The Influence of Physical Network Topologies on Wavelength Requirements in Optical Networks

In wavelength division multiplexed optical networks each connection is assigned a light-path. Given a set of connection requests, how to set up a light-path for each of them is called the static routing and wavelength assignment (RWA) problem. The physical networks impose significant effects on the number of wavelengths required to accommodate all the connections as light-paths are directly set up on it. Wavelength requirements in the small-world and scale-free networks are investigated in this paper for the first time to the best of our knowledge. The two important characteristics of networks are considered: average shortest path length and 1-shell structure. Wavelength requirements in the case of network evolution are investigated, too. Mean light-path length is proved to be directly proportional to the average shortest path length of networks. Simulation results have shown that fewer wavelengths are required in networks with smaller average shortest path lengths, and the rate of increase of the number of wavelengths required is smaller too while traffic load and network size increasing. The emergence of 1-shell structure may result in the increase of the number of wavelengths required due to lack of flexibility in 1-shell structure. The larger the cardinality of 1-shell is, the more wavelengths the network requires.