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An Improved Analytical Model for the Estimation of Blocking Probability in WDM Networks with First-Fit Wavelength Assignment

Wavelength Division Multiplexing (WDM) optical networks are often operated using first-fit (FF) wavelength assignment algorithms. These FF algorithms have the advantage of reducing wavelength fragmentation in the network fiber links. Unfortunately, analytically quantifying the blocking probability due to fragmentation and lack of wavelength availability is a challenging problem when using a FF wavelength assignment algorithm. Contributing to the model complexity are two factors: the traffic peakedness which is wavelength dependent, and the strong dependency of wavelength availability between link pairs. The former is caused by the incoming lightpath requests which overflow from wavelength to wavelength in the order chosen by the FF algorithm. The latter is caused by the wavelength continuity constraint, which must be satisfied in order to avoid the use of costly wavelength converters. In this paper, the authors present an improved approximate analytical model, which takes both factors into consideration while estimating the blocking probability in WDM networks that operate with fixed routing scheme, FF wavelength assignment algorithm, and wavelength continuity constraint. The results show that the model can accurately estimate the blocking probability in relatively small WDM networks with less than ten wavelengths. The model is then applied to estimate the performance gap between two fixed routing schemes, one minimizing the lightpath hop count, and the other maximizing the lightpath signal to noise ratio at the receiver.