In this paper 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 (1996) model for no wavelength conversion and derive an analytical expression to compute the blocking probabilities in networks for fixed routing. The proposed model 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. When d=0 and d=((C-1)/2), where C is the capacity of a link, the proposed model reduces to the model previously given for no wavelength conversion and the model previously given for full wavelength conversion respectively. 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-range wavelength conversion with the degree of conversion, d, being only 1 or 2. In the 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. Comparisons to simulations show that our analytical model is accurate for a variety of networks, for various values of the conversion degree (d=1,2,3), and hop length (1-4), and over a wide range of blocking probabilities (>0.0001). The method is also accurate in estimating the blocking probabilities on individual paths (and not just the average blocking probability in the network).

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.