C# Console App + Multithread + UnityContainer + Design Pattern

I hava a program that needs to run any threads at the same time. I don't know what is the best way to inject the same services in any thread and don't care about concurrency exception.

For example:

Console Main

public class Program
{
    static void Main()
    {
        IUnityContainer container = new UnityContainer();
        container.RegisterType<IMySharedService, MySharedService>(new PerThreadLifetimeManager());
        ProgramService service = container.Resolve<ProgramService>();
        service.Run();
    }
}

public class ProgramService : IProgramService
{
    public static ConcurrentQueue<string> queue = new ConcurrentQueue<string>();
    private readonly IMySharedService _mySharedService;

    public ProgramService(IMySharedService mySharedService)
    {
        _mySharedService = mySharedService;
    }

    public void Run()
    {
        FirstThread firstThread = new FirstThread(_mySharedService);
        SecondThread secondThread = new SecondThread(_mySharedService);
        firstThread.Start();
        secondThread.Start();

        while (!_shouldStop)
        {
            string message;
            if (queue.TryDequeue(out message))
            {
                firstThread.DoSomething(message);
                secondThread.DoSomething(message);
            }
            System.Threading.Thread.Sleep(250);
        }
    }
}

In MySharedService I use to find some object (like UserModel) and the service return null object. I believe that some concurrency error are invalidating the object.

Someone have some design pattern for this kind of example?