How do I instantiate a Queue object in java?

A Queue is an interface, which means you cannot construct a Queue directly.

The best option is to construct off a class that already implements the Queue interface, like one of the following: AbstractQueue, ArrayBlockingQueue, ArrayDeque, ConcurrentLinkedQueue, DelayQueue, LinkedBlockingQueue, LinkedList, PriorityBlockingQueue, PriorityQueue, or SynchronousQueue.

An alternative is to write your own class which implements the necessary Queue interface. It is not needed except in those rare cases where you wish to do something special while providing the rest of your program with a Queue.

public class MyQueue<T extends Tree> implements Queue<T> {
   public T element() {
     ... your code to return an element goes here ...
   }

   public boolean offer(T element) {
     ... your code to accept a submission offer goes here ...
   }

   ... etc ...
}

An even less used alternative is to construct an anonymous class that implements Queue. You probably don't want to do this, but it's listed as an option for the sake of covering all the bases.

new Queue<Tree>() {
   public Tree element() {
     ...
   };

   public boolean offer(Tree element) {
     ...
   };
   ...
};

Queue is an interface. You can't instantiate an interface directly except via an anonymous inner class. Typically this isn't what you want to do for a collection. Instead, choose an existing implementation. For example:

Queue<Integer> q = new LinkedList<Integer>();

or

Queue<Integer> q = new ArrayDeque<Integer>();

Typically you pick a collection implementation by the performance and concurrency characteristics you're interested in.