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.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, doublings=1):
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 :param doublings: How many doublings to do in external search step.
132 Default 1 is suitable for fairly stable tests,
133 less stable tests might get better overal duration with 2 or more.
134 :type measurer: AbstractMeasurer.AbstractMeasurer
135 :type final_relative_width: float
136 :type final_trial_duration: float
137 :type initial_trial_duration: int
138 :type number_of_intermediate_phases: int
142 super(MultipleLossRatioSearch, self).__init__(measurer)
143 self.final_trial_duration = float(final_trial_duration)
144 self.final_relative_width = float(final_relative_width)
145 self.number_of_intermediate_phases = int(number_of_intermediate_phases)
146 self.initial_trial_duration = float(initial_trial_duration)
147 self.timeout = float(timeout)
148 self.doublings = int(doublings)
152 def double_relative_width(relative_width):
153 """Return relative width corresponding to double logarithmic width.
155 :param relative_width: The base relative width to double.
156 :type relative_width: float
157 :returns: The relative width of double logarithmic size.
160 return 1.999 * relative_width - relative_width * relative_width
161 # The number should be 2.0, but we want to avoid rounding errors,
162 # and ensure half of double is not larger than the original value.
165 def double_step_down(relative_width, current_bound):
166 """Return rate of double logarithmic width below.
168 :param relative_width: The base relative width to double.
169 :param current_bound: The current target transmit rate to move [pps].
170 :type relative_width: float
171 :type current_bound: float
172 :returns: Transmit rate smaller by logarithmically double width [pps].
175 return current_bound * (
176 1.0 - MultipleLossRatioSearch.double_relative_width(
180 def expand_down(relative_width, doublings, current_bound):
181 """Return rate of expanded logarithmic width below.
183 :param relative_width: The base relative width to double.
184 :param doublings: How many doublings to do for expansion.
185 :param current_bound: The current target transmit rate to move [pps].
186 :type relative_width: float
188 :type current_bound: float
189 :returns: Transmit rate smaller by logarithmically double width [pps].
192 for _ in range(doublings):
193 relative_width = MultipleLossRatioSearch.double_relative_width(
195 return current_bound * (1.0 - relative_width)
198 def double_step_up(relative_width, current_bound):
199 """Return rate of double logarithmic width above.
201 :param relative_width: The base relative width to double.
202 :param current_bound: The current target transmit rate to move [pps].
203 :type relative_width: float
204 :type current_bound: float
205 :returns: Transmit rate larger by logarithmically double width [pps].
208 return current_bound / (
209 1.0 - MultipleLossRatioSearch.double_relative_width(
213 def expand_up(relative_width, doublings, current_bound):
214 """Return rate of expanded logarithmic width above.
216 :param relative_width: The base relative width to double.
217 :param doublings: How many doublings to do for expansion.
218 :param current_bound: The current target transmit rate to move [pps].
219 :type relative_width: float
221 :type current_bound: float
222 :returns: Transmit rate smaller by logarithmically double width [pps].
225 for _ in range(doublings):
226 relative_width = MultipleLossRatioSearch.double_relative_width(
228 return current_bound / (1.0 - relative_width)
231 def half_relative_width(relative_width):
232 """Return relative width corresponding to half logarithmic width.
234 :param relative_width: The base relative width to halve.
235 :type relative_width: float
236 :returns: The relative width of half logarithmic size.
239 return 1.0 - math.sqrt(1.0 - relative_width)
242 def half_step_up(relative_width, current_bound):
243 """Return rate of half logarithmic width above.
245 :param relative_width: The base relative width to halve.
246 :param current_bound: The current target transmit rate to move [pps].
247 :type relative_width: float
248 :type current_bound: float
249 :returns: Transmit rate larger by logarithmically half width [pps].
252 return current_bound / (
253 1.0 - MultipleLossRatioSearch.half_relative_width(relative_width))
255 def narrow_down_ndr_and_pdr(
256 self, minimum_transmit_rate, maximum_transmit_rate,
258 """Perform initial phase, create state object, proceed with next phases.
260 :param minimum_transmit_rate: Minimal target transmit rate [pps].
261 :param maximum_transmit_rate: Maximal target transmit rate [pps].
262 :param packet_loss_ratio: Fraction of packets lost, for PDR [1].
263 :type minimum_transmit_rate: float
264 :type maximum_transmit_rate: float
265 :type packet_loss_ratio: float
266 :returns: Structure containing narrowed down intervals
267 and their measurements.
268 :rtype: NdrPdrResult.NdrPdrResult
269 :raises RuntimeError: If total duration is larger than timeout.
271 minimum_transmit_rate = float(minimum_transmit_rate)
272 maximum_transmit_rate = float(maximum_transmit_rate)
273 packet_loss_ratio = float(packet_loss_ratio)
274 line_measurement = self.measurer.measure(
275 self.initial_trial_duration, maximum_transmit_rate)
276 initial_width_goal = self.final_relative_width
277 for _ in range(self.number_of_intermediate_phases):
278 initial_width_goal = self.double_relative_width(initial_width_goal)
279 max_lo = maximum_transmit_rate * (1.0 - initial_width_goal)
281 minimum_transmit_rate,
282 min(max_lo, line_measurement.receive_rate))
283 mrr_measurement = self.measurer.measure(
284 self.initial_trial_duration, mrr)
285 # Attempt to get narrower width.
286 if mrr_measurement.loss_fraction > 0.0:
287 max2_lo = mrr * (1.0 - initial_width_goal)
288 mrr2 = min(max2_lo, mrr_measurement.receive_rate)
290 mrr2 = mrr / (1.0 - initial_width_goal)
291 if mrr2 > minimum_transmit_rate and mrr2 < maximum_transmit_rate:
292 line_measurement = mrr_measurement
293 mrr_measurement = self.measurer.measure(
294 self.initial_trial_duration, mrr2)
296 buf = line_measurement
297 line_measurement = mrr_measurement
298 mrr_measurement = buf
299 starting_interval = ReceiveRateInterval(
300 mrr_measurement, line_measurement)
301 starting_result = NdrPdrResult(starting_interval, starting_interval)
302 state = self.ProgressState(
303 starting_result, self.number_of_intermediate_phases,
304 self.final_trial_duration, self.final_relative_width,
305 packet_loss_ratio, minimum_transmit_rate, maximum_transmit_rate)
306 state = self.ndrpdr(state)
309 def _measure_and_update_state(self, state, transmit_rate):
310 """Perform trial measurement, update bounds, return new state.
312 :param state: State before this measurement.
313 :param transmit_rate: Target transmit rate for this measurement [pps].
314 :type state: ProgressState
315 :type transmit_rate: float
316 :returns: State after the measurement.
317 :rtype: ProgressState
319 # TODO: Implement https://stackoverflow.com/a/24683360
320 # to avoid the string manipulation if log verbosity is too low.
321 logging.info("result before update: %s", state.result)
323 "relative widths in goals: %s", state.result.width_in_goals(
324 self.final_relative_width))
325 measurement = self.measurer.measure(state.duration, transmit_rate)
326 ndr_interval = self._new_interval(
327 state.result.ndr_interval, measurement, 0.0)
328 pdr_interval = self._new_interval(
329 state.result.pdr_interval, measurement, state.packet_loss_ratio)
330 state.result = NdrPdrResult(ndr_interval, pdr_interval)
334 def _new_interval(old_interval, measurement, packet_loss_ratio):
335 """Return new interval with bounds updated according to the measurement.
337 :param old_interval: The current interval before the measurement.
338 :param measurement: The new meaqsurement to take into account.
339 :param packet_loss_ratio: Fraction for PDR (or zero for NDR).
340 :type old_interval: ReceiveRateInterval.ReceiveRateInterval
341 :type measurement: ReceiveRateMeasurement.ReceiveRateMeasurement
342 :type packet_loss_ratio: float
343 :returns: The updated interval.
344 :rtype: ReceiveRateInterval.ReceiveRateInterval
346 old_lo, old_hi = old_interval.measured_low, old_interval.measured_high
347 new_lo = new_hi = None
348 # Priority zero: direct replace if the target Tr is the same.
349 if measurement.target_tr in (old_lo.target_tr, old_hi.target_tr):
350 if measurement.target_tr == old_lo.target_tr:
354 # Priority one: invalid lower bound allows only one type of update.
355 elif old_lo.loss_fraction > packet_loss_ratio:
356 # We can only expand down, old bound becomes valid upper one.
357 if measurement.target_tr < old_lo.target_tr:
358 new_lo, new_hi = measurement, old_lo
362 # Lower bound is now valid.
363 # Next priorities depend on target Tr.
364 elif measurement.target_tr < old_lo.target_tr:
365 # Lower external measurement, relevant only
366 # if the new measurement has high loss rate.
367 if measurement.loss_fraction > packet_loss_ratio:
368 # Returning the broader interval as old_lo
369 # would be invalid upper bound.
371 elif measurement.target_tr > old_hi.target_tr:
372 # Upper external measurement, only relevant for invalid upper bound.
373 if old_hi.loss_fraction <= packet_loss_ratio:
374 # Old upper bound becomes valid new lower bound.
375 new_lo, new_hi = old_hi, measurement
377 # Internal measurement, replaced boundary
378 # depends on measured loss fraction.
379 if measurement.loss_fraction > packet_loss_ratio:
380 # We have found a narrow valid interval,
381 # regardless of whether old upper bound was valid.
384 # In ideal world, we would not want to shrink interval
385 # if upper bound is not valid.
386 # In the real world, we want to shrink it for
387 # "invalid upper bound at maximal rate" case.
390 return ReceiveRateInterval(old_lo if new_lo is None else new_lo,
391 old_hi if new_hi is None else new_hi)
393 def ndrpdr(self, state):
394 """Pefrom trials for this phase. Return the new state when done.
396 :param state: State before this phase.
397 :type state: ProgressState
398 :returns: The updated state.
399 :rtype: ProgressState
400 :raises RuntimeError: If total duration is larger than timeout.
402 start_time = time.time()
404 # We need to finish preceding intermediate phases first.
405 saved_phases = state.phases
407 # Preceding phases have shorter duration.
408 saved_duration = state.duration
409 duration_multiplier = state.duration / self.initial_trial_duration
410 phase_exponent = float(state.phases) / saved_phases
411 state.duration = self.initial_trial_duration * math.pow(
412 duration_multiplier, phase_exponent)
413 # Shorter durations do not need that narrow widths.
414 saved_width = state.width_goal
415 state.width_goal = self.double_relative_width(state.width_goal)
417 state = self.ndrpdr(state)
418 # Restore the state for current phase.
419 state.duration = saved_duration
420 state.width_goal = saved_width
421 state.phases = saved_phases # Not needed, but just in case.
424 "starting iterations with duration %s and relative width goal %s",
425 state.duration, state.width_goal)
427 if time.time() > start_time + self.timeout:
428 raise RuntimeError("Optimized search takes too long.")
429 # Order of priorities: invalid bounds (nl, pl, nh, ph),
430 # then narrowing relative Tr widths.
431 # Durations are not priorities yet,
432 # they will settle on their own hopefully.
433 ndr_lo = state.result.ndr_interval.measured_low
434 ndr_hi = state.result.ndr_interval.measured_high
435 pdr_lo = state.result.pdr_interval.measured_low
436 pdr_hi = state.result.pdr_interval.measured_high
438 state.width_goal, state.result.ndr_interval.rel_tr_width)
440 state.width_goal, state.result.pdr_interval.rel_tr_width)
441 # If we are hitting maximal or minimal rate, we cannot shift,
442 # but we can re-measure.
443 new_tr = self._ndrpdr_loss_fraction(state,
444 ndr_lo, ndr_hi, pdr_lo, pdr_hi,
445 ndr_rel_width, pdr_rel_width)
447 if new_tr is not None:
448 state = self._measure_and_update_state(state, new_tr)
451 # If we are hitting maximum_transmit_rate,
452 # it is still worth narrowing width,
453 # hoping large enough loss fraction will happen.
454 # But if we are hitting the minimal rate (at current duration),
455 # no additional measurement will help with that,
456 # so we can stop narrowing in this phase.
457 if (ndr_lo.target_tr <= state.minimum_transmit_rate
458 and ndr_lo.loss_fraction > 0.0):
460 if (pdr_lo.target_tr <= state.minimum_transmit_rate
461 and pdr_lo.loss_fraction > state.packet_loss_ratio):
464 new_tr = self._ndrpdr_width_goal(state, ndr_lo, pdr_lo,
465 ndr_rel_width, pdr_rel_width)
467 if new_tr is not None:
468 state = self._measure_and_update_state(state, new_tr)
471 # We do not need to improve width, but there still might be
472 # some measurements with smaller duration.
473 new_tr = self._ndrpdr_duration(state,
474 ndr_lo, ndr_hi, pdr_lo, pdr_hi,
475 ndr_rel_width, pdr_rel_width)
477 if new_tr is not None:
478 state = self._measure_and_update_state(state, new_tr)
481 # Widths are narrow (or lower bound minimal), bound measurements
482 # are long enough, we can return.
483 logging.info("phase done")
487 def _ndrpdr_loss_fraction(self, state, ndr_lo, ndr_hi, pdr_lo, pdr_hi,
488 ndr_rel_width, pdr_rel_width):
489 """Perform loss_fraction-based trials within a ndrpdr phase
491 :param state: current state
492 :param ndr_lo: ndr interval measured low
493 :param ndr_hi: ndr interval measured high
494 :param pdr_lo: pdr interval measured low
495 :param pdr_hi: pdr interval measured high
496 :param ndr_rel_width: ndr interval relative width
497 :param pdr_rel_width: pdr interval relative width
498 :type state: ProgressState
499 :type ndr_lo: ReceiveRateMeasurement.ReceiveRateMeasurement
500 :type ndr_hi: ReceiveRateMeasurement.ReceiveRateMeasurement
501 :type pdr_lo: ReceiveRateMeasurement.ReceiveRateMeasurement
502 :type pdr_hi: ReceiveRateMeasurement.ReceiveRateMeasurement
503 :type ndr_rel_width: float
504 :type pdr_rel_width: float
505 :returns: a new transmit rate if one should be applied
509 if ndr_lo.loss_fraction > 0.0:
510 if ndr_lo.target_tr > state.minimum_transmit_rate:
512 state.minimum_transmit_rate,
514 ndr_rel_width, self.doublings, ndr_lo.target_tr))
515 logging.info("ndr lo external %s", result)
516 elif ndr_lo.duration < state.duration:
517 result = state.minimum_transmit_rate
518 logging.info("ndr lo minimal re-measure")
520 if result is None and pdr_lo.loss_fraction > state.packet_loss_ratio:
521 if pdr_lo.target_tr > state.minimum_transmit_rate:
523 state.minimum_transmit_rate,
525 pdr_rel_width, self.doublings, pdr_lo.target_tr))
526 logging.info("pdr lo external %s", result)
527 elif pdr_lo.duration < state.duration:
528 result = state.minimum_transmit_rate
529 logging.info("pdr lo minimal re-measure")
531 if result is None and ndr_hi.loss_fraction <= 0.0:
532 if ndr_hi.target_tr < state.maximum_transmit_rate:
534 state.maximum_transmit_rate,
536 ndr_rel_width, self.doublings, ndr_hi.target_tr))
537 logging.info("ndr hi external %s", result)
538 elif ndr_hi.duration < state.duration:
539 result = state.maximum_transmit_rate
540 logging.info("ndr hi maximal re-measure")
542 if result is None and pdr_hi.loss_fraction <= state.packet_loss_ratio:
543 if pdr_hi.target_tr < state.maximum_transmit_rate:
545 state.maximum_transmit_rate,
547 pdr_rel_width, self.doublings, pdr_hi.target_tr))
548 logging.info("pdr hi external %s", result)
549 elif pdr_hi.duration < state.duration:
550 result = state.maximum_transmit_rate
551 logging.info("ndr hi maximal re-measure")
554 def _ndrpdr_width_goal(self, state, ndr_lo, pdr_lo,
555 ndr_rel_width, pdr_rel_width):
556 """Perform width_goal-based trials within a ndrpdr phase
558 :param state: current state
559 :param ndr_lo: ndr interval measured low
560 :param pdr_lo: pdr interval measured low
561 :param ndr_rel_width: ndr interval relative width
562 :param pdr_rel_width: pdr interval relative width
563 :type state: ProgressState
564 :type ndr_lo: ReceiveRateMeasurement.ReceiveRateMeasurement
565 :type pdr_lo: ReceiveRateMeasurement.ReceiveRateMeasurement
566 :type ndr_rel_width: float
567 :type pdr_rel_width: float
568 :returns: a new transmit rate if one should be applied
570 Return a new transmit rate if one should be applied.
572 if ndr_rel_width > state.width_goal:
573 # We have to narrow NDR width first, as NDR internal search
574 # can invalidate PDR (but not vice versa).
575 result = self.half_step_up(ndr_rel_width, ndr_lo.target_tr)
576 logging.info("Bisecting for NDR at %s", result)
577 elif pdr_rel_width > state.width_goal:
578 # PDR iternal search.
579 result = self.half_step_up(pdr_rel_width, pdr_lo.target_tr)
580 logging.info("Bisecting for PDR at %s", result)
586 def _ndrpdr_duration(state, ndr_lo, pdr_lo, ndr_hi, pdr_hi,
587 ndr_rel_width, pdr_rel_width):
588 """Perform duration-based trials within a ndrpdr phase
590 :param state: current state
591 :param ndr_lo: ndr interval measured low
592 :param ndr_hi: ndr interval measured high
593 :param pdr_lo: pdr interval measured low
594 :param pdr_hi: pdr interval measured high
595 :param ndr_rel_width: ndr interval relative width
596 :param pdr_rel_width: pdr interval relative width
597 :type state: ProgressState
598 :type ndr_lo: ReceiveRateMeasurement.ReceiveRateMeasurement
599 :type ndr_hi: ReceiveRateMeasurement.ReceiveRateMeasurement
600 :type pdr_lo: ReceiveRateMeasurement.ReceiveRateMeasurement
601 :type pdr_hi: ReceiveRateMeasurement.ReceiveRateMeasurement
602 :type ndr_rel_width: float
603 :type pdr_rel_width: float
604 :returns: a new transmit rate if one should be applied
607 # We need to re-measure with full duration, possibly
608 # creating invalid bounds to resolve (thus broadening width).
609 if ndr_lo.duration < state.duration:
610 result = ndr_lo.target_tr
611 logging.info("re-measuring NDR lower bound")
612 elif pdr_lo.duration < state.duration:
613 result = pdr_lo.target_tr
614 logging.info("re-measuring PDR lower bound")
615 # Except when lower bounds have high loss fraction, in that case
616 # we do not need to re-measure _upper_ bounds.
617 elif ndr_hi.duration < state.duration and ndr_rel_width > 0.0:
618 result = ndr_hi.target_tr
619 logging.info("re-measuring NDR upper bound")
620 elif pdr_hi.duration < state.duration and pdr_rel_width > 0.0:
621 result = pdr_hi.target_tr
622 logging.info("re-measuring PDR upper bound")