The middle approach is the only one that is not lock-free.

The first approach is lock-free, but as the author says, it wastes an element.

But here's the thing. If your element is a character, and your buffer size is, say, 256 bytes, and you are using 8-bit unsigned characters for indices, the one wasted byte is less than one percent of your buffer space, and also is compensated for by the simplicity and reduced code size.