C# how to make a action que, where actions have different parameters

Question

my question is how to run different functions with params on an existing thread? I'm aware that I should form a que such as this code from this thread by @user2864740:

using System;
using System.Collections.Concurrent;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading;

namespace DogPark
{
    internal class DogPark
    {

        private readonly string _parkName;
        private readonly Thread _thread;
        private readonly ConcurrentQueue<Action> _actions = new ConcurrentQueue<Action>();
        private volatile bool _isOpen;

        public DogPark(string parkName)
        {
            _parkName = parkName;
            _isOpen = true;
            _thread = new Thread(OpenPark);
            _thread.Name = parkName;
            _thread.Start();
        }

        // Runs in "target" thread
        private void OpenPark(object obj)
        {
            while (true)
            {
                Action action;
                if (_actions.TryDequeue(out action))
                {
                    Program.WriteLine("Something is happening at {0}!", _parkName);
                    try
                    {
                        action();
                    }
                    catch (Exception ex)
                    {
                        Program.WriteLine("Bad dog did {0}!", ex.Message);
                    }
                }
                else
                {
                    // Nothing left!
                    if (!_isOpen && _actions.IsEmpty)
                    {
                        return;
                    }
                }

                Thread.Sleep(0); // Don't toaster CPU
            }
        }

        // Called from external thread
        public void DoItInThePark(Action action)
        {
            if (_isOpen)
            {
                _actions.Enqueue(action);
            }
        }

        // Called from external thread
        public void ClosePark()
        {
            _isOpen = false;
            Program.WriteLine("{0} is closing for the day!", _parkName);
            // Block until queue empty.
            while (!_actions.IsEmpty)
            {
                Program.WriteLine("Waiting for the dogs to finish at {0}, {1} actions left!", _parkName, _actions.Count);

                Thread.Sleep(0); // Don't toaster CPU
            }
            Program.WriteLine("{0} is closed!", _parkName);
        }

    }

    internal class Dog
    {

        private readonly string _name;

        public Dog(string name)
        {
            _name = name;
        }

        public void Run()
        {
            Program.WriteLine("{0} is running at {1}!", _name, Thread.CurrentThread.Name);
        }

        public void Bark()
        {
            Program.WriteLine("{0} is barking at {1}!", _name, Thread.CurrentThread.Name);
        }

    }

    internal class Program
    {
        // "Thread Safe WriteLine"
        public static void WriteLine(params string[] arguments)
        {
            lock (Console.Out)
            {
                Console.Out.WriteLine(arguments);
            }
        }

        private static void Main(string[] args)
        {
            Thread.CurrentThread.Name = "Home";

            var yorkshire = new DogPark("Yorkshire");
            var thunderpass = new DogPark("Thunder Pass");

            var bill = new Dog("Bill the Terrier");
            var rosemary = new Dog("Rosie");

            bill.Run();

            yorkshire.DoItInThePark(rosemary.Run);
            yorkshire.DoItInThePark(rosemary.Bark);

            thunderpass.DoItInThePark(bill.Bark);

            yorkshire.DoItInThePark(rosemary.Run);

            thunderpass.ClosePark();
            yorkshire.ClosePark();
        }

    }
}

but the example uses only functions that take 0 parameters. What would be approach if "Dog.Run" and "Dog.Bark" were taking different(length) params?

4 example:

public void Bark(int value)
{
   //do something
}
public void Run (string speed, string direction)
{
   //do something
}

best thing I've come up so far is using lamba expression, but I'd like to have as many different angles to tackling this problem, as to be able to make the most elegant solution.

public void SendRun(string speed, string direction)
{
    this.DoItInThePark(new Action(() => Run(speed,direction)));
}
public void Run(string speed, string direction)
{
    //do something
}

if you happen to have a different approach to the same problem, please do suggest.

In my project, the Dog and Park would not even need to be separate classes, but all actions could be performed within a single class (but I guess that doesnt make lot difference discussion wise)