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In transparent Dense Wavelength Division Multiplexing (DWDM) networks, Physical Layer Impairments (PLI) degrade the signal quality of optical connections (referred to as light-paths) when they traverse the optical fibers and components. Non-linear physical layer impairments make the mathematical programming formulation of off-line Impairment-Aware (IA) Routing and Wavelength Assignment (RWA) problem to be non-linear. To alleviate that, this paper presents for the first time a statistical linear model to compute the Cross Phase Modulation (XPM) noise variance. Exhaustive evaluation reveals that the proposed linear model provides an accurate Q-factor estimation. An example of Integer Linear Programming (ILP) formulation integrating the XPM model is also given.
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