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

In recent years, space division multiplexing (SDM) technology, particularly multi-core and multi-mode fibers (MCMMFs), has been investigated to overcome physical limitations and enhance transport capacity. When SDM is integrated with elastic optical networks (EONs), it gives rise to an emerging technology known as spectrally-spatially elastic optical networks (SS-EONs). However, SS-EONs face significant challenges, such as fragmentation and crosstalk (XT), which increase blocking probability. Defragmentation is widely regarded as the most effective technique to mitigate fragmentation and reduce blocking probability. However, analytically assessing blocking probability with defragmentation is challenging due to the added constraints. Current studies on MCMMF-based SS-EONs typically rely on simulations or overlook defragmentation in their analytical models. This paper proposes AnDefrag, the first exact analytical continuous-time Markov chain model designed to calculate blocking probabilities in SS-EONs, taking into account defragmentation and the XT-avoided approach. AnDefrag generates all possible states and transitions, avoiding inter-core and inter-mode XTs for both single-class and multi-class requests. Single-class requests utilize an equal number of slots, while multi-class requests require different numbers of slots to meet clients’ needs. For cases where AnDefrag is not scalable, we introduce an iterative approximate model for single-hop links, which is extended to multi-hop networks. Numerical evaluations indicate that AnDefrag outperforms a non-defragmentation-aware benchmark model, as demonstrated through comparison with Monte Carlo simulations for a single-hop link.