author = "Rosa, A. N. F. and Wiatr, P. and Cavdar, C. and Carvalho, Solon 
                         Ven{\^a}ncio de and Costa, J. C. W. A. and Wosinska, L.",
          affiliation = "{Universidade Federal do Par{\'a} (UFPA)} and {KTH Royal of 
                         Technology} and {KTH Royal of Technology} and {Instituto Nacional 
                         de Pesquisas Espaciais (INPE)} and {Universidade Federal do 
                         Par{\'a} (UFPA)} and {KTH Royal of Technology}",
                title = "Statistical analysis of blocking probability and fragmentation 
                         based on Markov modeling of elastic spectrum allocation on fiber 
              journal = "Opitcs Communications",
                 year = "2015",
               volume = "354",
                pages = "362--373",
                month = "Nov.",
             keywords = "Blocking probability, Elastic optical networks, Markov modeling, 
                         Spectrum allocation, Spectrum fragmentation.",
             abstract = "In Elastic Optical Network (EON), spectrum fragmentation refers to 
                         the existence of non-aligned, small-sized blocks of free 
                         subcarrier slots in the optical spectrum. 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 sizes of connection requests and do not allow in-depth 
                         investigation of blocking events and their relation to 
                         fragmentation. The analytical study of the effect of fragmentation 
                         on requests' blocking probability is still under-explored. In this 
                         work, we introduce new definitions for blocking that differentiate 
                         between the reasons for the blocking events. We developed a 
                         framework based on Markov modeling to calculate steady-state 
                         probabilities for the different blocking events and to analyze 
                         fragmentation related problems in elastic optical links under 
                         dynamic traffic conditions. This framework can also be used for 
                         evaluation of different definitions of fragmentation in terms of 
                         their relation to the blocking probability. We investigate how 
                         different allocation request sizes contribute to fragmentation and 
                         blocking probability. Moreover, we show to which extend blocking 
                         events, due to insufficient amount of available resources, become 
                         inevitable and, compared 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 
                  doi = "10.1016/j.optcom.2015.03.039",
                  url = "http://dx.doi.org/10.1016/j.optcom.2015.03.039",
                 issn = "0030-4018",
             language = "en",
        urlaccessdate = "30 nov. 2020"