState
354 :returns: The updated state.
355 :rtype: ProgressState
356 :raises RuntimeError: If total duration is larger than timeout.
358 start_time = time.time()
360 # We need to finish preceding intermediate phases first.
361 saved_phases = state.phases
363 # Preceding phases have shorter duration.
364 saved_duration = state.duration
365 duration_multiplier = state.duration / self.initial_trial_duration
366 phase_exponent = float(state.phases) / saved_phases
367 state.duration = self.initial_trial_duration * math.pow(
368 duration_multiplier, phase_exponent)
369 # Shorter durations do not need that narrow widths.
370 saved_width = state.width_goal
371 state.width_goal = self.double_relative_width(state.width_goal)
373 state = self.ndrpdr(state)
374 # Restore the state for current phase.
375 state.duration = saved_duration
376 state.width_goal = saved_width
377 state.phases = saved_phases # Not needed, but just in case.
379 "starting iterations with duration %s and relative width goal %s",
380 state.duration, state.width_goal)
382 if time.time() > start_time + self.timeout:
383 raise RuntimeError("Optimized search takes too long.")
384 # Order of priorities: invalid bounds (nl, pl, nh, ph),
385 # then narrowing relative Tr widths.
386 # Durations are not priorities yet,
387 # they will settle on their own hopefully.
388 ndr_lo = state.result.ndr_interval.measured_low
389 ndr_hi = state.result.ndr_interval.measured_high
390 pdr_lo = state.result.pdr_interval.measured_low
391 pdr_hi = state.result.pdr_interval.measured_high
393 state.width_goal, state.result.ndr_interval.rel_tr_width)
395 state.width_goal, state.result.pdr_interval.rel_tr_width)
396 # If we are hitting maximal or minimal rate, we cannot shift,
397 # but we can re-measure.
398 if ndr_lo.loss_fraction > 0.0:
399 if ndr_lo.target_tr > state.minimum_transmit_rate:
401 state.minimum_transmit_rate,
402 self.double_step_down(ndr_rel_width, ndr_lo.target_tr))
403 logging.info("ndr lo external %s", new_tr)
404 state = self._measure_and_update_state(state, new_tr)
406 elif ndr_lo.duration < state.duration:
407 logging.info("ndr lo minimal re-measure")
408 state = self._measure_and_update_state(
409 state, state.minimum_transmit_rate)
411 if pdr_lo.loss_fraction > state.packet_loss_ratio:
412 if pdr_lo.target_tr > state.minimum_transmit_rate:
414 state.minimum_transmit_rate,
415 self.double_step_down(pdr_rel_width, pdr_lo.target_tr))
416 logging.info("pdr lo external %s", new_tr)
417 state = self._measure_and_update_state(state, new_tr)
419 elif pdr_lo.duration < state.duration:
420 logging.info("pdr lo minimal re-measure")
421 state = self._measure_and_update_state(
422 state, state.minimum_transmit_rate)
424 if ndr_hi.loss_fraction <= 0.0:
425 if ndr_hi.target_tr < state.maximum_transmit_rate:
427 state.maximum_transmit_rate,
428 self.double_step_up(ndr_rel_width, ndr_hi.target_tr))
429 logging.info("ndr hi external %s", new_tr)
430 state = self._measure_and_update_state(state, new_tr)
432 elif ndr_hi.duration < state.duration:
433 logging.info("ndr hi maximal re-measure")
434 state = self._measure_and_update_state(
435 state, state.maximum_transmit_rate)
437 if pdr_hi.loss_fraction <= state.packet_loss_ratio:
438 if pdr_hi.target_tr < state.maximum_transmit_rate:
440 state.maximum_transmit_rate,
441 self.double_step_up(pdr_rel_width, pdr_hi.target_tr))
442 logging.info("pdr hi external %s", new_tr)
443 state = self._measure_and_update_state(state, new_tr)
445 elif pdr_hi.duration < state.duration:
446 logging.info("ndr hi maximal re-measure")
447 state = self._measure_and_update_state(
448 state, state.maximum_transmit_rate)
450 # If we are hitting maximum_transmit_rate,
451 # it is still worth narrowing width,
452 # hoping large enough loss fraction will happen.
453 # But if we are hitting the minimal rate (at current duration),
454 # no additional measurement will help with that,
455 # so we can stop narrowing in this phase.
456 if (ndr_lo.target_tr <= state.minimum_transmit_rate
457 and ndr_lo.loss_fraction > 0.0):
459 if (pdr_lo.target_tr <= state.minimum_transmit_rate
460 and pdr_lo.loss_fraction > state.packet_loss_ratio):
462 if ndr_rel_width > state.width_goal:
463 # We have to narrow NDR width first, as NDR internal search
464 # can invalidate PDR (but not vice versa).
465 new_tr = self.half_step_up(ndr_rel_width, ndr_lo.target_tr)
466 logging.info("Bisecting for NDR at %s", new_tr)
467 state = self._measure_and_update_state(state, new_tr)
469 if pdr_rel_width > state.width_goal:
470 # PDR iternal search.
471 new_tr = self.half_step_up(pdr_rel_width, pdr_lo.target_tr)
472 logging.info("Bisecting for PDR at %s", new_tr)
473 state = self._measure_and_update_state(state, new_tr)
475 # We do not need to improve width, but there still might be
476 # some measurements with smaller duration.
477 # We need to re-measure with full duration, possibly
478 # creating invalid bounds to resolve (thus broadening width).
479 if ndr_lo.duration < state.duration:
480 logging.info("re-measuring NDR lower bound")
481 self._measure_and_update_state(state, ndr_lo.target_tr)
483 if pdr_lo.duration < state.duration:
484 logging.info("re-measuring PDR lower bound")
485 self._measure_and_update_state(state, pdr_lo.target_tr)
487 # Except when lower bounds have high loss fraction, in that case
488 # we do not need to re-measure _upper_ bounds.
489 if ndr_hi.duration < state.duration and ndr_rel_width > 0.0:
490 logging.info("re-measuring NDR upper bound")
491 self._measure_and_update_state(state, ndr_hi.target_tr)
493 if pdr_hi.duration < state.duration and pdr_rel_width > 0.0:
494 logging.info("re-measuring PDR upper bound")
495 self._measure_and_update_state(state, pdr_hi.target_tr)
497 # Widths are narrow (or lower bound minimal), bound measurements
498 # are long enough, we can return.
499 logging.info("phase done")