Analytical calculation of blocking probabilities in WDM rings with the first-fit algorithm

The estimation of blocking probabilities in optical path networks has been investigated mainly for the case in which wavelengths are chosen randomly among the available ones on a route. Even though algorithms that unbalance the load among wavelengths usually have a superior performance when compared with the random algorithm, the modeling complexity of these better-performance algorithms often limits their analytical analysis. This article proposes a per-wavelength plane blocking probability estimation for the first-fit algorithm in WDM rings with wavelength continuity constraint. Moreover, the estimation method allows the calculation of the probability distribution of the constellations of active wavelengths in the network links under the first-fit rule for a given blocking probability.