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Fiber nonlinearity is one of the major effects that limits the performance of optical fiber communications systems. Such systems can be modeled by a set of nonlinear stochastic equations, which generally cannot be solved analytically. Due to involved complexity, these equations most often are solved using direct Monte Carlo simulations, which can be prohibitively time consuming. In this work, we discuss several useful techniques to make the system performance predictions more efficient and accurate. We review the split-step Fourier method and introduce efficient algorithms to improve its efficiency. We review biased Monte Carlo methods and show how to apply them to model nonlinear effects in optical fibers. We finally present a deterministic method based on isolating the dominant nonlinear effects and calculating the complete probability density function of the nonlinearly-induced impairment and combining it with the noise-induced penalty. Although not comprehensive, these methods show how to identify the critical physical effects in a complex system and design an efficient solution. The scope of application of these techniques may extend beyond the problems studied in this work
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