Given the current state of the technology, the Optical Burst Switched (OBS) architecture is a practical optical switching solution for the optical networks. In OBS, the user data is transmitted in variable size data units, called bursts, which travel as an optical signal along the entire route. The control information for each burst is transmitted prior to its corresponding burst and it is electronically processed at each hop along the route. The dynamic nature of OBS allows for network adaptability and scalability, which makes it very suitable for the transmission of bursty traffic. In this thesis we study and analyze the performance of OBS networks. We consider the case when the bursts are large enough to simultaneously hold wavelengths on multiple links along the route. Since the size of the bursts varies and the link distance between two adjacent network nodes also varies, a burst may simultaneously occupy wavelengths on a variable number of links as it travels from its source to its destination. As the burst propagates through the network, it dynamically acquires and releases wavelengths from link to link. In this thesis, we propose queueing network models that feature dynamic simultaneous link possession and analyze them in order to obtain the end-to-end burst loss probabilities. This thesis is structured into five parts. In the first part, we describe the Optical Burst Switch architecture and summarize its main design components. In the second part, we define and motivate the simultaneous link possession problem. In the third part, we study an OBS network where the bursts are large enough to simultaneously hold wavelengths on one or two consecutive links. In the fourth part of this thesis, we analytically study an OBS network with simultaneous link possession and a very large number of wavelengths per link. In the fifth part, we address the problem of how to analytically evaluate the performance of OBS networks when the arrival traffic is bursty.