A mathematic model is presented for the noise accumulation within optical paths in optical transport networks according to the hypothetical reference model (HRM) defined in ITU-T recommendation G.873. The optical paths may pass through multiple optical nodes and fiber links with optical amplifiers. Analytic calculation formulae are derived and simplified according to the node isolation principle. An engineering equivalent model is given, as well as the corresponding calculation formulae. The impact of the gain (attenuation) distribution within an optical node on the noise power is analyzed. Optimum design principles are proposed for optical nodes to reduce noise power in optical paths. The noise models for optical path can be used as a reference for designing optical nodes and fiber transmission spans in optical networks.