On the fractal dimension of computer programs and its application to the prediction of the cache miss ratio

Fractal geometry is proposed as a powerful measure of program behavior, and its application to the prediction of the miss ratio of programs in fully associative caches is presented. Programs are modeled as one-dimensional fractal random-walks. The fractal cache model is based on the parameterization of a program trace by a small number of constants, one of which is the fractal dimension of the program. The model is validated by trace-driven simulations of several program traces. With this model, it is possible to read the trace of a program once, and then predict the behavior of the miss ratio curve of that program in fully associative caches of varying sizes