# Routing and Wavelength Assignment in All-Optical Networks

## Abstract

This paper considers the problem of routing connections in a reconfigurable optical network using wavelength division multiplexing. Each connection between a pair of nodes in the network is assigned a path through the network and a wavelength on that path, such that connections whose paths share a common link in the network are assigned different wavelengths. We derive an upper bound on the carried traffic of connections (or equivalently, a lower bound on the blocking probability) for any routing and wavelength assignment (RWA) algorithm in such a network. The bound scales with the number of wavelengths and is achieved asymptotically (when a large number of wavelengths is available) by a fixed RWA algorithm. Although computationally intensive, our bound can be used as a metric against which the performance of different RWA algorithms can be compared for networks of moderate size. We illustrate this by comparing the performance of a simple shortest-path RWA (SP-RWA) algorithm via simulation relative to our bound. We also derive a similar bound for optical networks using dynamic wavelength converters, which are equivalent to circuit-switched telephone networks, and compare the two cases for different examples. Finally, we quantify the amount of wavelength reuse achievable in large networks using the SP-RWA via simulation as a function of the number of wavelengths, number of edges, and number of nodes for randomly constructed networks as well as deBruijn networks. We also quantify the difference in wavelength reuse between two different optical node architectures. The results show that it is feasible to provide several all-optical connections to each node in a large network using a limited number of wavelengths. For instance, using 32 wavelengths, it is possible to provide 10 full-duplex connections to each node in a 128-node random network with average degree 4, and 5 full-duplex connections per node in a 1000-node random network with average degree 4. The results also show that wavelength converters offer a 10-40% increase in the amount of reuse achievable for our sampling of 14 networks ranging from 16 to 1000 nodes when the number of wavelengths available is small (10 or 32). © 1995 IEEE