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// Implements a data structure for quality attenuation.
package qualityattenuation
import (
"fmt"
"math"
"github.com/influxdata/tdigest"
)
type cablelabsHist struct {
hist [256]float64
}
func (h *cablelabsHist) GetHistogram() [256]float64 {
return h.hist
}
func (h *cablelabsHist) AddSample(sample float64) error {
bin := 0
if sample < 0.050 {
// Round down
bin = int(sample / 0.0005)
h.hist[bin]++
} else if sample < 0.150 {
bin = int((sample - 0.050) / 0.001)
h.hist[100+bin]++
} else if sample < 1.150 {
bin = int((sample - 0.150) / 0.020)
h.hist[200+bin]++
} else if sample < 1.400 {
bin = 250
h.hist[bin]++
} else if sample < 3.000 {
bin = int((sample - 1.400) / 0.400)
h.hist[251+bin]++
} else {
bin = 255
h.hist[bin]++
}
return nil
}
type SimpleQualityAttenuation struct {
empiricalDistribution *tdigest.TDigest
offset float64
offsetSum float64
offsetSumOfSquares float64
numberOfSamples int64
numberOfLosses int64
latencyEqLossThreshold float64
minimumLatency float64
maximumLatency float64
}
type percentileLatencyPair struct {
percentile float64
perfectLatency float64
uselessLatency float64
}
type qualityRequirement struct {
latencyRequirements []percentileLatencyPair
}
func NewSimpleQualityAttenuation() *SimpleQualityAttenuation {
return &SimpleQualityAttenuation{
empiricalDistribution: tdigest.NewWithCompression(50),
offset: 0.1,
offsetSum: 0.0,
offsetSumOfSquares: 0.0,
numberOfSamples: 0,
numberOfLosses: 0,
latencyEqLossThreshold: 15.0, // Count latency greater than this value as a loss.
minimumLatency: 0.0,
maximumLatency: 0.0,
}
}
func (qa *SimpleQualityAttenuation) AddSample(sample float64) error {
if sample <= 0.0 {
// Ignore zero or negative samples because they cannot be valid.
// TODO: This should raise a warning and/or trigger error handling.
return fmt.Errorf("sample is zero or negative")
}
qa.numberOfSamples++
if sample > qa.latencyEqLossThreshold {
qa.numberOfLosses++
return nil
} else {
if qa.minimumLatency == 0.0 || sample < qa.minimumLatency {
qa.minimumLatency = sample
}
if qa.maximumLatency == 0.0 || sample > qa.maximumLatency {
qa.maximumLatency = sample
}
qa.empiricalDistribution.Add(sample, 1)
qa.offsetSum += sample - qa.offset
qa.offsetSumOfSquares += (sample - qa.offset) * (sample - qa.offset)
}
return nil
}
func (qa *SimpleQualityAttenuation) GetNumberOfLosses() int64 {
return qa.numberOfLosses
}
func (qa *SimpleQualityAttenuation) GetNumberOfSamples() int64 {
return qa.numberOfSamples
}
func (qa *SimpleQualityAttenuation) GetPercentile(percentile float64) float64 {
return qa.empiricalDistribution.Quantile(percentile / 100)
}
func (qa *SimpleQualityAttenuation) GetAverage() float64 {
return qa.offsetSum/float64(qa.numberOfSamples-qa.numberOfLosses) + qa.offset
}
func (qa *SimpleQualityAttenuation) GetVariance() float64 {
number_of_latency_samples := float64(qa.numberOfSamples) - float64(qa.numberOfLosses)
return (qa.offsetSumOfSquares - (qa.offsetSum * qa.offsetSum / number_of_latency_samples)) / (number_of_latency_samples - 1)
}
func (qa *SimpleQualityAttenuation) GetStandardDeviation() float64 {
return math.Sqrt(qa.GetVariance())
}
func (qa *SimpleQualityAttenuation) GetMinimum() float64 {
return qa.minimumLatency
}
func (qa *SimpleQualityAttenuation) GetMaximum() float64 {
return qa.maximumLatency
}
func (qa *SimpleQualityAttenuation) GetMedian() float64 {
return qa.GetPercentile(50.0)
}
func (qa *SimpleQualityAttenuation) GetLossPercentage() float64 {
return 100 * float64(qa.numberOfLosses) / float64(qa.numberOfSamples)
}
func (qa *SimpleQualityAttenuation) GetRPM() float64 {
return 60.0 / qa.GetAverage()
}
func (qa *SimpleQualityAttenuation) GetPDV(percentile float64) float64 {
return qa.GetPercentile(percentile) - qa.GetMinimum()
}
func (qa *SimpleQualityAttenuation) PrintCablelabsStatisticsSummary() string {
// Prints a digest based on Cablelabs Latency Measurements Metrics and Architeture, CL-TR-LM-Arch-V01-221123, https://www.cablelabs.com/specifications/CL-TR-LM-Arch
// The recommendation is to report the following percentiles: 0, 10, 25, 50, 75, 90, 95, 99, 99.9 and 100
return fmt.Sprintf("Cablelabs Statistics Summary:\n"+
"0th Percentile: %f\n"+
"10th Percentile: %f\n"+
"25th Percentile: %f\n"+
"50th Percentile: %f\n"+
"75th Percentile: %f\n"+
"90th Percentile: %f\n"+
"95th Percentile: %f\n"+
"99th Percentile: %f\n"+
"99.9th Percentile: %f\n"+
"100th Percentile: %f\n",
qa.GetPercentile(0.0),
qa.GetPercentile(10.0),
qa.GetPercentile(25.0),
qa.GetPercentile(50.0),
qa.GetPercentile(75.0),
qa.GetPercentile(90.0),
qa.GetPercentile(95.0),
qa.GetPercentile(99.0),
qa.GetPercentile(99.9),
qa.GetPercentile(100.0))
}
// Merge two quality attenuation values. This operation assumes the two samples have the same offset and latency_eq_loss_threshold, and
// will return an error if they do not.
// It also assumes that the two quality attenuation values are measurements of the same thing (path, outcome, etc.).
func (qa *SimpleQualityAttenuation) Merge(other *SimpleQualityAttenuation) error {
// Check that offsets are the same
if qa.offset != other.offset ||
qa.latencyEqLossThreshold != other.latencyEqLossThreshold {
return fmt.Errorf("merge quality attenuation values with different offset or latency_eq_loss_threshold")
}
for _, centroid := range other.empiricalDistribution.Centroids() {
mean := centroid.Mean
weight := centroid.Weight
qa.empiricalDistribution.Add(mean, weight)
}
qa.offsetSum += other.offsetSum
qa.offsetSumOfSquares += other.offsetSumOfSquares
qa.numberOfSamples += other.numberOfSamples
qa.numberOfLosses += other.numberOfLosses
if other.minimumLatency < qa.minimumLatency {
qa.minimumLatency = other.minimumLatency
}
if other.maximumLatency > qa.maximumLatency {
qa.maximumLatency = other.maximumLatency
}
return nil
}
func (qa *SimpleQualityAttenuation) EmpiricalDistributionHistogram() []float64 {
// Convert the tdigest to a histogram on the format defined by CableLabs, with the following bucket edges:
// 100 bins from 0 to 50 ms, each 0.5 ms wide
// 100 bins from 50 to 100 ms, each 1 ms wide
// 50 bins from 150 to 1150 ms, each 20 ms wide
// 1 bin from 1150 to 1400 ms, 250 ms wide
// 4 bins from 1400 to 3000 ms, each 400 ms wide
hist := make([]float64, 256)
for i := 0; i < 100; i++ {
hist[i] = float64(qa.numberOfSamples) * (qa.empiricalDistribution.CDF(float64(i+1)*0.0005) - qa.empiricalDistribution.CDF(float64(i)*0.0005))
}
for i := 100; i < 200; i++ {
hist[i] = float64(qa.numberOfSamples) * (qa.empiricalDistribution.CDF(0.050+float64(i-99)*0.001) - qa.empiricalDistribution.CDF(0.050+float64(i-100)*0.001))
}
for i := 200; i < 250; i++ {
hist[i] = float64(qa.numberOfSamples) * (qa.empiricalDistribution.CDF(0.150+float64(i-199)*0.020) - qa.empiricalDistribution.CDF(0.150+float64(i-200)*0.020))
}
for i := 250; i < 251; i++ {
hist[i] = float64(qa.numberOfSamples) * (qa.empiricalDistribution.CDF(1.150+0.250) - qa.empiricalDistribution.CDF(1.150))
}
for i := 251; i < 255; i++ {
hist[i] = float64(qa.numberOfSamples) * (qa.empiricalDistribution.CDF(1.400+float64(i-250)*0.400) - qa.empiricalDistribution.CDF(1.400+float64(i-251)*0.400))
}
hist[255] = float64(qa.numberOfSamples) * (1 - qa.empiricalDistribution.CDF(3.000))
return hist
}
// Compute the Quality of Outcome (QoO) for a given quality requirement.
// The details and motivation for the QoO metric are described in the following internet draft:
// https://datatracker.ietf.org/doc/draft-olden-ippm-qoo/
func (qa *SimpleQualityAttenuation) QoO(requirement qualityRequirement) float64 {
QoO := 100.0
for _, percentileLatencyPair := range requirement.latencyRequirements {
score := 0.0
percentile := percentileLatencyPair.percentile
perfectLatency := percentileLatencyPair.perfectLatency
uselessLatency := percentileLatencyPair.uselessLatency
latency := qa.GetPercentile(percentile)
if latency >= uselessLatency {
score = 0.0
} else if latency <= perfectLatency {
score = 100.0
} else {
score = 100 * ((uselessLatency - latency) / (uselessLatency - perfectLatency))
}
if score < QoO {
QoO = score
}
}
return QoO
}
func (qa *SimpleQualityAttenuation) GetGamingQoO() float64 {
qualReq := qualityRequirement{}
qualReq.latencyRequirements = []percentileLatencyPair{}
qualReq.latencyRequirements = append(qualReq.latencyRequirements, percentileLatencyPair{percentile: 50.0, perfectLatency: 0.030, uselessLatency: 0.150})
qualReq.latencyRequirements = append(qualReq.latencyRequirements, percentileLatencyPair{percentile: 95.0, perfectLatency: 0.065, uselessLatency: 0.200})
qualReq.latencyRequirements = append(qualReq.latencyRequirements, percentileLatencyPair{percentile: 99.0, perfectLatency: 0.100, uselessLatency: 0.250})
return qa.QoO(qualReq)
}
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