// ## Dumb-dumb initial solution

​

using System;

using System.Threading.Tasks;

using System.Collections.Generic;

​

public class Program 

{

    public static async Task Main()

    {

        var p = new LimitedPar<int>(3);

        var rnd = new Random(42);

        List<Task> awaited = new(5);

        for (var i = 0; i < 5; ++i)

        {

            var j = p.RunAsync(i, async n =>

            {   

                var randomDelay = (int)rnd.NextInt64(1000, 3000);

                Console.WriteLine($"Starting job #{n}, expected finish in {randomDelay}ms...");

                await Task.Delay(randomDelay);

                Console.WriteLine($"Finished job #{n}.");

            });

            if (!j.IsCompleted)

               awaited.Add(j);

        }

        await Task.WhenAll(awaited);

    }

    public static class LimitedPar

    {

        public const int DefaultParLevel = 3;

    }

    public sealed class LimitedPar<S>

    {

        public readonly int ParLevel;

        private Queue<(Func<S, Task>, S)>? _queue;

        private int _currentJobRunning;

        public LimitedPar(int parLevel = LimitedPar.DefaultParLevel) =>

            ParLevel = parLevel;

        public async Task RunAsync(S state, Func<S, Task> job)

        {

            if (_currentJobRunning < ParLevel)

            {

                ++_currentJobRunning;

                try

                {

                    await job.Invoke(state);

                }

                finally 

                {

                    --_currentJobRunning;

                }

                if (_queue?.TryDequeue(out var next) == true)

                {

                    var (j, s) = next;

                    ++_currentJobRunning;

                    try 

                    {

                        await j.Invoke(s);

                    }

                    finally

                    {

                        --_currentJobRunning;

                    }

                }                

            }

            else

            {

                _queue ??= new(4);

                _queue.Enqueue((job, state));

            }

        }

    }

}