One of the motivations for this work is the observation of high-energy cosmic rays that appear to violate the Greisen-Zatsepin-Kuzmin limit: the so-called GZK paradox.
External references Giovanni Amelino-Camelia, "Doubly-Special Relativity: First Results and Key Open Problems." Int. J. Mod. Phys. D11 (2002) 1643. Online copy at http://arxiv.org/abs/gr-qc/0210063 Giovanni Amelino-Camelia, Doubly-Special Relativity.' http://lanl.arxiv.org/abs/gr-qc/0207049 -- a non-technical review