MICROSCOPIC MODEL OF SOFTWARE BUG DYNAMICS: CLOSED SOURCE VERSUS OPEN SOURCE

We introduce a simple microscopic description of software bug dynamics where users, programmers and a maintainer of a given program interact through bug creation, detection and correction. When the program is written from scratch, the first phase of development is characterized by a fast decline of the number of bugs, followed by a slow phase where most bugs have been fixed, hence, are hard to find. Releasing immediately bug fixes speeds up the debugging process, which substantiates bazaar open-source methodology. We provide a mathematical analysis that supports our numerical simulations. Finally, we apply our model to Linux history and determine the existence of a lower bound to the quality of its programmers.