+# Copyright (c) 2018 Cisco and/or its affiliates.
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at:
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Module defining MultipleLossRatioSearch class."""
+
+import logging
+import math
+import time
+
+from AbstractSearchAlgorithm import AbstractSearchAlgorithm
+from NdrPdrResult import NdrPdrResult
+from ReceiveRateInterval import ReceiveRateInterval
+
+
+class MultipleLossRatioSearch(AbstractSearchAlgorithm):
+ """Optimized binary search algorithm for finding NDR and PDR bounds.
+
+ Traditional binary search algorithm needs initial interval
+ (lower and upper bound), and returns final interval after bisecting
+ (until some exit condition is met).
+ The exit condition is usually related to the interval width,
+ (upper bound value minus lower bound value).
+
+ The optimized algorithm contains several improvements
+ aimed to reduce overall search time.
+
+ One improvement is searching for two intervals at once.
+ The intervals are for NDR (No Drop Rate) and PDR (Partial Drop Rate).
+
+ Next improvement is that the initial interval does not need to be valid.
+ Imagine initial interval (10, 11) where 11 is smaller
+ than the searched value.
+ The algorithm will try (11, 13) interval next, and if 13 is still smaller,
+ (13, 17) and so on, doubling width until the upper bound is valid.
+ The part when interval expands is called external search,
+ the part when interval is bisected is called internal search.
+
+ Next improvement is that trial measurements at small trial duration
+ can be used to find a reasonable interval for full trial duration search.
+ This results in more trials performed, but smaller overall duration
+ in general.
+
+ Next improvement is bisecting in logarithmic quantities,
+ so that exit criteria can be independent of measurement units.
+
+ Next improvement is basing the initial interval on receive rates.
+
+ Final improvement is exiting early if the minimal value
+ is not a valid lower bound.
+
+ The complete search consist of several phases,
+ each phase performing several trial measurements.
+ Initial phase creates initial interval based on receive rates
+ at maximum rate and at maximum receive rate (MRR).
+ Final phase and preceding intermediate phases are performing
+ external and internal search steps,
+ each resulting interval is the starting point for the next phase.
+ The resulting interval of final phase is the result of the whole algorithm.
+
+ Each non-initial phase uses its own trial duration and width goal.
+ Any non-initial phase stops searching (for NDR or PDR independently)
+ when minimum is not a valid lower bound (at current duration),
+ or all of the following is true:
+ Both bounds are valid, bound bounds are measured at the current phase
+ trial duration, interval width is less than the width goal
+ for current phase.
+
+ TODO: Review and update this docstring according to rst docs.
+ TODO: Support configurable number of Packet Loss Ratios.
+ """
+
+ class ProgressState(object):
+ """Structure containing data to be passed around in recursion."""
+
+ def __init__(
+ self, result, phases, duration, width_goal, packet_loss_ratio,
+ minimum_transmit_rate, maximum_transmit_rate):
+ """Convert and store the argument values.
+
+ :param result: Current measured NDR and PDR intervals.
+ :param phases: How many intermediate phases to perform
+ before the current one.
+ :param duration: Trial duration to use in the current phase [s].
+ :param width_goal: The goal relative width for the curreent phase.
+ :param packet_loss_ratio: PDR fraction for the current search.
+ :param minimum_transmit_rate: Minimum target transmit rate
+ for the current search [pps].
+ :param maximum_transmit_rate: Maximum target transmit rate
+ for the current search [pps].
+ :type result: NdrPdrResult
+ :type phases: int
+ :type duration: float
+ :type width_goal: float
+ :type packet_loss_ratio: float
+ :type minimum_transmit_rate: float
+ :type maximum_transmit_rate: float
+ """
+ self.result = result
+ self.phases = int(phases)
+ self.duration = float(duration)
+ self.width_goal = float(width_goal)
+ self.packet_loss_ratio = float(packet_loss_ratio)
+ self.minimum_transmit_rate = float(minimum_transmit_rate)
+ self.maximum_transmit_rate = float(maximum_transmit_rate)
+
+ def __init__(self, measurer, final_relative_width=0.005,
+ final_trial_duration=30.0, initial_trial_duration=1.0,
+ number_of_intermediate_phases=2, timeout=600.0):
+ """Store the measurer object and additional arguments.
+
+ :param measurer: Rate provider to use by this search object.
+ :param final_relative_width: Final lower bound transmit rate
+ cannot be more distant that this multiple of upper bound [1].
+ :param final_trial_duration: Trial duration for the final phase [s].
+ :param initial_trial_duration: Trial duration for the initial phase
+ and also for the first intermediate phase [s].
+ :param number_of_intermediate_phases: Number of intermediate phases
+ to perform before the final phase [1].
+ :param timeout: The search will fail itself when not finished
+ before this overall time [s].
+ :type measurer: AbstractMeasurer
+ :type final_relative_width: float
+ :type final_trial_duration: float
+ :type initial_trial_duration: int
+ :type number_of_intermediate_phases: int
+ :type timeout: float
+ """
+ super(MultipleLossRatioSearch, self).__init__(measurer)
+ self.final_trial_duration = float(final_trial_duration)
+ self.final_relative_width = float(final_relative_width)
+ self.number_of_intermediate_phases = int(number_of_intermediate_phases)
+ self.initial_trial_duration = float(initial_trial_duration)
+ self.timeout = float(timeout)
+
+
+ @staticmethod
+ def double_relative_width(relative_width):
+ """Return relative width corresponding to double logarithmic width.
+
+ :param relative_width: The base relative width to double.
+ :type relative_width: float
+ :returns: The relative width of double logarithmic size.
+ :rtype: float
+ """
+ return 1.999 * relative_width - relative_width * relative_width
+ # The number should be 2.0, but we want to avoid rounding errors,
+ # and ensure half of double is not larger than the original value.
+
+ @staticmethod
+ def double_step_down(relative_width, current_bound):
+ """Return rate of double logarithmic width below.
+
+ :param relative_width: The base relative width to double.
+ :param current_bound: The current target transmit rate to move [pps].
+ :type relative_width: float
+ :type current_bound: float
+ :returns: Transmit rate smaller by logarithmically double width [pps].
+ :rtype: float
+ """
+ return current_bound * (
+ 1.0 - MultipleLossRatioSearch.double_relative_width(
+ relative_width))
+
+ @staticmethod
+ def double_step_up(relative_width, current_bound):
+ """Return rate of double logarithmic width above.
+
+ :param relative_width: The base relative width to double.
+ :param current_bound: The current target transmit rate to move [pps].
+ :type relative_width: float
+ :type current_bound: float
+ :returns: Transmit rate larger by logarithmically double width [pps].
+ :rtype: float
+ """
+ return current_bound / (
+ 1.0 - MultipleLossRatioSearch.double_relative_width(
+ relative_width))
+
+ @staticmethod
+ def half_relative_width(relative_width):
+ """Return relative width corresponding to half logarithmic width.
+
+ :param relative_width: The base relative width to halve.
+ :type relative_width: float
+ :returns: The relative width of half logarithmic size.
+ :rtype: float
+ """
+ return 1.0 - math.sqrt(1.0 - relative_width)
+
+ @staticmethod
+ def half_step_up(relative_width, current_bound):
+ """Return rate of half logarithmic width above.
+
+ :param relative_width: The base relative width to halve.
+ :param current_bound: The current target transmit rate to move [pps].
+ :type relative_width: float
+ :type current_bound: float
+ :returns: Transmit rate larger by logarithmically half width [pps].
+ :rtype: float
+ """
+ return current_bound / (
+ 1.0 - MultipleLossRatioSearch.half_relative_width(relative_width))
+
+ def narrow_down_ndr_and_pdr(
+ self, minimum_transmit_rate, maximum_transmit_rate,
+ packet_loss_ratio):
+ """Perform initial phase, create state object, proceed with next phases.
+
+ :param minimum_transmit_rate: Minimal target transmit rate [pps].
+ :param maximum_transmit_rate: Maximal target transmit rate [pps].
+ :param packet_loss_ratio: Fraction of packets lost, for PDR [1].
+ :type minimum_transmit_rate: float
+ :type maximum_transmit_rate: float
+ :type packet_loss_ratio: float
+ :returns: Structure containing narrowed down intervals
+ and their measurements.
+ :rtype: NdrPdrResult
+ :raises RuntimeError: If total duration is larger than timeout.
+ """
+ minimum_transmit_rate = float(minimum_transmit_rate)
+ maximum_transmit_rate = float(maximum_transmit_rate)
+ packet_loss_ratio = float(packet_loss_ratio)
+ line_measurement = self.measurer.measure(
+ self.initial_trial_duration, maximum_transmit_rate)
+ initial_width_goal = self.final_relative_width
+ for _ in range(self.number_of_intermediate_phases):
+ initial_width_goal = self.double_relative_width(initial_width_goal)
+ max_lo = maximum_transmit_rate * (1.0 - initial_width_goal)
+ mrr = max(
+ minimum_transmit_rate,
+ min(max_lo, line_measurement.receive_rate))
+ mrr_measurement = self.measurer.measure(
+ self.initial_trial_duration, mrr)
+ # Attempt to get narrower width.
+ if mrr_measurement.loss_fraction > 0.0:
+ max2_lo = mrr * (1.0 - initial_width_goal)
+ mrr2 = min(max2_lo, mrr_measurement.receive_rate)
+ else:
+ mrr2 = mrr / (1.0 - initial_width_goal)
+ if mrr2 > minimum_transmit_rate and mrr2 < maximum_transmit_rate:
+ line_measurement = mrr_measurement
+ mrr_measurement = self.measurer.measure(
+ self.initial_trial_duration, mrr2)
+ if mrr2 > mrr:
+ buf = line_measurement
+ line_measurement = mrr_measurement
+ mrr_measurement = buf
+ starting_interval = ReceiveRateInterval(
+ mrr_measurement, line_measurement)
+ starting_result = NdrPdrResult(starting_interval, starting_interval)
+ state = self.ProgressState(
+ starting_result, self.number_of_intermediate_phases,
+ self.final_trial_duration, self.final_relative_width,
+ packet_loss_ratio, minimum_transmit_rate, maximum_transmit_rate)
+ state = self.ndrpdr(state)
+ return state.result
+
+ def _measure_and_update_state(self, state, transmit_rate):
+ """Perform trial measurement, update bounds, return new state.
+
+ :param state: State before this measurement.
+ :param transmit_rate: Target transmit rate for this measurement [pps].
+ :type state: ProgressState
+ :type transmit_rate: float
+ :returns: State after the measurement.
+ :rtype: ProgressState
+ """
+ # TODO: Implement https://stackoverflow.com/a/24683360
+ # to avoid the string manipulation if log verbosity is too low.
+ logging.info("result before update: %s", state.result)
+ logging.debug(
+ "relative widths in goals: %s", state.result.width_in_goals(
+ self.final_relative_width))
+ measurement = self.measurer.measure(state.duration, transmit_rate)
+ ndr_interval = self._new_interval(
+ state.result.ndr_interval, measurement, 0.0)
+ pdr_interval = self._new_interval(
+ state.result.pdr_interval, measurement, state.packet_loss_ratio)
+ state.result = NdrPdrResult(ndr_interval, pdr_interval)
+ return state
+
+ @staticmethod
+ def _new_interval(old_interval, measurement, packet_loss_ratio):
+ """Return new interval with bounds updated according to the measurement.
+
+ :param old_interval: The current interval before the measurement.
+ :param measurement: The new meaqsurement to take into account.
+ :param packet_loss_ratio: Fraction for PDR (or zero for NDR).
+ :type old_interval: ReceiveRateInterval
+ :type measurement: ReceiveRateMeasurement
+ :type packet_loss_ratio: float
+ :returns: The updated interval.
+ :rtype: ReceiveRateInterval
+ """
+ old_lo, old_hi = old_interval.measured_low, old_interval.measured_high
+ # Priority zero: direct replace if the target Tr is the same.
+ if measurement.target_tr in (old_lo.target_tr, old_hi.target_tr):
+ if measurement.target_tr == old_lo.target_tr:
+ return ReceiveRateInterval(measurement, old_hi)
+ else:
+ return ReceiveRateInterval(old_lo, measurement)
+ # Priority one: invalid lower bound allows only one type of update.
+ if old_lo.loss_fraction > packet_loss_ratio:
+ # We can only expand down, old bound becomes valid upper one.
+ if measurement.target_tr < old_lo.target_tr:
+ return ReceiveRateInterval(measurement, old_lo)
+ else:
+ return old_interval
+ # Lower bound is now valid.
+ # Next priorities depend on target Tr.
+ if measurement.target_tr < old_lo.target_tr:
+ # Lower external measurement, relevant only
+ # if the new measurement has high loss rate.
+ if measurement.loss_fraction > packet_loss_ratio:
+ # Returning the broader interval as old_lo
+ # would be invalid upper bound.
+ return ReceiveRateInterval(measurement, old_hi)
+ elif measurement.target_tr > old_hi.target_tr:
+ # Upper external measurement, only relevant for invalid upper bound.
+ if old_hi.loss_fraction <= packet_loss_ratio:
+ # Old upper bound becomes valid new lower bound.
+ return ReceiveRateInterval(old_hi, measurement)
+ else:
+ # Internal measurement, replaced boundary
+ # depends on measured loss fraction.
+ if measurement.loss_fraction > packet_loss_ratio:
+ # We have found a narrow valid interval,
+ # regardless of whether old upper bound was valid.
+ return ReceiveRateInterval(old_lo, measurement)
+ else:
+ # In ideal world, we would not want to shrink interval
+ # if upper bound is not valid.
+ # In the real world, we want to shrink it for
+ # "invalid upper bound at maximal rate" case.
+ return ReceiveRateInterval(measurement, old_hi)
+ # Fallback, the interval is unchanged by the measurement.
+ return old_interval
+
+ def ndrpdr(self, state):
+ """Pefrom trials for this phase. Return the new state when done.
+
+ :param state: State before this phase.
+ :type state: ProgressState
+ :returns: The updated state.
+ :rtype: ProgressState
+ :raises RuntimeError: If total duration is larger than timeout.
+ """
+ start_time = time.time()
+ if state.phases > 0:
+ # We need to finish preceding intermediate phases first.
+ saved_phases = state.phases
+ state.phases -= 1
+ # Preceding phases have shorter duration.
+ saved_duration = state.duration
+ duration_multiplier = state.duration / self.initial_trial_duration
+ phase_exponent = float(state.phases) / saved_phases
+ state.duration = self.initial_trial_duration * math.pow(
+ duration_multiplier, phase_exponent)
+ # Shorter durations do not need that narrow widths.
+ saved_width = state.width_goal
+ state.width_goal = self.double_relative_width(state.width_goal)
+ # Recurse.
+ state = self.ndrpdr(state)
+ # Restore the state for current phase.
+ state.duration = saved_duration
+ state.width_goal = saved_width
+ state.phases = saved_phases # Not needed, but just in case.
+ logging.info(
+ "starting iterations with duration %s and relative width goal %s",
+ state.duration, state.width_goal)
+ while 1:
+ if time.time() > start_time + self.timeout:
+ raise RuntimeError("Optimized search takes too long.")
+ # Order of priorities: invalid bounds (nl, pl, nh, ph),
+ # then narrowing relative Tr widths.
+ # Durations are not priorities yet,
+ # they will settle on their own hopefully.
+ ndr_lo = state.result.ndr_interval.measured_low
+ ndr_hi = state.result.ndr_interval.measured_high
+ pdr_lo = state.result.pdr_interval.measured_low
+ pdr_hi = state.result.pdr_interval.measured_high
+ ndr_rel_width = max(
+ state.width_goal, state.result.ndr_interval.rel_tr_width)
+ pdr_rel_width = max(
+ state.width_goal, state.result.pdr_interval.rel_tr_width)
+ # If we are hitting maximal or minimal rate, we cannot shift,
+ # but we can re-measure.
+ if ndr_lo.loss_fraction > 0.0:
+ if ndr_lo.target_tr > state.minimum_transmit_rate:
+ new_tr = max(
+ state.minimum_transmit_rate,
+ self.double_step_down(ndr_rel_width, ndr_lo.target_tr))
+ logging.info("ndr lo external %s", new_tr)
+ state = self._measure_and_update_state(state, new_tr)
+ continue
+ elif ndr_lo.duration < state.duration:
+ logging.info("ndr lo minimal re-measure")
+ state = self._measure_and_update_state(
+ state, state.minimum_transmit_rate)
+ continue
+ if pdr_lo.loss_fraction > state.packet_loss_ratio:
+ if pdr_lo.target_tr > state.minimum_transmit_rate:
+ new_tr = max(
+ state.minimum_transmit_rate,
+ self.double_step_down(pdr_rel_width, pdr_lo.target_tr))
+ logging.info("pdr lo external %s", new_tr)
+ state = self._measure_and_update_state(state, new_tr)
+ continue
+ elif pdr_lo.duration < state.duration:
+ logging.info("pdr lo minimal re-measure")
+ state = self._measure_and_update_state(
+ state, state.minimum_transmit_rate)
+ continue
+ if ndr_hi.loss_fraction <= 0.0:
+ if ndr_hi.target_tr < state.maximum_transmit_rate:
+ new_tr = min(
+ state.maximum_transmit_rate,
+ self.double_step_up(ndr_rel_width, ndr_hi.target_tr))
+ logging.info("ndr hi external %s", new_tr)
+ state = self._measure_and_update_state(state, new_tr)
+ continue
+ elif ndr_hi.duration < state.duration:
+ logging.info("ndr hi maximal re-measure")
+ state = self._measure_and_update_state(
+ state, state.maximum_transmit_rate)
+ continue
+ if pdr_hi.loss_fraction <= state.packet_loss_ratio:
+ if pdr_hi.target_tr < state.maximum_transmit_rate:
+ new_tr = min(
+ state.maximum_transmit_rate,
+ self.double_step_up(pdr_rel_width, pdr_hi.target_tr))
+ logging.info("pdr hi external %s", new_tr)
+ state = self._measure_and_update_state(state, new_tr)
+ continue
+ elif pdr_hi.duration < state.duration:
+ logging.info("ndr hi maximal re-measure")
+ state = self._measure_and_update_state(
+ state, state.maximum_transmit_rate)
+ continue
+ # If we are hitting maximum_transmit_rate,
+ # it is still worth narrowing width,
+ # hoping large enough loss fraction will happen.
+ # But if we are hitting the minimal rate (at current duration),
+ # no additional measurement will help with that,
+ # so we can stop narrowing in this phase.
+ if (ndr_lo.target_tr <= state.minimum_transmit_rate
+ and ndr_lo.loss_fraction > 0.0):
+ ndr_rel_width = 0.0
+ if (pdr_lo.target_tr <= state.minimum_transmit_rate
+ and pdr_lo.loss_fraction > state.packet_loss_ratio):
+ pdr_rel_width = 0.0
+ if ndr_rel_width > state.width_goal:
+ # We have to narrow NDR width first, as NDR internal search
+ # can invalidate PDR (but not vice versa).
+ new_tr = self.half_step_up(ndr_rel_width, ndr_lo.target_tr)
+ logging.info("Bisecting for NDR at %s", new_tr)
+ state = self._measure_and_update_state(state, new_tr)
+ continue
+ if pdr_rel_width > state.width_goal:
+ # PDR iternal search.
+ new_tr = self.half_step_up(pdr_rel_width, pdr_lo.target_tr)
+ logging.info("Bisecting for PDR at %s", new_tr)
+ state = self._measure_and_update_state(state, new_tr)
+ continue
+ # We do not need to improve width, but there still might be
+ # some measurements with smaller duration.
+ # We need to re-measure with full duration, possibly
+ # creating invalid bounds to resolve (thus broadening width).
+ if ndr_lo.duration < state.duration:
+ logging.info("re-measuring NDR lower bound")
+ self._measure_and_update_state(state, ndr_lo.target_tr)
+ continue
+ if pdr_lo.duration < state.duration:
+ logging.info("re-measuring PDR lower bound")
+ self._measure_and_update_state(state, pdr_lo.target_tr)
+ continue
+ # Except when lower bounds have high loss fraction, in that case
+ # we do not need to re-measure _upper_ bounds.
+ if ndr_hi.duration < state.duration and ndr_rel_width > 0.0:
+ logging.info("re-measuring NDR upper bound")
+ self._measure_and_update_state(state, ndr_hi.target_tr)
+ continue
+ if pdr_hi.duration < state.duration and pdr_rel_width > 0.0:
+ logging.info("re-measuring PDR upper bound")
+ self._measure_and_update_state(state, pdr_hi.target_tr)
+ continue
+ # Widths are narrow (or lower bound minimal), bound measurements
+ # are long enough, we can return.
+ logging.info("phase done")
+ break
+ return state
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