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// Copyright 2016 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#ifndef QUICHE_QUIC_CORE_CONGESTION_CONTROL_BANDWIDTH_SAMPLER_H_
#define QUICHE_QUIC_CORE_CONGESTION_CONTROL_BANDWIDTH_SAMPLER_H_
#include "quic/core/congestion_control/send_algorithm_interface.h"
#include "quic/core/congestion_control/windowed_filter.h"
#include "quic/core/packet_number_indexed_queue.h"
#include "quic/core/quic_bandwidth.h"
#include "quic/core/quic_packet_number.h"
#include "quic/core/quic_packets.h"
#include "quic/core/quic_time.h"
#include "quic/core/quic_types.h"
#include "quic/core/quic_unacked_packet_map.h"
#include "quic/platform/api/quic_export.h"
#include "quic/platform/api/quic_flags.h"
#include "common/quiche_circular_deque.h"
namespace quic {
namespace test {
class BandwidthSamplerPeer;
} // namespace test
// A subset of BandwidthSampler::ConnectionStateOnSentPacket which is returned
// to the caller when the packet is acked or lost.
struct QUIC_EXPORT_PRIVATE SendTimeState {
SendTimeState()
: is_valid(false),
is_app_limited(false),
total_bytes_sent(0),
total_bytes_acked(0),
total_bytes_lost(0),
bytes_in_flight(0) {}
SendTimeState(bool is_app_limited,
QuicByteCount total_bytes_sent,
QuicByteCount total_bytes_acked,
QuicByteCount total_bytes_lost,
QuicByteCount bytes_in_flight)
: is_valid(true),
is_app_limited(is_app_limited),
total_bytes_sent(total_bytes_sent),
total_bytes_acked(total_bytes_acked),
total_bytes_lost(total_bytes_lost),
bytes_in_flight(bytes_in_flight) {}
SendTimeState(const SendTimeState& other) = default;
SendTimeState& operator=(const SendTimeState& other) = default;
friend QUIC_EXPORT_PRIVATE std::ostream& operator<<(std::ostream& os,
const SendTimeState& s);
// Whether other states in this object is valid.
bool is_valid;
// Whether the sender is app limited at the time the packet was sent.
// App limited bandwidth sample might be artificially low because the sender
// did not have enough data to send in order to saturate the link.
bool is_app_limited;
// Total number of sent bytes at the time the packet was sent.
// Includes the packet itself.
QuicByteCount total_bytes_sent;
// Total number of acked bytes at the time the packet was sent.
QuicByteCount total_bytes_acked;
// Total number of lost bytes at the time the packet was sent.
QuicByteCount total_bytes_lost;
// Total number of inflight bytes at the time the packet was sent.
// Includes the packet itself.
// It should be equal to |total_bytes_sent| minus the sum of
// |total_bytes_acked|, |total_bytes_lost| and total neutered bytes.
QuicByteCount bytes_in_flight;
};
struct QUIC_NO_EXPORT ExtraAckedEvent {
// The excess bytes acknowlwedged in the time delta for this event.
QuicByteCount extra_acked = 0;
// The bytes acknowledged and time delta from the event.
QuicByteCount bytes_acked = 0;
QuicTime::Delta time_delta = QuicTime::Delta::Zero();
// The round trip of the event.
QuicRoundTripCount round = 0;
inline bool operator>=(const ExtraAckedEvent& other) const {
return extra_acked >= other.extra_acked;
}
inline bool operator==(const ExtraAckedEvent& other) const {
return extra_acked == other.extra_acked;
}
};
struct QUIC_EXPORT_PRIVATE BandwidthSample {
// The bandwidth at that particular sample. Zero if no valid bandwidth sample
// is available.
QuicBandwidth bandwidth = QuicBandwidth::Zero();
// The RTT measurement at this particular sample. Zero if no RTT sample is
// available. Does not correct for delayed ack time.
QuicTime::Delta rtt = QuicTime::Delta::Zero();
// |send_rate| is computed from the current packet being acked('P') and an
// earlier packet that is acked before P was sent.
QuicBandwidth send_rate = QuicBandwidth::Infinite();
// States captured when the packet was sent.
SendTimeState state_at_send;
};
// MaxAckHeightTracker is part of the BandwidthSampler. It is called after every
// ack event to keep track the degree of ack aggregation(a.k.a "ack height").
class QUIC_EXPORT_PRIVATE MaxAckHeightTracker {
public:
explicit MaxAckHeightTracker(QuicRoundTripCount initial_filter_window)
: max_ack_height_filter_(initial_filter_window, ExtraAckedEvent(), 0) {}
QuicByteCount Get() const {
return max_ack_height_filter_.GetBest().extra_acked;
}
QuicByteCount Update(QuicBandwidth bandwidth_estimate,
bool is_new_max_bandwidth,
QuicRoundTripCount round_trip_count,
QuicPacketNumber last_sent_packet_number,
QuicPacketNumber last_acked_packet_number,
QuicTime ack_time, QuicByteCount bytes_acked);
void SetFilterWindowLength(QuicRoundTripCount length) {
max_ack_height_filter_.SetWindowLength(length);
}
void Reset(QuicByteCount new_height, QuicRoundTripCount new_time) {
ExtraAckedEvent new_event;
new_event.extra_acked = new_height;
new_event.round = new_time;
max_ack_height_filter_.Reset(new_event, new_time);
}
void SetAckAggregationBandwidthThreshold(double threshold) {
ack_aggregation_bandwidth_threshold_ = threshold;
}
void SetStartNewAggregationEpochAfterFullRound(bool value) {
start_new_aggregation_epoch_after_full_round_ = value;
}
void SetReduceExtraAckedOnBandwidthIncrease(bool value) {
reduce_extra_acked_on_bandwidth_increase_ = value;
}
double ack_aggregation_bandwidth_threshold() const {
return ack_aggregation_bandwidth_threshold_;
}
uint64_t num_ack_aggregation_epochs() const {
return num_ack_aggregation_epochs_;
}
private:
// Tracks the maximum number of bytes acked faster than the estimated
// bandwidth.
using MaxAckHeightFilter =
WindowedFilter<ExtraAckedEvent, MaxFilter<ExtraAckedEvent>,
QuicRoundTripCount, QuicRoundTripCount>;
MaxAckHeightFilter max_ack_height_filter_;
// The time this aggregation started and the number of bytes acked during it.
QuicTime aggregation_epoch_start_time_ = QuicTime::Zero();
QuicByteCount aggregation_epoch_bytes_ = 0;
// The last sent packet number before the current aggregation epoch started.
QuicPacketNumber last_sent_packet_number_before_epoch_;
// The number of ack aggregation epochs ever started, including the ongoing
// one. Stats only.
uint64_t num_ack_aggregation_epochs_ = 0;
double ack_aggregation_bandwidth_threshold_ =
GetQuicFlag(FLAGS_quic_ack_aggregation_bandwidth_threshold);
bool start_new_aggregation_epoch_after_full_round_ = false;
bool reduce_extra_acked_on_bandwidth_increase_ = false;
};
// An interface common to any class that can provide bandwidth samples from the
// information per individual acknowledged packet.
class QUIC_EXPORT_PRIVATE BandwidthSamplerInterface {
public:
virtual ~BandwidthSamplerInterface() {}
// Inputs the sent packet information into the sampler. Assumes that all
// packets are sent in order. The information about the packet will not be
// released from the sampler until it the packet is either acknowledged or
// declared lost.
virtual void OnPacketSent(
QuicTime sent_time,
QuicPacketNumber packet_number,
QuicByteCount bytes,
QuicByteCount bytes_in_flight,
HasRetransmittableData has_retransmittable_data) = 0;
virtual void OnPacketNeutered(QuicPacketNumber packet_number) = 0;
struct QUIC_NO_EXPORT CongestionEventSample {
// The maximum bandwidth sample from all acked packets.
// QuicBandwidth::Zero() if no samples are available.
QuicBandwidth sample_max_bandwidth = QuicBandwidth::Zero();
// Whether |sample_max_bandwidth| is from a app-limited sample.
bool sample_is_app_limited = false;
// The minimum rtt sample from all acked packets.
// QuicTime::Delta::Infinite() if no samples are available.
QuicTime::Delta sample_rtt = QuicTime::Delta::Infinite();
// For each packet p in acked packets, this is the max value of INFLIGHT(p),
// where INFLIGHT(p) is the number of bytes acked while p is inflight.
QuicByteCount sample_max_inflight = 0;
// The send state of the largest packet in acked_packets, unless it is
// empty. If acked_packets is empty, it's the send state of the largest
// packet in lost_packets.
SendTimeState last_packet_send_state;
// The number of extra bytes acked from this ack event, compared to what is
// expected from the flow's bandwidth. Larger value means more ack
// aggregation.
QuicByteCount extra_acked = 0;
};
// Notifies the sampler that at |ack_time|, all packets in |acked_packets|
// have been acked, and all packets in |lost_packets| have been lost.
// See the comments in CongestionEventSample for the return value.
// |max_bandwidth| is the windowed maximum observed bandwidth.
// |est_bandwidth_upper_bound| is an upper bound of estimated bandwidth used
// to calculate extra_acked.
virtual CongestionEventSample OnCongestionEvent(
QuicTime ack_time,
const AckedPacketVector& acked_packets,
const LostPacketVector& lost_packets,
QuicBandwidth max_bandwidth,
QuicBandwidth est_bandwidth_upper_bound,
QuicRoundTripCount round_trip_count) = 0;
// Informs the sampler that the connection is currently app-limited, causing
// the sampler to enter the app-limited phase. The phase will expire by
// itself.
virtual void OnAppLimited() = 0;
// Remove all the packets lower than the specified packet number.
virtual void RemoveObsoletePackets(QuicPacketNumber least_unacked) = 0;
// Total number of bytes sent/acked/lost/neutered in the connection.
virtual QuicByteCount total_bytes_sent() const = 0;
virtual QuicByteCount total_bytes_acked() const = 0;
virtual QuicByteCount total_bytes_lost() const = 0;
virtual QuicByteCount total_bytes_neutered() const = 0;
// Application-limited information exported for debugging.
virtual bool is_app_limited() const = 0;
virtual QuicPacketNumber end_of_app_limited_phase() const = 0;
};
// BandwidthSampler keeps track of sent and acknowledged packets and outputs a
// bandwidth sample for every packet acknowledged. The samples are taken for
// individual packets, and are not filtered; the consumer has to filter the
// bandwidth samples itself. In certain cases, the sampler will locally severely
// underestimate the bandwidth, hence a maximum filter with a size of at least
// one RTT is recommended.
//
// This class bases its samples on the slope of two curves: the number of bytes
// sent over time, and the number of bytes acknowledged as received over time.
// It produces a sample of both slopes for every packet that gets acknowledged,
// based on a slope between two points on each of the corresponding curves. Note
// that due to the packet loss, the number of bytes on each curve might get
// further and further away from each other, meaning that it is not feasible to
// compare byte values coming from different curves with each other.
//
// The obvious points for measuring slope sample are the ones corresponding to
// the packet that was just acknowledged. Let us denote them as S_1 (point at
// which the current packet was sent) and A_1 (point at which the current packet
// was acknowledged). However, taking a slope requires two points on each line,
// so estimating bandwidth requires picking a packet in the past with respect to
// which the slope is measured.
//
// For that purpose, BandwidthSampler always keeps track of the most recently
// acknowledged packet, and records it together with every outgoing packet.
// When a packet gets acknowledged (A_1), it has not only information about when
// it itself was sent (S_1), but also the information about a previously
// acknowledged packet before it was sent (S_0 and A_0).
//
// Based on that data, send and ack rate are estimated as:
// send_rate = (bytes(S_1) - bytes(S_0)) / (time(S_1) - time(S_0))
// ack_rate = (bytes(A_1) - bytes(A_0)) / (time(A_1) - time(A_0))
//
// Here, the ack rate is intuitively the rate we want to treat as bandwidth.
// However, in certain cases (e.g. ack compression) the ack rate at a point may
// end up higher than the rate at which the data was originally sent, which is
// not indicative of the real bandwidth. Hence, we use the send rate as an upper
// bound, and the sample value is
// rate_sample = min(send_rate, ack_rate)
//
// An important edge case handled by the sampler is tracking the app-limited
// samples. There are multiple meaning of "app-limited" used interchangeably,
// hence it is important to understand and to be able to distinguish between
// them.
//
// Meaning 1: connection state. The connection is said to be app-limited when
// there is no outstanding data to send. This means that certain bandwidth
// samples in the future would not be an accurate indication of the link
// capacity, and it is important to inform consumer about that. Whenever
// connection becomes app-limited, the sampler is notified via OnAppLimited()
// method.
//
// Meaning 2: a phase in the bandwidth sampler. As soon as the bandwidth
// sampler becomes notified about the connection being app-limited, it enters
// app-limited phase. In that phase, all *sent* packets are marked as
// app-limited. Note that the connection itself does not have to be
// app-limited during the app-limited phase, and in fact it will not be
// (otherwise how would it send packets?). The boolean flag below indicates
// whether the sampler is in that phase.
//
// Meaning 3: a flag on the sent packet and on the sample. If a sent packet is
// sent during the app-limited phase, the resulting sample related to the
// packet will be marked as app-limited.
//
// With the terminology issue out of the way, let us consider the question of
// what kind of situation it addresses.
//
// Consider a scenario where we first send packets 1 to 20 at a regular
// bandwidth, and then immediately run out of data. After a few seconds, we send
// packets 21 to 60, and only receive ack for 21 between sending packets 40 and
// 41. In this case, when we sample bandwidth for packets 21 to 40, the S_0/A_0
// we use to compute the slope is going to be packet 20, a few seconds apart
// from the current packet, hence the resulting estimate would be extremely low
// and not indicative of anything. Only at packet 41 the S_0/A_0 will become 21,
// meaning that the bandwidth sample would exclude the quiescence.
//
// Based on the analysis of that scenario, we implement the following rule: once
// OnAppLimited() is called, all sent packets will produce app-limited samples
// up until an ack for a packet that was sent after OnAppLimited() was called.
// Note that while the scenario above is not the only scenario when the
// connection is app-limited, the approach works in other cases too.
class QUIC_EXPORT_PRIVATE BandwidthSampler : public BandwidthSamplerInterface {
public:
BandwidthSampler(const QuicUnackedPacketMap* unacked_packet_map,
QuicRoundTripCount max_height_tracker_window_length);
// Copy states from |other|. This is useful when changing send algorithms in
// the middle of a connection.
BandwidthSampler(const BandwidthSampler& other);
~BandwidthSampler() override;
void OnPacketSent(QuicTime sent_time,
QuicPacketNumber packet_number,
QuicByteCount bytes,
QuicByteCount bytes_in_flight,
HasRetransmittableData has_retransmittable_data) override;
void OnPacketNeutered(QuicPacketNumber packet_number) override;
CongestionEventSample OnCongestionEvent(
QuicTime ack_time,
const AckedPacketVector& acked_packets,
const LostPacketVector& lost_packets,
QuicBandwidth max_bandwidth,
QuicBandwidth est_bandwidth_upper_bound,
QuicRoundTripCount round_trip_count) override;
QuicByteCount OnAckEventEnd(QuicBandwidth bandwidth_estimate,
bool is_new_max_bandwidth,
QuicRoundTripCount round_trip_count);
void OnAppLimited() override;
void RemoveObsoletePackets(QuicPacketNumber least_unacked) override;
QuicByteCount total_bytes_sent() const override;
QuicByteCount total_bytes_acked() const override;
QuicByteCount total_bytes_lost() const override;
QuicByteCount total_bytes_neutered() const override;
bool is_app_limited() const override;
QuicPacketNumber end_of_app_limited_phase() const override;
QuicByteCount max_ack_height() const { return max_ack_height_tracker_.Get(); }
uint64_t num_ack_aggregation_epochs() const {
return max_ack_height_tracker_.num_ack_aggregation_epochs();
}
void SetMaxAckHeightTrackerWindowLength(QuicRoundTripCount length) {
max_ack_height_tracker_.SetFilterWindowLength(length);
}
void ResetMaxAckHeightTracker(QuicByteCount new_height,
QuicRoundTripCount new_time) {
max_ack_height_tracker_.Reset(new_height, new_time);
}
void SetStartNewAggregationEpochAfterFullRound(bool value) {
max_ack_height_tracker_.SetStartNewAggregationEpochAfterFullRound(value);
}
void SetLimitMaxAckHeightTrackerBySendRate(bool value) {
limit_max_ack_height_tracker_by_send_rate_ = value;
}
void SetReduceExtraAckedOnBandwidthIncrease(bool value) {
max_ack_height_tracker_.SetReduceExtraAckedOnBandwidthIncrease(value);
}
// AckPoint represents a point on the ack line.
struct QUIC_NO_EXPORT AckPoint {
QuicTime ack_time = QuicTime::Zero();
QuicByteCount total_bytes_acked = 0;
friend QUIC_NO_EXPORT std::ostream& operator<<(std::ostream& os,
const AckPoint& ack_point) {
return os << ack_point.ack_time << ":" << ack_point.total_bytes_acked;
}
};
// RecentAckPoints maintains the most recent 2 ack points at distinct times.
class QUIC_NO_EXPORT RecentAckPoints {
public:
void Update(QuicTime ack_time, QuicByteCount total_bytes_acked) {
QUICHE_DCHECK_GE(total_bytes_acked, ack_points_[1].total_bytes_acked);
if (ack_time < ack_points_[1].ack_time) {
// This can only happen when time goes backwards, we use the smaller
// timestamp for the most recent ack point in that case.
// TODO(wub): Add a QUIC_BUG if ack time stops going backwards.
ack_points_[1].ack_time = ack_time;
} else if (ack_time > ack_points_[1].ack_time) {
ack_points_[0] = ack_points_[1];
ack_points_[1].ack_time = ack_time;
}
ack_points_[1].total_bytes_acked = total_bytes_acked;
}
void Clear() { ack_points_[0] = ack_points_[1] = AckPoint(); }
const AckPoint& MostRecentPoint() const { return ack_points_[1]; }
const AckPoint& LessRecentPoint() const {
if (ack_points_[0].total_bytes_acked != 0) {
return ack_points_[0];
}
return ack_points_[1];
}
private:
AckPoint ack_points_[2];
};
void EnableOverestimateAvoidance();
bool IsOverestimateAvoidanceEnabled() const {
return overestimate_avoidance_;
}
private:
friend class test::BandwidthSamplerPeer;
// ConnectionStateOnSentPacket represents the information about a sent packet
// and the state of the connection at the moment the packet was sent,
// specifically the information about the most recently acknowledged packet at
// that moment.
struct QUIC_EXPORT_PRIVATE ConnectionStateOnSentPacket {
// Time at which the packet is sent.
QuicTime sent_time;
// Size of the packet.
QuicByteCount size;
// The value of |total_bytes_sent_at_last_acked_packet_| at the time the
// packet was sent.
QuicByteCount total_bytes_sent_at_last_acked_packet;
// The value of |last_acked_packet_sent_time_| at the time the packet was
// sent.
QuicTime last_acked_packet_sent_time;
// The value of |last_acked_packet_ack_time_| at the time the packet was
// sent.
QuicTime last_acked_packet_ack_time;
// Send time states that are returned to the congestion controller when the
// packet is acked or lost.
SendTimeState send_time_state;
// Snapshot constructor. Records the current state of the bandwidth
// sampler.
// |bytes_in_flight| is the bytes in flight right after the packet is sent.
ConnectionStateOnSentPacket(QuicTime sent_time,
QuicByteCount size,
QuicByteCount bytes_in_flight,
const BandwidthSampler& sampler)
: sent_time(sent_time),
size(size),
total_bytes_sent_at_last_acked_packet(
sampler.total_bytes_sent_at_last_acked_packet_),
last_acked_packet_sent_time(sampler.last_acked_packet_sent_time_),
last_acked_packet_ack_time(sampler.last_acked_packet_ack_time_),
send_time_state(sampler.is_app_limited_,
sampler.total_bytes_sent_,
sampler.total_bytes_acked_,
sampler.total_bytes_lost_,
bytes_in_flight) {}
// Default constructor. Required to put this structure into
// PacketNumberIndexedQueue.
ConnectionStateOnSentPacket()
: sent_time(QuicTime::Zero()),
size(0),
total_bytes_sent_at_last_acked_packet(0),
last_acked_packet_sent_time(QuicTime::Zero()),
last_acked_packet_ack_time(QuicTime::Zero()) {}
friend QUIC_EXPORT_PRIVATE std::ostream& operator<<(
std::ostream& os,
const ConnectionStateOnSentPacket& p) {
os << "{sent_time:" << p.sent_time << ", size:" << p.size
<< ", total_bytes_sent_at_last_acked_packet:"
<< p.total_bytes_sent_at_last_acked_packet
<< ", last_acked_packet_sent_time:" << p.last_acked_packet_sent_time
<< ", last_acked_packet_ack_time:" << p.last_acked_packet_ack_time
<< ", send_time_state:" << p.send_time_state << "}";
return os;
}
};
BandwidthSample OnPacketAcknowledged(QuicTime ack_time,
QuicPacketNumber packet_number);
SendTimeState OnPacketLost(QuicPacketNumber packet_number,
QuicPacketLength bytes_lost);
// Copy a subset of the (private) ConnectionStateOnSentPacket to the (public)
// SendTimeState. Always set send_time_state->is_valid to true.
void SentPacketToSendTimeState(const ConnectionStateOnSentPacket& sent_packet,
SendTimeState* send_time_state) const;
// Choose the best a0 from |a0_candidates_| to calculate the ack rate.
// |total_bytes_acked| is the total bytes acked when the packet being acked is
// sent. The best a0 is chosen as follows:
// - If there's only one candidate, use it.
// - If there are multiple candidates, let a[n] be the nth candidate, and
// a[n-1].total_bytes_acked <= |total_bytes_acked| < a[n].total_bytes_acked,
// use a[n-1].
// - If all candidates's total_bytes_acked is > |total_bytes_acked|, use a[0].
// This may happen when acks are received out of order, and ack[n] caused
// some candidates of ack[n-x] to be removed.
// - If all candidates's total_bytes_acked is <= |total_bytes_acked|, use
// a[a.size()-1].
bool ChooseA0Point(QuicByteCount total_bytes_acked, AckPoint* a0);
// The total number of congestion controlled bytes sent during the connection.
QuicByteCount total_bytes_sent_;
// The total number of congestion controlled bytes which were acknowledged.
QuicByteCount total_bytes_acked_;
// The total number of congestion controlled bytes which were lost.
QuicByteCount total_bytes_lost_;
// The total number of congestion controlled bytes which have been neutered.
QuicByteCount total_bytes_neutered_;
// The value of |total_bytes_sent_| at the time the last acknowledged packet
// was sent. Valid only when |last_acked_packet_sent_time_| is valid.
QuicByteCount total_bytes_sent_at_last_acked_packet_;
// The time at which the last acknowledged packet was sent. Set to
// QuicTime::Zero() if no valid timestamp is available.
QuicTime last_acked_packet_sent_time_;
// The time at which the most recent packet was acknowledged.
QuicTime last_acked_packet_ack_time_;
// The most recently sent packet.
QuicPacketNumber last_sent_packet_;
// The most recently acked packet.
QuicPacketNumber last_acked_packet_;
// Indicates whether the bandwidth sampler is currently in an app-limited
// phase.
bool is_app_limited_;
// The packet that will be acknowledged after this one will cause the sampler
// to exit the app-limited phase.
QuicPacketNumber end_of_app_limited_phase_;
// Record of the connection state at the point where each packet in flight was
// sent, indexed by the packet number.
PacketNumberIndexedQueue<ConnectionStateOnSentPacket> connection_state_map_;
RecentAckPoints recent_ack_points_;
quiche::QuicheCircularDeque<AckPoint> a0_candidates_;
// Maximum number of tracked packets.
const QuicPacketCount max_tracked_packets_;
// The main unacked packet map. Used for outputting extra debugging details.
// May be null.
// TODO(vasilvv): remove this once it's no longer useful for debugging.
const QuicUnackedPacketMap* unacked_packet_map_;
// Handles the actual bandwidth calculations, whereas the outer method handles
// retrieving and removing |sent_packet|.
BandwidthSample OnPacketAcknowledgedInner(
QuicTime ack_time,
QuicPacketNumber packet_number,
const ConnectionStateOnSentPacket& sent_packet);
MaxAckHeightTracker max_ack_height_tracker_;
QuicByteCount total_bytes_acked_after_last_ack_event_;
// True if connection option 'BSAO' is set.
bool overestimate_avoidance_;
// True if connection option 'BBRB' is set.
bool limit_max_ack_height_tracker_by_send_rate_;
};
} // namespace quic
#endif // QUICHE_QUIC_CORE_CONGESTION_CONTROL_BANDWIDTH_SAMPLER_H_