Producer-consumer with a variation - How to synchronize with thread signal / wait?

While working on a large project I realized I was making a lot of calls to be scheduled in the future. Since these were fairly light-weight, I thought it might be better to use a separate scheduler.

ThreadPool.QueueUserWorkItem (() =>
{
    Thread.Sleep (5000);
    Foo (); // Call is to be executed after sometime
});

So I created a separate scheduler class that runs on its own thread and executes these events. I have 2 functions that access a shared queue from separate threads. I'd use a lock, but since one of the threads needs to sleep-wait, I wasn't sure how to release the lock.

class Scheduler
{
    SortedDictionary <DateTime, Action> _queue;
    EventWaitHandle _sync;

    // Runs on its own thread
    void Run ()
    {
        while (true)
        {
            // Calculate time till first event
            // If queue empty, use pre-defined value
            TimeSpan timeDiff = _queue.First().Key - DateTime.Now;

            // Execute action if in the next 100ms
            if (timeDiff < 100ms)
                ...
            // Wait on event handle for time
            else
                _sync.WaitOne (timeDiff);
        }
    }

    // Can be called by any thread
    void ScheduleEvent (Action action, DataTime time)
    {
        _queue.Add (time, action);
        // Signal thread to wake up and check again
        _sync.Set ();
    }
}

• The trouble is, I'm not sure how to synchronize access to the queue between the 2 functions. I can't use a monitor or mutex, because Run() will sleep-wait, thus causing a deadlock. What is the right synchronization mechanism to use here? (If there a mechanism to atomically start the sleep-wait process and immediately release the lock, that might solve my problem)
• How can I verify there is no race-condition?
• Is this a variation of the producer consumer problem, or is there a more relevant synchronization problem-description?

  While this is somewhat geared towards C#, I'd be happy to hear a general solution to this. Thanks!

OK, take 2 with Monitor/Pulse.

    void Run ()
    {
        while (true)
        {
            Action doit = null;

            lock(_queueLock)
            {
                while (_queue.IsEmpty())
                    Monitor.Wait(_queueLock);

                TimeSpan timeDiff = _queue.First().Key - DateTime.Now;
                if (timeDiff < 100ms)
                    doit = _queue.Dequeue();
            }

            if (doit != null)
                ; //execute doit
            else
             _sync.WaitOne (timeDiff);
        }
    }

void ScheduleEvent (Action action, DataTime time)
{
    lock (_queueLock)
    {
        _queue.Add(time, action);
        // Signal thread to wake up and check again
        _sync.Set ();
        if (_queue.Count == 1)
             Monitor.Pulse(_queuLock);
    }
}