AnalyticalDF: Analytical Model for Blocking Probabilities Considering Spectrum Defragmentation in Spectrally-Spatially Elastic Optical Networks

Recently, multi-core and multi-mode fibers (MCMMFs) have been considered to overcome physical limitations and increase transport capacity. They are combined with elastic optical networks (EONs) to form spectrally-spatially elastic optical networks (SS-EONs), an emerging technology. Fragmentation and crosstalk (XT) are well-known drawbacks of SS-EONs that increase blocking probability; evaluating blocking probability analytically is difficult due to additional constraints. When calculating blocking probabilities in MCMMFs-based SS-EONs, it is observed that all current studies either employ simulation-based techniques or do not consider defragmentation of their analytical models. This paper proposes an exact analytical continuous-time Markov chain model for blocking probabilities, named AnalyticalDF, in SS-EONs, which considers defragmentation and the XT-avoided approach. AnalyticalDF generates all possible states and transitions while avoiding inter-core and inter-mode XTs for single-class and multi-class requests. Single-class requests utilize the same number of slots, whereas multi-class requests adopt varying numbers of slots to accommodate client needs. We introduce an iterative approximation model for a single-hop link when AnalyticalDF is not tractable due to scalability. We evaluate AnalyticalDF, the iterative approximate model, and simulation studies for a single-hop link. The numerical results indicate that AnalyticalDF outperforms a non-defragmentation-aware benchmark model.