The Throughput of Wavelength Routing Networks

We consider the problem of interconnecting N local area networks LANs through a wavelength routing all optical network wavelength-routing AON supporting F wavelengths at R bs per wavelength. A wavelength-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 session, i.e. connection between a transmitter and a receiver, is assumed to require one frequency-time slot of bandwidth, i.e. RT bs. 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. Therefore the network supports N-squared sessions. Define the capacity, C, as the largest value of N-squared possible as a function of F and T.