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Bandwidth throttling in C#

I am developing a program that continually sends a stream of data in the background and I want to allow the user to set a cap for both upload and download limit.

I have read up on the token bucket and leaky bucket alghorhithms, and seemingly the latter seems to fit the description since this is not a matter of maximizing the network bandwidth but rather being as unobtrusive as possible.

I am however a bit unsure on how I would implement this. A natural approach is to extend the abstract Stream class to make it simple to extend existing traffic, but would this not require the involvement of extra threads to send the data while simultaneously receiving (leaky bucket)? Any hints on other implementations that do the same would be appreciated.

Also, although I can modify how much data the program receives, how well does bandwidth throttling work at the C# level? Will the computer still receive the data and simply save it, effectively canceling the throttling effect or will it wait until I ask to receive more?

EDIT: I am interested in throttling both incoming and outgoing data, where I have no control over the opposite end of the stream.

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Based on @0xDEADBEEF's solution I created the following (testable) solution based on Rx schedulers:

public class ThrottledStream : Stream
{
    private readonly Stream parent;
    private readonly int maxBytesPerSecond;
    private readonly IScheduler scheduler;
    private readonly IStopwatch stopwatch;

    private long processed;

    public ThrottledStream(Stream parent, int maxBytesPerSecond, IScheduler scheduler)
    {
        this.maxBytesPerSecond = maxBytesPerSecond;
        this.parent = parent;
        this.scheduler = scheduler;
        stopwatch = scheduler.StartStopwatch();
        processed = 0;
    }

    public ThrottledStream(Stream parent, int maxBytesPerSecond)
        : this (parent, maxBytesPerSecond, Scheduler.Immediate)
    {
    }

    protected void Throttle(int bytes)
    {
        processed += bytes;
        var targetTime = TimeSpan.FromSeconds((double)processed / maxBytesPerSecond);
        var actualTime = stopwatch.Elapsed;
        var sleep = targetTime - actualTime;
        if (sleep > TimeSpan.Zero)
        {
            using (var waitHandle = new AutoResetEvent(initialState: false))
            {
                scheduler.Sleep(sleep).GetAwaiter().OnCompleted(() => waitHandle.Set());
                waitHandle.WaitOne();
            }
        }
    }

    public override bool CanRead
    {
        get { return parent.CanRead; }
    }

    public override bool CanSeek
    {
        get { return parent.CanSeek; }
    }

    public override bool CanWrite
    {
        get { return parent.CanWrite; }
    }

    public override void Flush()
    {
        parent.Flush();
    }

    public override long Length
    {
        get { return parent.Length; }
    }

    public override long Position
    {
        get
        {
            return parent.Position;
        }
        set
        {
            parent.Position = value;
        }
    }

    public override int Read(byte[] buffer, int offset, int count)
    {
        var read = parent.Read(buffer, offset, count);
        Throttle(read);
        return read;
    }

    public override long Seek(long offset, SeekOrigin origin)
    {
        return parent.Seek(offset, origin);
    }

    public override void SetLength(long value)
    {
        parent.SetLength(value);
    }

    public override void Write(byte[] buffer, int offset, int count)
    {
        Throttle(count);
        parent.Write(buffer, offset, count);
    }
}

and some tests that just take some milliseconds:

[TestMethod]
public void ShouldThrottleReading()
{
    var content = Enumerable
        .Range(0, 1024 * 1024)
        .Select(_ => (byte)'a')
        .ToArray();
    var scheduler = new TestScheduler();
    var source = new ThrottledStream(new MemoryStream(content), content.Length / 8, scheduler);
    var target = new MemoryStream();

    var t = source.CopyToAsync(target);

    t.Wait(10).Should().BeFalse();
    scheduler.AdvanceTo(TimeSpan.FromSeconds(4).Ticks);
    t.Wait(10).Should().BeFalse();
    scheduler.AdvanceTo(TimeSpan.FromSeconds(8).Ticks - 1);
    t.Wait(10).Should().BeFalse();
    scheduler.AdvanceTo(TimeSpan.FromSeconds(8).Ticks);
    t.Wait(10).Should().BeTrue();
}

[TestMethod]
public void ShouldThrottleWriting()
{
    var content = Enumerable
        .Range(0, 1024 * 1024)
        .Select(_ => (byte)'a')
        .ToArray();
    var scheduler = new TestScheduler();
    var source = new MemoryStream(content);
    var target = new ThrottledStream(new MemoryStream(), content.Length / 8, scheduler);

    var t = source.CopyToAsync(target);

    t.Wait(10).Should().BeFalse();
    scheduler.AdvanceTo(TimeSpan.FromSeconds(4).Ticks);
    t.Wait(10).Should().BeFalse();
    scheduler.AdvanceTo(TimeSpan.FromSeconds(8).Ticks - 1);
    t.Wait(10).Should().BeFalse();
    scheduler.AdvanceTo(TimeSpan.FromSeconds(8).Ticks);
    t.Wait(10).Should().BeTrue();
}

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