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 OptimizedSearchAlgorithm class."""
20 from .AbstractSearchAlgorithm import AbstractSearchAlgorithm
21 from .NdrPdrResult import NdrPdrResult
22 from .ReceiveRateInterval import ReceiveRateInterval
25 class OptimizedSearchAlgorithm(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 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: Reviwew and update this docstring according to rst docs.
79 TODO: Initial phase: Larger min width and search up on zero.
80 TODO: Support configurable number of Packet Loss Ratios.
81 TODO: Rename to MultipleDropRateSearch (or MultipleLossRatioSearch).
84 class ProgressState(object):
85 """Structure containing data to be passed around in recursion."""
88 self, result, phases, duration, width_goal, packet_loss_ratio,
89 minimum_transmit_rate, maximum_transmit_rate):
90 """Convert and store the argument values.
92 :param result: Current measured NDR and PDR intervals.
93 :param phases: How many intermediate phases to perform
94 before the current one.
95 :param duration: Trial duration to use in the current phase [s].
96 :param width_goal: The goal relative width for the curreent phase.
97 :param packet_loss_ratio: PDR fraction for the current search.
98 :param minimum_transmit_rate: Minimum target transmit rate
99 for the current search [pps].
100 :param maximum_transmit_rate: Maximum target transmit rate
101 for the current search [pps].
102 :type result: NdrPdrResult
104 :type duration: float
105 :type width_goal: float
106 :type packet_loss_ratio: float
107 :type minimum_transmit_rate: float
108 :type maximum_transmit_rate: float
111 self.phases = int(phases)
112 self.duration = float(duration)
113 self.width_goal = float(width_goal)
114 self.packet_loss_ratio = float(packet_loss_ratio)
115 self.minimum_transmit_rate = float(minimum_transmit_rate)
116 self.maximum_transmit_rate = float(maximum_transmit_rate)
118 def __init__(self, rate_provider, final_relative_width=0.005,
119 final_trial_duration=30.0, initial_trial_duration=1.0,
120 number_of_intermediate_phases=2, timeout=600.0):
121 """Store rate provider and additional arguments.
123 :param rate_provider: Rate provider to use by this search object.
124 :param final_relative_width: Final lower bound transmit rate
125 cannot be more distant that this multiple of upper bound [1].
126 :param final_trial_duration: Trial duration for the final phase [s].
127 :param initial_trial_duration: Trial duration for the initial phase
128 and also for the first intermediate phase [s].
129 :param number_of_intermediate_phases: Number of intermediate phases
130 to perform before the final phase [1].
131 :param timeout: The search will fail itself when not finished
132 before this overall time [s].
133 :type rate_provider: AbstractRateProvider
134 :type final_relative_width: float
135 :type final_trial_duration: float
136 :type initial_trial_duration: int
137 :type number_of_intermediate_phases: int
140 super(OptimizedSearchAlgorithm, self).__init__(rate_provider)
141 self.final_trial_duration = float(final_trial_duration)
142 self.final_relative_width = float(final_relative_width)
143 self.number_of_intermediate_phases = int(number_of_intermediate_phases)
144 self.initial_trial_duration = float(initial_trial_duration)
145 self.timeout = float(timeout)
147 def narrow_down_ndr_and_pdr(
148 self, minimum_transmit_rate, maximum_transmit_rate,
150 """Perform initial phase, create state object, proceed with next phases.
152 :param minimum_transmit_rate: Minimal target transmit rate [pps].
153 :param maximum_transmit_rate: Maximal target transmit rate [pps].
154 :param packet_loss_ratio: Fraction of packets lost, for PDR [1].
155 :type minimum_transmit_rate: float
156 :type maximum_transmit_rate: float
157 :type packet_loss_ratio: float
158 :returns: Structure containing narrowed down intervals
159 and their measurements.
161 :raises RuntimeError: If total duration is larger than timeout.
163 minimum_transmit_rate = float(minimum_transmit_rate)
164 maximum_transmit_rate = float(maximum_transmit_rate)
165 packet_loss_ratio = float(packet_loss_ratio)
166 line_measurement = self.rate_provider.measure(
167 self.initial_trial_duration, maximum_transmit_rate)
168 # 0.999 is to avoid rounding errors which make
169 # the subsequent logic think the width is too broad.
171 minimum_transmit_rate,
172 maximum_transmit_rate * (1.0 - 0.999 * self.final_relative_width))
174 max_lo, max(minimum_transmit_rate, line_measurement.receive_rate))
175 mrr_measurement = self.rate_provider.measure(
176 self.initial_trial_duration, mrr)
177 # Attempt to get narrower width.
179 minimum_transmit_rate,
180 mrr * (1.0 - 0.999 * self.final_relative_width))
181 mrr2 = min(max2_lo, mrr_measurement.receive_rate)
182 if mrr2 > minimum_transmit_rate:
183 line_measurement = mrr_measurement
184 mrr_measurement = self.rate_provider.measure(
185 self.initial_trial_duration, mrr2)
186 starting_interval = ReceiveRateInterval(
187 mrr_measurement, line_measurement)
188 starting_result = NdrPdrResult(starting_interval, starting_interval)
189 state = self.ProgressState(
190 starting_result, self.number_of_intermediate_phases,
191 self.final_trial_duration, self.final_relative_width,
192 packet_loss_ratio, minimum_transmit_rate, maximum_transmit_rate)
193 state = self.ndrpdr(state)
196 def _measure_and_update_state(self, state, transmit_rate):
197 """Perform trial measurement, update bounds, return new state.
199 :param state: State before this measurement.
200 :param transmit_rate: Target transmit rate for this measurement [pps].
201 :type state: ProgressState
202 :type transmit_rate: float
203 :returns: State after the measurement.
204 :rtype: ProgressState
206 # TODO: Implement https://stackoverflow.com/a/24683360
207 # to avoid the string manipulation if log verbosity is too low.
208 logging.info("result before update: %s", state.result)
210 "relative widths in goals: %s", state.result.width_in_goals(
211 self.final_relative_width))
212 measurement = self.rate_provider.measure(state.duration, transmit_rate)
213 ndr_interval = self._new_interval(
214 state.result.ndr_interval, measurement, 0.0)
215 pdr_interval = self._new_interval(
216 state.result.pdr_interval, measurement, state.packet_loss_ratio)
217 state.result = NdrPdrResult(ndr_interval, pdr_interval)
221 def _new_interval(old_interval, measurement, packet_loss_ratio):
222 """Return new interval with bounds updated according to the measurement.
224 :param old_interval: The current interval before the measurement.
225 :param measurement: The new meaqsurement to take into account.
226 :param packet_loss_ratio: Fraction for PDR (or zero for NDR).
227 :type old_interval: ReceiveRateInterval
228 :type measurement: ReceiveRateMeasurement
229 :type packet_loss_ratio: float
230 :returns: The updated interval.
231 :rtype: ReceiveRateInterval
233 old_lo, old_hi = old_interval.measured_low, old_interval.measured_high
234 # Priority zero: direct replace if the target Tr is the same.
235 if measurement.target_tr in (old_lo.target_tr, old_hi.target_tr):
236 if measurement.target_tr == old_lo.target_tr:
237 return ReceiveRateInterval(measurement, old_hi)
239 return ReceiveRateInterval(old_lo, measurement)
240 # Priority one: invalid lower bound allows only one type of update.
241 if old_lo.loss_fraction > packet_loss_ratio:
242 # We can only expand down, old bound becomes valid upper one.
243 if measurement.target_tr < old_lo.target_tr:
244 return ReceiveRateInterval(measurement, old_lo)
247 # Lower bound is now valid.
248 # Next priorities depend on target Tr.
249 if measurement.target_tr < old_lo.target_tr:
250 # Lower external measurement, relevant only
251 # if the new measurement has high loss rate.
252 if measurement.loss_fraction > packet_loss_ratio:
253 # Returning the broader interval as old_lo
254 # would be invalid upper bound.
255 return ReceiveRateInterval(measurement, old_hi)
256 elif measurement.target_tr > old_hi.target_tr:
257 # Upper external measurement, only relevant for invalid upper bound.
258 if old_hi.loss_fraction <= packet_loss_ratio:
259 # Old upper bound becomes valid new lower bound.
260 return ReceiveRateInterval(old_hi, measurement)
262 # Internal measurement, replaced boundary
263 # depends on measured loss fraction.
264 if measurement.loss_fraction > packet_loss_ratio:
265 # We have found a narrow valid interval,
266 # regardless of whether old upper bound was valid.
267 return ReceiveRateInterval(old_lo, measurement)
269 # In ideal world, we would not want to shrink interval
270 # if upper bound is not valid.
271 # In the real world, we want to shrink it for
272 # "invalid upper bound at maximal rate" case.
273 return ReceiveRateInterval(measurement, old_hi)
274 # Fallback, the interval is unchanged by the measurement.
278 def double_relative_width(relative_width):
279 """Return relative width corresponding to double logarithmic width.
281 :param relative_width: The base relative width to double.
282 :type relative_width: float
283 :returns: The relative width of double logarithmic size.
286 return 1.999 * relative_width - relative_width * relative_width
287 # The number should be 2.0, but we want to avoid rounding errors,
288 # and ensure half of double is not larger than the original value.
291 def double_step_down(relative_width, current_bound):
292 """Return rate of double logarithmic width below.
294 :param relative_width: The base relative width to double.
295 :param current_bound: The current target transmit rate to move [pps].
296 :type relative_width: float
297 :type current_bound: float
298 :returns: Transmit rate smaller by logarithmically double width [pps].
301 return current_bound * (
302 1.0 - OptimizedSearchAlgorithm.double_relative_width(
306 def double_step_up(relative_width, current_bound):
307 """Return rate of double logarithmic width above.
309 :param relative_width: The base relative width to double.
310 :param current_bound: The current target transmit rate to move [pps].
311 :type relative_width: float
312 :type current_bound: float
313 :returns: Transmit rate larger by logarithmically double width [pps].
316 return current_bound / (
317 1.0 - OptimizedSearchAlgorithm.double_relative_width(
321 def half_relative_width(relative_width):
322 """Return relative width corresponding to half logarithmic width.
324 :param relative_width: The base relative width to halve.
325 :type relative_width: float
326 :returns: The relative width of half logarithmic size.
329 return 1.0 - math.sqrt(1.0 - relative_width)
332 def half_step_up(relative_width, current_bound):
333 """Return rate of half logarithmic width above.
335 :param relative_width: The base relative width to halve.
336 :param current_bound: The current target transmit rate to move [pps].
337 :type relative_width: float
338 :type current_bound: float
339 :returns: Transmit rate larger by logarithmically half width [pps].
342 return current_bound / (
343 1.0 - OptimizedSearchAlgorithm.half_relative_width(relative_width))
345 def ndrpdr(self, state):
346 """Pefrom trials for this phase. Return the new state when done.
348 :param state: State before this phase.
349 :type state: ProgressState
350 :returns: The updates state.
351 :rtype: ProgressState
352 :raises RuntimeError: If total duration is larger than timeout.
355 # We need to finish preceding intermediate phases first.
356 saved_phases = state.phases
358 # Preceding phases have shorter duration.
359 saved_duration = state.duration
360 duration_multiplier = state.duration / self.initial_trial_duration
361 phase_exponent = float(state.phases) / saved_phases
362 state.duration = self.initial_trial_duration * math.pow(
363 duration_multiplier, phase_exponent)
364 # Shorter durations do not need that narrow widths.
365 saved_width = state.width_goal
366 state.width_goal = self.double_relative_width(state.width_goal)
368 state = self.ndrpdr(state)
369 # Restore the state for current phase.
370 state.duration = saved_duration
371 state.width_goal = saved_width
372 state.phases = saved_phases # Not needed, but just in case.
374 "starting iterations with duration %s and relative width goal %s",
375 state.duration, state.width_goal)
376 start_time = time.time()
378 if time.time() > start_time + self.timeout:
379 raise RuntimeError("Optimized search takes too long.")
380 # Order of priorities: improper bounds (nl, pl, nh, ph),
381 # then narrowing relative Tr widths.
382 # Durations are not priorities yet,
383 # they will settle on their own hopefully.
384 ndr_lo = state.result.ndr_interval.measured_low
385 ndr_hi = state.result.ndr_interval.measured_high
386 pdr_lo = state.result.pdr_interval.measured_low
387 pdr_hi = state.result.pdr_interval.measured_high
389 state.width_goal, state.result.ndr_interval.rel_tr_width)
391 state.width_goal, state.result.pdr_interval.rel_tr_width)
392 # If we are hitting maximal or minimal rate, we cannot shift,
393 # but we can re-measure.
394 if ndr_lo.loss_fraction > 0.0:
395 if ndr_lo.target_tr > state.minimum_transmit_rate:
397 state.minimum_transmit_rate,
398 self.double_step_down(ndr_rel_width, ndr_lo.target_tr))
399 logging.info("ndr lo external %s", new_tr)
400 state = self._measure_and_update_state(state, new_tr)
402 elif ndr_lo.duration < state.duration:
403 logging.info("ndr lo minimal re-measure")
404 state = self._measure_and_update_state(
405 state, state.minimum_transmit_rate)
407 if pdr_lo.loss_fraction > state.packet_loss_ratio:
408 if pdr_lo.target_tr > state.minimum_transmit_rate:
410 state.minimum_transmit_rate,
411 self.double_step_down(pdr_rel_width, pdr_lo.target_tr))
412 logging.info("pdr lo external %s", new_tr)
413 state = self._measure_and_update_state(state, new_tr)
415 elif pdr_lo.duration < state.duration:
416 logging.info("pdr lo minimal re-measure")
417 state = self._measure_and_update_state(
418 state, state.minimum_transmit_rate)
420 if ndr_hi.loss_fraction <= 0.0:
421 if ndr_hi.target_tr < state.maximum_transmit_rate:
423 state.maximum_transmit_rate,
424 self.double_step_up(ndr_rel_width, ndr_hi.target_tr))
425 logging.info("ndr hi external %s", new_tr)
426 state = self._measure_and_update_state(state, new_tr)
428 elif ndr_hi.duration < state.duration:
429 logging.info("ndr hi maximal re-measure")
430 state = self._measure_and_update_state(
431 state, state.maximum_transmit_rate)
433 if pdr_hi.loss_fraction <= state.packet_loss_ratio:
434 if pdr_hi.target_tr < state.maximum_transmit_rate:
436 state.maximum_transmit_rate,
437 self.double_step_up(pdr_rel_width, pdr_hi.target_tr))
438 logging.info("pdr hi external %s", new_tr)
439 state = self._measure_and_update_state(state, new_tr)
441 elif pdr_hi.duration < state.duration:
442 logging.info("ndr hi maximal re-measure")
443 state = self._measure_and_update_state(
444 state, state.maximum_transmit_rate)
446 # If we are hitting maximum_transmit_rate,
447 # it is still worth narrowing width,
448 # hoping large enough loss fraction will happen.
449 # But if we are hitting the minimal rate (at current duration),
450 # no additional measurement will help with that,
451 # so we can stop narrowing in this phase.
452 if (ndr_lo.target_tr <= state.minimum_transmit_rate
453 and ndr_lo.loss_fraction > 0.0):
455 if (pdr_lo.target_tr <= state.minimum_transmit_rate
456 and pdr_lo.loss_fraction > state.packet_loss_ratio):
458 if max(ndr_rel_width, pdr_rel_width) > state.width_goal:
459 # We have to narrow some width.
460 # TODO: Prefer NDR, it could invalidate PDR (not vice versa).
461 if ndr_rel_width >= pdr_rel_width:
462 new_tr = self.half_step_up(ndr_rel_width, ndr_lo.target_tr)
463 logging.info("Bisecting for NDR at %s", new_tr)
464 state = self._measure_and_update_state(state, new_tr)
467 new_tr = self.half_step_up(pdr_rel_width, pdr_lo.target_tr)
468 logging.info("Bisecting for PDR at %s", new_tr)
469 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 # We need to re-measure with full duration, possibly
474 # creating invalid bounds to resolve (thus broadening width).
475 if ndr_lo.duration < state.duration:
476 logging.info("re-measuring NDR lower bound")
477 self._measure_and_update_state(state, ndr_lo.target_tr)
479 if pdr_lo.duration < state.duration:
480 logging.info("re-measuring PDR lower bound")
481 self._measure_and_update_state(state, pdr_lo.target_tr)
483 # Except when lower bounds have high loss fraction, in that case
484 # we do not need to re-measure _upper_ bounds.
485 if ndr_hi.duration < state.duration and ndr_rel_width > 0.0:
486 logging.info("re-measuring NDR upper bound")
487 self._measure_and_update_state(state, ndr_hi.target_tr)
489 if pdr_hi.duration < state.duration and pdr_rel_width > 0.0:
490 logging.info("re-measuring PDR upper bound")
491 self._measure_and_update_state(state, pdr_hi.target_tr)
493 # Widths are narrow (or lower bound minimal), bound measurements
494 # are long enough, we can return.
495 logging.info("phase done")