This paper analyses the wavelength assignment problem in case of WDM optical networks. The random wavelength assignment algorithm is compared with the first – fit wavelength assignment algorithm .These two assignment strategies are also compared with wavelength conversion case. These comparisons are made on the basis of blocking probability,  keeping the number of channels and number of links constant and the response is calculated by varying load per link ( in erlangs).  Blocking probability on a link is calculated by using famous Erlang B formula. It is seen that blocking probability in case of random wavelength assignment is always greater than first –fit wavelength assignment algorithm. The blocking probability in case of WDM networks employing wavelength converters is minimum but it increases the overall cost of the optical network.