Previous works have considered analytical models of TDM wavelength networks to evaluate the blocking performance, but they differ in their underlying assumptions and have varying computation complexities. In this paper, we present an analytical model of TDM WDM optical networks with optical time-slot interchangers and without wavelength converter for minimum fixed hop routing. In order to make the analysis tractable, we proposed an algorithm that works for any number of partition patterns regardless of numbers of links, wavelengths in each link, and time-slots in each wavelength. Our analytical model provides good accuracies in average network blocking probabilities when compared with the simulation results.