Numerous studies have been carried out to quantify the benefits of wavelength conversion.61-63 These efforts employed either probabilistic models or they used deterministic algorithms on specific network topologies The studies indicate that the benefits are greater in a mesh network than in a ring or fully connected network.
To illustrate the effect of wavelength conversion we show a simple model that is based on standard series independent-link assumption commonly used in circuit-switched networks58.61.In this simplified example during a request for establishing a lightpatch connection between two stations ,the usage of a wavelength on a fiber is statistically independent of other fiber link and other wavelengths. Although this model tends to overestimate the probability that a wavelength is blocked along a path, it provides insight into the network performance improvement when using wavelength conversion.