On the number of wavelengths and switches in all-optical networks

|We consider optical networks using wavelength division multiplexing, where the path a signal takes is determined by the network switches, the wavelength of the signal, and the location the signal originated. Therefore, a signal is routed through a combination of circuit switching and wavelength routing (assigning it a wavelength). We present a bound on the minimum number of wavelengths needed based on the connectivity requirements of the users and the number of switching states. In addition, we present a lower bound on the number of switching states in a network using a combination of circuit switching, wavelength routing, and frequency changing. The bounds hold for all networks with switches, wavelength routing, and wavelength changing devices. Several examples are presented including a network with near optimal wavelength re-use.