One of the main problems with the linear queue is the lack of appropriate utilization of space. Assume that the queue can store 100 elements & the complete queue is full. Thus, it means that the queue is holding 100 elements. In case, some elements at the front are deleted, at the last position the element in the queue continues to be at the similar position and there is no competent way to determine that the queue is not full. In this way, space utilization in the case of linear queues is not competent. This problem is arising because of the representation of the queue.
The substitute representation is to illustrate the queue as circular. In case, we are representing the queue by using arrays, then, a queue along n elements begin from index 0 and ends at n-1.So, obviously , the first element in the queue will be at index 0 and the last element will be at n-1 while all the positions among index 0 & n-1(both inclusive) are filled. Under such situation, front will point to 0 and rear will point to n-1. Though, while a new element is to be inserted and if the rear is pointing to n-1, then, it has to be checked if the position at index 0 is free. If yes, then the element can be inserted to that position & rear can be adjusted accordingly. In this way, the utilization of space is enhanced in the case of a circular queue.
In a circular queue, front will point to one position less to the first element anti-clock wise. Thus, if in the array the first element is at position 4, then the front will point to position 3. While the circular queue is created, then both front & rear point to index 1. Also, we can conclude that the circular queue is empty in case front & rear both point to the same index. Figure illustrates a circular queue.