The throughput of wavelength routing networks

We consider the problem of interconnecting N local area networks (LANs) through a wavelength routing all optical network supporting F wavelengths at R b/s per wavelength. A λ-routing AON is one in which the path of a signal is a function only of the signal wavelength and the origin of the signal. We allow the possibility of wavelength changing so that a signal may arrive at a destination on a different wavelength than it originated on. Furthermore, we assume a slotted system, where each wavelength supports T periodic time slots. A connection between a transmitter and a receiver is assumed to require one frequency-time slot of bandwidth. Each LAN has one outgoing fiber, one incoming fiber, and an unspecified but large number of users. The outgoing (incoming) fiber of a LAN is connected by a broadcast star to all the transmitters (receivers) of that LAN. We assume that there is exactly one active session between each pair of LANs