AnalyticalCP: Blocking Probability Analysis Considering Counter-Propagation in Spectrally-Spatially Elastic Optical Networks

Signal transmission using counter-propagation is increasingly adopted to enhance resource utilization in spectrally-spatially elastic optical networks (SS-EONs). Crosstalk is a well-known drawback of SS-EONs that increases blocking probability. Evaluating blocking probability analytically in counter-propagation is challenging due to additional constraints. Current studies typically employ simulation-based techniques or do not consider dynamic scenarios in their analytical models to estimate blocking probability. This paper proposes AnalyticalCP, an exact analytical continuous-time Markov chain model (CTMC) for SS-EONs considering counter-propagation, which estimates blocking probabilities and enhances resource utilization. AnalyticalCP is constructed in two phases: (i) First, a bipartite graph is formed to generate two separate sets of cores and modes, using an optimization approach focused on minimizing interference among cores and modes. (ii) Second, the resultant sets of cores and modes serve as input parameters for the analytical model, streamlining the generation of all feasible states and transitions to estimate exact blocking probability. AnalyticalCP accommodates both single- and multi-class requests: single-class requests uniformly utilize spectrum slots, while multi-class requests adapt slot usage to match bandwidth requirements. Numerical results indicate that AnalyticalCP and the simulations yield comparable performances in terms of blocking probabilities and resource utilization, with the iterative approximate model also demonstrating acceptable accuracy. AnalyticalCP outperforms a benchmark model that considers vertex elimination during bi-partitioning. We extend our CTMC model with a Markov-modulated Poisson process (MMPP) to evaluate bursty-traffic behavior in SS-EONS.