Wavelength division multiplexing (WDM) provides the ability to utilize the enormous bandwidth offered by optical networks, using today's electronics. WDM-based optical networks employing passive-star couplers have been proposed for deployment in local and metropolitan areas. Optical amplification is often required in such networks to compensate for the signal attenuation along the fiber links and the splitting and coupling losses in the network. However, an optical amplifier has constraints on the maximum gain and the maximum output power it can supply; thus optical amplifier placement becomes a challenging problem. A simplifying assumption for analytical tractability requires that all wavelengths, present at a particular point in a fiber, be at the same power level, viz. the equally powered-wavelengths case. However, previous studies did not minimize the total number of amplifiers while achieving power equalization. In this paper, we formulate the minimization of amplifiers with power equalization as a mixed integer linear program (MILP) that can be solved by a linear program solver. Illustrative examples on sample networks are presented, which demonstrate the characteristics and the advantages of our optimal amplifier placement algorithm.
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