Optimal Amplifier Placement for Optical Networks

Amplifiers are one of the most important components in an optical WDM network, and they are used to restore the strength of optical signals which are attenuated by optical fibers as they propagate through the network. However, amplifiers also introduce the spontaneous emission noise which degrades the optical signal-to-noise ratio (OSNR). In this paper, we study the amplifier placement problem with the objective of minimizing the total amplifier cost subject to the constraint on the cumulative spontaneous emission noise. We assume that there are several different types of amplifiers. Therefore, we need to decide not only where to place amplifiers, but also what type of amplifier to use at each location. We consider two different cases: 1) the discrete case (brown-field design) in which the possible locations where amplifiers can be placed are given, and 2) the continuous case (green-field design) in which amplifiers can be placed anywhere in the network with no restriction. For the discrete case, we propose two methods: one based on dynamic programming and the other based on heuristics. For the continuous case, we first formulate the problem as a mixed integer optimization problem, and then propose a numerical method to solve it. Some numerical examples are also provided.