Computing approximate blocking probabilities in wavelength routed all-optical networks with limited-range wavelength conversion

We propose a method to calculate the average blocking probability in all-optical networks using limited-range wavelength conversion. Previous works have shown that there is a remarkable improvement in blocking probability while using limited-range wavelength conversion but these analytical models were either for a path or for a mesh-torus network. Using a graph-theoretical approach, we extend Birman´s model (see IEEE JSAC/JLT Special I on Optical Networks, vol.14, no.5, p.852-57, 1996) for no wavelength conversion and derive an analytical expression to compute the blocking probabilities in networks with limited-range wavelength conversion for fixed routing. The proposed analytical model is a generalization of Birman´s model and is applicable to any network topology. We consider the case where an incoming wavelength can be converted to d adjacent outgoing wavelengths on either side of the input wavelength, in addition to the input wavelength itself, where d is the degree of conversion. Using this model we demonstrate that the performance improvement obtained by full wavelength conversion over no wavelength conversion can almost be achieved by using limited-wavelength conversion with the degree of conversion, d, being only 1 or 2. In a few example networks we considered, for blocking probabilities up to a few percent, the carried traffic with limited-conversion degree d=2 was almost equal to the carried traffic for full wavelength conversion. The results obtained show that significant improvements in blocking performance can be obtained by providing limited-range wavelength conversion of small degree within the network