throttling an await delay for inbound messages to a number of messages per second

Question

I am trying to throttle a loop (which is sending messages) to a particular number of messages per second. _throttle is the number of messages per second.

My initial algorithm is depicted below, but the delays are not smooth.
What improvements can I make to smooth out the rather bumpy delays and bursts of messages.

I have played around with the tick, and the interval max, but the inbound count is so large it's hard to compensate. The maximum rate I can achieve with the throttle off in my implementation is about 15000/second. I am testing with rates between 300 and 1000 per second, so I am trying to slow it down quite a bit.

private class ThrottleCalculator
{
    private readonly int _throttle;
    private DateTime _lastCalculation = DateTime.Now;
    private int _count = 0;
    private int _interval = 0;

    public ThrottleCalculator(int throttle)
    {
        this._throttle = throttle;
    }

    public async Task CalculateThrottle()
    {
        this._count += 1;
        var elapsed = DateTime.Now.Subtract(this._lastCalculation).TotalMilliseconds;
        var tick = 50;
        if (elapsed > tick)
        {
            this._lastCalculation = DateTime.Now;
            int projection = this._count * (1000 / tick);
            var errorTerm = this._throttle - projection;
            this._interval = this._interval - errorTerm;
            if (this._interval < 0)
                this._interval = 0;

            // this is often several thousand, so I have to limit.
            if (this._interval > 100)
                this._interval = 100;
            await Task.Delay(this._interval);
            this._count = 0;
        }
    }
}

The code that uses this just calls this every iteration.

var throttle = new ThrottleCalculator(600); // 600/s
while (message = getMessage())
{
    ... // do stuff with message.
    if (throttle != null)
       await throttle.CalculateThrottle();

Sync

I have no idea what you're trying to accomplish but ok. – Recount

Answer 1

PID Controller Algorithm

for anyone else attempting this, the correct approach is the PID controller algorithm.
Proportional / Integral / Derivative Controller

I used the algorithm at the bottom of the wiki as a base. My kp / ki / kd seem to work well with the values here, keeping them in proportion seems to result in a nice steady stream of messages, and very tight delay values.

private class ThrottleCalculator
{
    private readonly int _throttle;
    private DateTime _lastCalculationTime;
    private double _measured = 0;
    private double _totalError = 0;
    private double _integral = 0;
    private double _lastError = 0;

    public ThrottleCalculator(int throttle)
    {
        this._throttle = throttle;
        this._lastCalculationTime = DateTime.MinValue;
    }

    public async Task CalculateThrottle()
    {
        var kp = -.1d;      // proportional gain
        var ki = -.1d;      // integral gain
        var kd = -.1d;      // derivative gain
        var dt = 30d;       // rate of change of time. calculcations every ms;

        this._measured += 1;
        if (this._lastCalculationTime == DateTime.MinValue)
            this._lastCalculationTime = DateTime.Now;
        var elapsed = (double)DateTime.Now.Subtract(this._lastCalculationTime)
                     .TotalMilliseconds;
        if (elapsed > dt)
        {
            this._lastCalculationTime = DateTime.Now;
            var error = ((double)this._throttle / (1000d / dt)) - this._measured;
            this._totalError += error;
            var integral = this._totalError;
            var derivative = (error - this._lastError) / elapsed;
            var actual = (kp * error) + (ki * integral) + (kd * derivative);
            var output = actual;
            if (output < 1)
                output = 0;

            // i don't like this, but it seems necessary
            // so that wild wait values are never used.
            if (output > dt * 4)
                output = dt * 4;
            if (output > 0)
                await Task.Delay((int)output);
            this._measured = 0;
            this._lastError = error;
        }
    }
}

My values look like this:

Actual: 19.2000 Output: 19.2000 Integral:   -209 Derivative:      .0000 Error:   17
Actual: 17.5000 Output: 17.5000 Integral:   -192 Derivative:      .0000 Error:   17
Actual: 15.8000 Output: 15.8000 Integral:   -175 Derivative:      .0000 Error:   17
Actual: 33.8104 Output: 33.8104 Integral:   -255 Derivative:    -3.1040 Error:  -80
Actual: 21.8931 Output: 21.8931 Integral:   -238 Derivative:     2.0686 Error:   17
Actual: 20.4000 Output: 20.4000 Integral:   -221 Derivative:      .0000 Error:   17
Actual: 18.7000 Output: 18.7000 Integral:   -204 Derivative:      .0000 Error:   17
Actual: 17.0000 Output: 17.0000 Integral:   -187 Derivative:      .0000 Error:   17
Actual: 15.3000 Output: 15.3000 Integral:   -170 Derivative:      .0000 Error:   17
Actual: 31.0752 Output: 31.0752 Integral:   -239 Derivative:    -2.7520 Error:  -69

Sync

Using a control loop for throttling is clever! To match the general PID equation, your integral term may need to be multiplied by elapsed. – Germainegerman