Results on N-Dimensional Discrete Space Self-Similarity

New formulations and models were proposed for describing statistical self-similarity in a general N-dimensional setting in our earlier work. It was shown that by using a matrix-scaling operator for defining statistical self-similarity, a wide class of continuous-space N-dimensional processes can be characterized as self-similar with respect to specific matrix classes. In this work we discuss the various classes of self-similar processes that can be generated by matrix scaling operation and the conditions under which they exist. We provide relationship with the Hurst exponent H and the fractional parameter r for these classes of self-similar processes. In the end, we provide some insights into the merging of self-similar traffic streams.