リング配列を使って簡単にキューを実現します.

主な違いは、frontとrearは0から始まります.以前はfrontは最初の元素の前の位置を指していました.rearは最後の元素を指しています.今はfrontに変えて直接に頭の元素を指します.
rearは最後の要素の次の位置を指し、最後に所定の位置を残し、列の実際の使用サイズはmaxSize-1です.

public class CircleArrayQueue {
    public static void main(String[] args) {
        //    
        CircleQueue circleQueue = new CircleQueue(3);

        char key = ' ';
        Scanner scanner = new Scanner(System.in);
        boolean loop = true;
        while ((loop)) {
            System.out.println("s:     ");
            System.out.println("e:     ");
            System.out.println("a:     ");
            System.out.println("g:       ");
            System.out.println("h:        ");
            key = scanner.next().charAt(0);//      
            switch (key) {
                case 's':
                    circleQueue.showQueue();
                    break;
                case 'a':
                    int value = scanner.nextInt();
                    circleQueue.addQueue(value);
                    break;
                case 'g':
                    try {
                        int result = circleQueue.getQueue();
                        System.out.printf("      %d
", result);
                    } catch (Exception e) {
                        System.out.println(e.getMessage());
                    }
                    break;
                case 'h':
                    try {
                        int peek = circleQueue.peek();
                        System.out.printf("    %d\t", peek);
                    } catch (Exception e) {
                        System.out.println(e.getMessage());
                    }
                    break;
                case 'e':
                    scanner.close();
                    loop = false;
                default:
                    break;
            }

        }
        System.out.println("    ");
    }
}
class CircleQueue{
    private int maxSize; //    
    private int front; //   
    private int rear; //   
    private int[] arr; //    

    public CircleQueue(int maxSize) {
        this.maxSize = maxSize;
        arr=new int[maxSize];
      //  front rear 0  
    }
    //     
    public boolean isFull() {
        return (rear+1+maxSize)%maxSize==front;
    }
    //      
    public boolean isEmpty() {
        return front == rear;
    }
    public void addQueue(int number) {
        boolean full = this.isFull();
        if (full) {
            System.out.println("    ，      ");
            return;
        }
        arr[rear] = number;
        // rear  
        rear=(rear+1)%maxSize;
    }

    //    
    public int getQueue() {
        boolean empty = this.isEmpty();
        if (empty) {
            throw new RuntimeException("    ！      ");
        }
        int number = arr[front];
        front=(front+1)%maxSize; //           
        return number;
    }

    //        
    public void showQueue() {
        boolean empty = this.isEmpty();
        if (empty) {
            System.out.println("    ");
            return;
        }
        for (int i = front; i < front+size(); i++) {
            System.out.printf("arr[%d]=%d
",i%maxSize,arr[i%maxSize]);
        }
    }
    //          
    public int size(){
        return (rear-front+maxSize)%maxSize;
    }
    //        
    public int peek() {
        boolean empty = this.isEmpty();
        if (empty) {
            throw new RuntimeException("   ，   ");
        }
        return arr[front + 1];
    }
}