Fixed size queue which automatically dequeues old values upon new enqueues

I would write a wrapper class that on Enqueue would check the Count and then Dequeue when the count exceeds the limit.

 public class FixedSizedQueue<T>
 {
     readonly ConcurrentQueue<T> q = new ConcurrentQueue<T>();
     private object lockObject = new object();

     public int Limit { get; set; }
     public void Enqueue(T obj)
     {
        q.Enqueue(obj);
        lock (lockObject)
        {
           T overflow;
           while (q.Count > Limit && q.TryDequeue(out overflow)) ;
        }
     }
 }