QKD-Analytical: Analytical Model for Blocking Probabilities in Priority-Aware Quantum Key Distribution over Space Division Multiplexed Elastic Optical Networks

Quantum key distribution (QKD) improves security in high-capacity space division multiplexing-based elastic optical networks (SDM-EONs) with multi-core fibers (MCFs). However, integrating QKD introduces inter-core crosstalk (IC-XT) and additional noise from quantum and classical channels, increasing blocking probability (BP) and complicating analytical evaluation. To address this, for the first time, we propose an exact analytical priority-based continuous-time Markov chain model, called QKD-Analytical, for QKD-enabled SDM-EONs. It computes BP by accounting for IC-XT and channel noise, while prioritizing cores based on node adjacency to optimize quantum channel placement and resource utilization. The model generates all feasible states and transitions to determine state probabilities accurately. It supports both single-class and multi-class traffic — using uniform slots for the former and variable slots for the latter to meet diverse bandwidth demands. To ensure scalability, we also develop an iterative approximation model for single-hop link analysis. Numerical results indicate that QKD-Analytical yields BP and resource utilization that closely match those obtained by Monte Carlo simulations, while the approximation model maintains good accuracy in larger scenarios. Additionally, QKD-Analytical outperforms non-priority-based models in terms of BP, highlighting the benefits of priority-aware core selection in QKD-enabled SDM-EONs.