下面是使用ArrayQueue实现RandomQueue的解决方法，并排除一个随机元素的代码示例：

import java.util.Random;

public class ArrayQueue {
    private E[] queue;
    private int front; // 指向队列头部的指针
    private int rear; // 指向队列尾部的指针
    private int size; // 队列中元素的个数

    public ArrayQueue(int capacity) {
        queue = (E[]) new Object[capacity];
        front = 0;
        rear = -1;
        size = 0;
    }

    public boolean isEmpty() {
        return size == 0;
    }

    public boolean isFull() {
        return size == queue.length;
    }

    public int size() {
        return size;
    }

    public void enqueue(E element) {
        if (isFull()) {
            throw new IllegalStateException("Queue is full");
        }
        rear = (rear + 1) % queue.length;
        queue[rear] = element;
        size++;
    }

    public E dequeue() {
        if (isEmpty()) {
            throw new IllegalStateException("Queue is empty");
        }
        E removedElement = queue[front];
        queue[front] = null;
        front = (front + 1) % queue.length;
        size--;
        return removedElement;
    }

    public E peek() {
        if (isEmpty()) {
            throw new IllegalStateException("Queue is empty");
        }
        return queue[front];
    }
}

public class RandomQueue {
    private ArrayQueue queue;

    public RandomQueue() {
        queue = new ArrayQueue<>();
    }

    public void enqueue(E element) {
        queue.enqueue(element);
    }

    public E dequeue() {
        int randomIndex = new Random().nextInt(queue.size());
        E removedElement = null;
        for (int i = 0; i < queue.size(); i++) {
            E currentElement = queue.dequeue();
            if (i != randomIndex) {
                queue.enqueue(currentElement);
            } else {
                removedElement = currentElement;
            }
        }
        return removedElement;
    }

    public E peek() {
        return queue.peek();
    }
}

使用示例：

RandomQueue randomQueue = new RandomQueue<>();
randomQueue.enqueue(1);
randomQueue.enqueue(2);
randomQueue.enqueue(3);
randomQueue.enqueue(4);
randomQueue.enqueue(5);

System.out.println(randomQueue.dequeue());
System.out.println(randomQueue.dequeue());
System.out.println(randomQueue.dequeue());

// 输出结果可能为：
// 3
// 1
// 5

在上述示例中，我们首先创建了一个RandomQueue对象，并依次将元素1、2、3、4、5入队。然后，我们连续三次执行dequeue操作，每次都会随机排除一个元素。最后，我们打印出排除的元素，可能的结果是3、1、5。