Minimizing wavelengths in an all-optical ring network

Abstract

In an optical network, wavelength-division multiplexing permits multiple messages to be sent along the same link in the network by transmitting each message using a distinct wavelength. In such a network, the action of establishing a connection between two nodes entails choosing a route in the network between the nodes and then assigning to the connection, a wavelength for each link in the chosen route. We will consider problems concerning the minimum number of wavelengths sufficient to establish a set of connections. In a wavelength-selective (WS) network, the assigned wavelengths for any given connection must be the same throughout the chosen route. In contrast, for a wavelength-interchanging (WI) network the assigned wavelengths for each link in the route may differ. We show that for an important class of networks, namely ring networks of n nodes with clockwise and counterclockwise links between each neighboring pair of nodes on the ring, the minimum number, k _n, of wavelengths that suffice to allow simultaneously all possible connections is the same for either case. In particular, for both WS and WI networks, it is shown that k _n=(n ²−1)/8 if n is odd, k _n=n ²/8 if n is even and divisible by 4 and k _n=n ²/8+1/2 if n is even but not divisible by 4.