{'fraction_non_alphanumeric': 0.016242937853107344, 'fraction_numerical': 0.0, 'mean_word_length': 5.297777777777778, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Computing Blocking Probabilities in Elastic Optical Networks with Spectrum Defragmentation

Spectrum defragmentation (DF) as a connection reconfiguration method is essential in elastic optical networks (EONs) in order to minimize connection blocking probability. This paper proposes the first exact Markov model to computing exact blocking probabilities in EONs with DF by taking into account the occupancy status of spectrum slices of all network links, and waiting and serving connections during a DF process. Since the complexity of the exact Markov model increases exponentially with the network capacity and size, we propose a reduced state model where a link occupancy state is defined by the total occupied slices on a fiber link. Furthermore, using a spectrum fragmentation factor in each occupancy state we calculate state-and class-dependent connection setup rates, which is used to compute approximate blocking in EONs with DF. Notably, we show individually the distinct blocking values, one due to resource unavailability and the other due to fragmentation, both under a random-fit and a first-fit spectrum allocation policies. Our numerical results show that the DF process is very useful in reducing overall connection blocking in EONs. We also observe that blocking due to spectrum fragmentation can be reduced, but not eliminated in a mesh network topology even when an optimal DF scheme is deployed.