Github user dragos commented on a diff in the pull request:

    https://github.com/apache/spark/pull/7648#discussion_r35869487
  
    --- Diff: 
streaming/src/main/scala/org/apache/spark/streaming/scheduler/rate/PIDRateEstimator.scala
 ---
    @@ -0,0 +1,100 @@
    +/*
    + * Licensed to the Apache Software Foundation (ASF) under one or more
    + * contributor license agreements.  See the NOTICE file distributed with
    + * this work for additional information regarding copyright ownership.
    + * The ASF licenses this file to You 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.
    + */
    +
    +package org.apache.spark.streaming.scheduler.rate
    +
    +/**
    + * Implements a proportional-integral-derivative (PID) controller which 
acts on
    + * the speed of ingestion of elements into Spark Streaming. A PID 
controller works
    + * by calculating an '''error''' between a measured output and a desired 
value. In the
    + * case of Spark Streaming the error is the difference between the 
measured processing
    + * rate (number of elements/processing delay) and the previous rate.
    + *
    + * @see https://en.wikipedia.org/wiki/PID_controller
    + *
    + * @param batchDurationMillis the batch duration, in milliseconds
    + * @param proportional how much the correction should depend on the current
    + *        error. This term usually provides the bulk of correction. A 
value too large would
    + *        make the controller overshoot the setpoint, while a small value 
would make the
    + *        controller too insensitive. The default value is -1.
    + * @param integral how much the correction should depend on the 
accumulation
    + *        of past errors. This term accelerates the movement towards the 
setpoint, but a large
    + *        value may lead to overshooting. The default value is -0.2.
    + * @param derivative how much the correction should depend on a prediction
    + *        of future errors, based on current rate of change. This term is 
not used very often,
    + *        as it impacts stability of the system. The default value is 0.
    + */
    +private[streaming] class PIDRateEstimator(
    +    batchIntervalMillis: Long,
    +    proportional: Double = -1D,
    +    integral: Double = -.2D,
    +    derivative: Double = 0D)
    +  extends RateEstimator {
    +
    +  private var firstRun: Boolean = true
    +  private var latestTime: Long = -1L
    +  private var latestRate: Double = -1D
    +  private var latestError: Double = -1L
    +
    +  require(
    +    batchIntervalMillis > 0,
    +    s"Specified batch interval $batchIntervalMillis in PIDRateEstimator is 
invalid.")
    +
    +  def compute(time: Long, // in milliseconds
    +      elements: Long,
    +      processingDelay: Long, // in milliseconds
    +      schedulingDelay: Long // in milliseconds
    +    ): Option[Double] = {
    +
    +    this.synchronized {
    +      if (time > latestTime && processingDelay > 0 && batchIntervalMillis 
> 0) {
    +
    +        // in seconds, should be close to batchDuration
    +        val delaySinceUpdate = (time - latestTime).toDouble / 1000
    +
    +        // in elements/second
    +        val processingRate = elements.toDouble / processingDelay * 1000
    +
    +        // in elements/second
    +        val error = latestRate - processingRate
    +
    +        // in elements/second
    +        val sumError = schedulingDelay.toDouble * processingRate / 
batchIntervalMillis
    --- End diff --
    
    Here's the gist of it:
    
    - we consider `schedulingDelay` as an indication of accumulated error, 
which corresponds to the integral part in a PID controller. Intuitively it 
makes sense: the fact that there is a delay means we had too many elements in 
previous batches, and the system can't process them in the given batch interval
    
    The challenge is to transform this indication from *time* to a rate, which 
is the quantity that our PID is measuring (and controlling). Here's the 
reasoning:
    
    - a scheduling delay `s` corresponds to `s * processingRate` *overflowing* 
elements. Those are elements that couldn't be processed in previous batches, 
leading to this delay. We assume the processingRate didn't change too much 
(since it's mostly a measure of the cluster performance, with small variations 
like checkpointing), but a good approximation
    -  from the number of overflowing elements we can calculate the rate at 
which they would be cleared by dividing it by the batch interval. This rate is 
our "historical" error, or integral part, since if we subtracted this rate from 
the previous "calculated rate", there wouldn't have been any overflowing 
elements, and the scheduling delay would have been zero.
    
    There's some additional details about units of measure, since 
schedulingDelay and the batchInterval are in milliseconds by rates are in 
elements/second, but if you do the math you'd notice that the 1000s cancel out.


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