Optimizing Ampliier Placements in a Multi-wavelength Optical Lan/man: the Unequally-powered-wavelengths Case

Optical networks based on passive star couplers and employing wavelength-division multi-plexing (WDM) have been proposed for deployment in local and metropolitan areas. These networks suuer from splitting, coupling, and attenuation losses. Since there is an upper bound on transmitter power and a lower bound on receiver sensitivity, optical ampliiers are usually required to compensate for the power losses mentioned above. Due to the high cost of am-pliiers, it is desirable to minimize their total number in the network. However, an optical ampliier has constraints on the maximum gain and the maximum output power it can supply; thus, optical ampliier placement becomes a challenging problem. In fact, the general problem of minimizing the total ampliier count is a mixed-integer nonlinear problem. Previous studies have attacked the ampliier-placement problem by adding the \artiicial" constraint that all wavelengths, which are present at a particular point in a ber, be at the same power level. This constraint simpliies the problem into a solvable mixed-integer linear program. Unfortunately, this artiicial constraint can miss feasible solutions that have a lower ampliier count but do not have the equally-powered wavelengths constraint. In this paper, we present a method to solve the minimum-ampliier-placement problem while avoiding the equally-powered-wavelength constraint. We demonstrate that, by allowing signals to operate at diierent power levels, our method can reduce the number of ampliiers required.