聊聊rsocket load balancer的Ewma

Posted 2021-04-25 码匠的流水账

序

本文主要研究一下rsocket load balancer的Ewma

Moving Average

SMA

SMA(Simple Moving Average)，即简单移动平均，其公式如下：

SMAt = (Pt + Pt-1 + Pt-2 + Pt-3 + ... + Pt-n+1) / n

这里的Pt到为Pt-n+1为最近的n个数据

WMA

WMA(Weighted Moving Average)，即加权移动平均，其公式如下：

WMAt = (Pt * Wt) + (Pt-1 * Wt-1) + ... + (Pt-n+1 * Wt-n+1)

WMA会给最近的n个数据加上权重，其中这些权重加起来和为1，一般是较近的数据权重比较大

EMA或EWMA

EMA(Exponentially Moving Average)指数移动平均或EWMA(Exponentially Weighted Moving Average)指数加权移动平均，其公式如下：

EMAt = (Pt * S) + (1- S) * EMAt-1

它有一个S参数为平滑指数，一般是取2/(N+1)

Ewma

rsocket-load-balancer-0.12.1-sources.jar!/io/rsocket/stat/Ewma.java

public class Ewma {
  private final long tau;
  private volatile long stamp;
  private volatile double ewma;

  public Ewma(long halfLife, TimeUnit unit, double initialValue) {
    this.tau = Clock.unit().convert((long) (halfLife / Math.log(2)), unit);
    stamp = 0L;
    ewma = initialValue;
  }

  public synchronized void insert(double x) {
    long now = Clock.now();
    double elapsed = Math.max(0, now - stamp);
    stamp = now;

    double w = Math.exp(-elapsed / tau);
    ewma = w * ewma + (1.0 - w) * x;
  }

  public synchronized void reset(double value) {
    stamp = 0L;
    ewma = value;
  }

  public double value() {
    return ewma;
  }

  @Override
  public String toString() {
    return "Ewma(value=" + ewma + ", age=" + (Clock.now() - stamp) + ")";
  }
}

• Ewma的构造器需要指定halfLife、timeunit、initialValue(ewma初始值)参数；ewma = w * ewma + (1.0 - w) * x，其中x为当前值，w为权重

• 权重w = Math.exp(-elapsed / tau)，即e的-elapsed / tau次方；elapsed为距离上次计算的时间长度；tau(希腊字母)为EWMA的时间常量

• 这里的tau = halfLife / Math.log(2)根据timeunit转换后的值；其中halfLife参数，代表speed of convergence，即收敛的速度

RSocketSupplier

rsocket-load-balancer-0.12.1-sources.jar!/io/rsocket/client/filter/RSocketSupplier.java

public class RSocketSupplier implements Availability, Supplier<Mono<RSocket>>, Closeable {

  private static final double EPSILON = 1e-4;

  private Supplier<Mono<RSocket>> rSocketSupplier;

  private final MonoProcessor<Void> onClose;

  private final long tau;
  private long stamp;
  private final Ewma errorPercentage;

  public RSocketSupplier(Supplier<Mono<RSocket>> rSocketSupplier, long halfLife, TimeUnit unit) {
    this.rSocketSupplier = rSocketSupplier;
    this.tau = Clock.unit().convert((long) (halfLife / Math.log(2)), unit);
    this.stamp = Clock.now();
    this.errorPercentage = new Ewma(halfLife, unit, 1.0);
    this.onClose = MonoProcessor.create();
  }

  public RSocketSupplier(Supplier<Mono<RSocket>> rSocketSupplier) {
    this(rSocketSupplier, 5, TimeUnit.SECONDS);
  }

  @Override
  public double availability() {
    double e = errorPercentage.value();
    if (Clock.now() - stamp > tau) {
      // If the window is expired artificially increase the availability
      double a = Math.min(1.0, e + 0.5);
      errorPercentage.reset(a);
    }
    if (e < EPSILON) {
      e = 0.0;
    } else if (1.0 - EPSILON < e) {
      e = 1.0;
    }

    return e;
  }

  private synchronized void updateErrorPercentage(double value) {
    errorPercentage.insert(value);
    stamp = Clock.now();
  }

  @Override
  public Mono<RSocket> get() {
    return rSocketSupplier
        .get()
        .doOnNext(o -> updateErrorPercentage(1.0))
        .doOnError(t -> updateErrorPercentage(0.0))
        .map(AvailabilityAwareRSocketProxy::new);
  }

  @Override
  public void dispose() {
    onClose.onComplete();
  }

  @Override
  public boolean isDisposed() {
    return onClose.isDisposed();
  }

  @Override
  public Mono<Void> onClose() {
    return onClose;
  }

  private class AvailabilityAwareRSocketProxy extends RSocketProxy {
    public AvailabilityAwareRSocketProxy(RSocket source) {
      super(source);

      onClose.doFinally(signalType -> source.dispose()).subscribe();
    }

    @Override
    public Mono<Void> fireAndForget(Payload payload) {
      return source
          .fireAndForget(payload)
          .doOnError(t -> errorPercentage.insert(0.0))
          .doOnSuccess(v -> updateErrorPercentage(1.0));
    }

    @Override
    public Mono<Payload> requestResponse(Payload payload) {
      return source
          .requestResponse(payload)
          .doOnError(t -> errorPercentage.insert(0.0))
          .doOnSuccess(p -> updateErrorPercentage(1.0));
    }

    @Override
    public Flux<Payload> requestStream(Payload payload) {
      return source
          .requestStream(payload)
          .doOnError(th -> errorPercentage.insert(0.0))
          .doOnComplete(() -> updateErrorPercentage(1.0));
    }

    @Override
    public Flux<Payload> requestChannel(Publisher<Payload> payloads) {
      return source
          .requestChannel(payloads)
          .doOnError(th -> errorPercentage.insert(0.0))
          .doOnComplete(() -> updateErrorPercentage(1.0));
    }

    @Override
    public Mono<Void> metadataPush(Payload payload) {
      return source
          .metadataPush(payload)
          .doOnError(t -> errorPercentage.insert(0.0))
          .doOnSuccess(v -> updateErrorPercentage(1.0));
    }

    @Override
    public double availability() {
      // If the window is expired set success and failure to zero and return
      // the child availability
      if (Clock.now() - stamp > tau) {
        updateErrorPercentage(1.0);
      }
      return source.availability() * errorPercentage.value();
    }
  }
}

• RSocketSupplier实现了Availability、Supplier、Closeable接口，其中它定义了errorPercentage变量，其类型为Ewma；如果没有指定halfLife值，则RSocketSupplier默认halfLife为5秒，ewma的初始值为1.0

• RSocketSupplier定义了一个常量EPSILON = 1e-4，其availability方法会先计算availability，然后在距离上次计算时间stamp超过tau值时会重置errorPercentage；之后当availability小于EPSILON时返回0，当availability + EPSILON大于1时返回1.0

• updateErrorPercentage方法用于往ewma插入新值，同时更新stamp；get方法的doOnNext方法updateErrorPercentage值为1.0，doOnError方法updateErrorPercentage值为0.0；map会将RSocket转换为AvailabilityAwareRSocketProxy；AvailabilityAwareRSocketProxy对目标RSocket进行代理，对相关方法的doOnError及doOnSuccess都织入errorPercentage的统计

小结

• Moving Average有好几种算法，包括SMA(Simple Moving Average)、WMA(Weighted Moving Average)、EMA(Exponentially Moving Average)或EWMA(Exponentially Weighted Moving Average)

• Ewma的构造器需要指定halfLife、timeunit、initialValue(ewma初始值)参数；ewma = w * ewma + (1.0 - w) * x，其中x为当前值，w为权重；权重w = Math.exp(-elapsed / tau)，即e的-elapsed / tau次方；elapsed为距离上次计算的时间长度；tau(希腊字母)为EWMA的时间常量；这里的tau = halfLife / Math.log(2)根据timeunit转换后的值；其中halfLife参数，代表speed of convergence，即收敛的速度

• rsocket load balancer使用了Ewma了统计服务的availability；其中RSocketSupplier实现了Availability、Supplier、Closeable接口，其中它定义了errorPercentage变量，其类型为Ewma；如果没有指定halfLife值，则RSocketSupplier默认halfLife为5秒，ewma的初始值为1.0；RSocketSupplier的get方法会将RSocket转换为AvailabilityAwareRSocketProxy，而AvailabilityAwareRSocketProxy则会对目标RSocket进行代理，对相关方法的doOnError及doOnSuccess都织入errorPercentage的统计

doc

• Simple Moving Average - SMA Definition

• Weighted Moving Averages: The Basics

• Exponential Moving Average - EMA Definition

• How Is the Exponential Moving Average (EMA) Formula Calculated?

• Moving Average, Weighted Moving Average, and Exponential Moving Average

• Exploring the Exponentially Weighted Moving Average

• EWMA 移动平均模型

• rsocket EWMA