Optical burst switching (OBS) appears to be the best available solution to the ever-increasing demand for Internet bandwidth. As a multifaceted paradigm, it has opened up various motivating challenges in optical networking. Several analytical models regarding optical networking have been proposed in the literature. However, to the best of our knowledge, these models follow an exponential burst length distribution which is unrealistic in the case of threshold-based burst aggregation occurring at edge switches. In this work, we present an insightful model which considers constant burst lengths and study the effect of employing wavelength converters (WC) to the resource utilization and contention resolution policy. We investigate two types of optical switches in terms of availability of WCs in the switch fabric and study their performance through mathematical modeling using the results of queuing theory. We then further extend our investigation by comparing these switches through simulation experiments and thus, confirm our mathematical model. For the purpose of tractability, we also present an approximate model of M/D/c/K queuing system with finite waiting room using an M/D/1/K system.