The current trends in optical fiber communications are rapidly approaching the physical capacity limit of standard optical fiber. It is becoming increasingly important to efficiently utilize spectral resources wisely to accommodate the ever-increasing Internet traffic demand. However, the rigid and coarse ITU-T grid specifications regarding the spectrum usage restrict the granularity of bandwidth segmentation and allocation, which frequently causes a mismatch between the allocated and the actual requested link bandwidth. This often leads to over provisioning, where usually more resources are provided than necessary. Recently, the concept of elastic optical networks (EONs) has been proposed in order to reduce the waste of spectra resources. In networks with such feature enabled, modulation parameters and central frequencies are not fixed as in the traditional WDM networks: the resources can be allocated with fine granularity, which can adapt to the granularity of the requested bandwidth without over provisioning. This results in efficient usage of spectra resources. However, elastic optical networks must satisfy dynamic connection add and drop over spectral resources that inevitable results in fragmentation of the spectrum. In EONs, spectrum fragmentation is an important and inevitable problem, because it reduces the spectral efficiency. As consequence, the blocking probability (BP) is increased due to scattered gaps in the optical grid. Currently, several metrics have been proposed in order to quantify a level of spectrum fragmentation. Approximation methods might be used for estimating average blocking probability and some fragmentation measures, but are so far unable to accurately evaluate the influence of different requested connection bandwidths and do not allow in-depth investigation of blocking events and their relation to fragmentation. This thesis presents the analytical study of the effect of fragmentation on requests' blocking probability, which is still under-explored. In this study, new definitions for blocking that differentiate between the reasons for the blocking events were introduced. An analytical framework based on Markov modeling was proposed in order to calculate steady-state probabilities for the different blocking events and to analyze fragmentation related problems in elastic optical links under dynamic traffic conditions. Statistical investigations were derived in order to investigate how different allocation request sizes contribute to fragmentation and blocking probability. This work is complemented with the introduction of a new accommodated fragmentation metric that allows better differentiating between very small variations of spectrum occupancy. Moreover, we show to which extend blocking events, due to insufficient amount of available resources, become inevitable and, comparing to the amount of blocking events due to fragmented spectrum, we draw conclusions on the possible gains one can achieve by system defragmentation. We also show how efficient spectrum allocation policies really are in reducing the part of fragmentation that in particular leads to actual blocking events. Simulation experiments are carried out showing good match with our analytical results for blocking probability in a small scale scenario. Simulated blocking probabilities for the different blocking events are provided for a larger scale elastic optical link.