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We present a statistical study of wavelength usage in relation to topology characteristics for optical WDM networks with static traffic requirements, where the traffic is routed both with and without wavelength conversion. We identify new general correlations between parameters describing network topologies and wavelength usage. We find that the regularity of a network and the number of spanning trees in a network are accurate and reliable measures of the routing efficiency in terms of wavelengths used to accommodate the required traffic. An empirical formula is given for the average number of wavelengths required to accommodate the traffic as a function of the number spanning trees in the network. We observe that in most cases, the wavelength usage with and without wavelength converters are identical. Consequently, the correlations between network topology and traffic assignment efficiency are true for both types of networks.

Statistical Study of the Correlation Between Topology and Wavelength Usage in Optical Networks with and without Conversion