In order to evaluate the performance of Reconfigurable Optical Add/Drop Multiplexers (ROADMs) consisting of a single large switch, in circuit switched Wavelength-Division Multiplexing (WDM) networks, a theoretical Queuing Network Model (QNM) is developed, which consists of two M/M/c/c loss systems each of which is analyzed in isolation. An overall analytical blocking probability of a ROADM is obtained. This model can also be used for the performance optimization of ROADMs with a single switch capable of switching all or a partial number of the wavelengths being used. It is demonstrated how the proposed model can be used for the performance evaluation of a ROADM for different number of wavelengths inside the switch, in various traffic intensity conditions producing an exact blocking probability solution. The accuracy of the analytical results is validated by simulation.