This is the first time I have really used Lists and Queues so this might be a very simple mistake. Is it because my queue is full of objects that can\'t be cast to integers?
My guess is that the issue is here:
Arrays.asList(numberarray);
If numberarray is an int[] rather than an Integer[], then that call will actually return a List of int[]s containing that array as one element.
The ClassCastException happens later when you try to cast the int[] object to an Integer.
Since Java doesn't support primitive collections there is no easy way to use Arrays.asList to wrap a primitive array - autoboxing doesn't work en masse like that. It's best to start off using an Integer[] if you plan to use it to back a Collection.
Part of the confusion comes from the fact that the method asList(T...) takes varargs. If it just took a T[] as an argument instead, the compiler wouldn't let you pass in an int[] since primitive arrays don't extend Object[]. But with varargs support, the compiler infers T as int[] and thinks you mean to build a List backed by a single-element int[][].
As others have noted, the use of generics will really help you out with ambiguities like this and it's always a good idea to program using them:
List<Integer> numList = Arrays.asList(numberarray);
This line gives the following compile error, instead of allowing your code to fail at runtime:
incompatible types
required: java.util.List<java.lang.Integer>
found: java.util.List<int[]>
Side note: Assuming you move to using an Integer[] don't forget that this means elements can now be null. Should this be the case a NullPointerException will be thrown when you unbox back to int - just be careful to ensure your implementation doesn't allow null elements or else check for null before unboxing.
You really should use Generics and ArrayList/ArrayDeque unless it's really performance critical and you use a lot of atomic types like int. Then you should have a look at http://labs.carrotsearch.com/hppc.html