On machining centers, the computer-aided manufacturing (CAM) system (and its operator) determines the depth of cut. Period. However, DOC here takes on a double meaning, as it is measured both axially (along the length of the end mill) and radially (on its diameter). For instance, using a 3/8-inch carbide end mill, you might "bury" the cutter along its entire 1-inch length and take light radial depths of cut (which, if performed in a circular manner, is known as a trochoidal toolpath), or you might take a heavy radial DOC and "step down" using relatively light axial DOC (most programmers consider this methodology old school).
DOC stands alone, in that whatever value you as a programmer (or as a manual machine operator) decide to take, no mathematical relationship exists between it and the feed rate and rpm. That said, it's important to recognize that heavy depths of cut may call for lighter feed rates and slightly slower rpm, while light depths of cut — because cutting forces are lower — allow more aggressive cutting parameters.