# Statistical Analysis and Modeling for Optical Networks
## 5 Statistical Analysis and Modeling for Optical Networks
### Dimensioning in Optical Networks
#### 5.3.5 AI and Machine Learning for Statistical Modeling of Optical Networks  
The relentless growth of data traffic and the increasing complexity of optical network architectures necessitate advanced tools for performance prediction, fault detection, and resource optimization. Traditionally, statistical modeling of optical networks has relied on analytical approaches and empirical measurements. However, the sheer volume of data generated by modern optical systems, coupled with the intricate interplay of physical layer impairments (e.g., chromatic dispersion, polarization mode dispersion, non-linear effects), demands more sophisticated techniques. This is where AI and machine learning (ML) emerge as transformative forces [84]. AI/ML algorithms, particularly supervised and unsupervised learning, offer an unparalleled ability to identify complex patterns, build predictive models, and classify anomalies within vast datasets that would overwhelm conventional methods. For instance, neural networks can be trained on historical network performance data to predict future quality of transmission (QoT) for various light-paths under dynamic traffic conditions, factoring in the impact of impairments and cross-talk [85]. Similarly, clustering algorithms can group similar network states, aiding in proactive fault identification and root cause analysis. Reinforcement learning (RL), on the other hand, presents a promising avenue for autonomous network control, allowing intelligent agents to learn optimal routing and resource allocation strategies through interaction with the network environment, continuously adapting to changing demands and degradation [86]. The shift towards AI/ML-driven statistical modeling marks a paradigm shift, enabling optical networks to become more resilient, efficient, and self-managing. RL offers a powerful framework for statistical modeling of optical networks by enabling intelligent agents to learn optimal decision-making policies through trial and error. Unlike traditional supervised learning, RL agents interact directly with the network environment, receiving feedback for their actions, and iteratively refining their strategies to maximize long-term performance. This makes RL particularly well-suited for dynamic problems in optical networks, such as real-time resource allocation (e.g., routing, spectrum assignment, and modulation format selection), proactive fault management, and power consumption optimization [86]. By learning from the statistical properties of network states and the consequences of various actions, RL models can adapt to unpredictable traffic patterns, evolving network conditions,  
Figure 8: An optical network with average shortest path length 930 km. It shows the shortest path probabilities in different intervals of shortest path lengths according to the half distance law proposed in [70]. and the stochastic nature of physical layer impairments, leading to more resilient, efficient, and self-optimizing optical networks. The application of AI and ML to statistical modeling of optical networks extends beyond prediction and classification; it fundamentally enhances operators' ability to understand and control these complex systems [87]. Traditional statistical methods often fall short in managing complex, multi-vendor, multi-layer optical networks because they struggle to capture the full range of operational intricacies. As AI/ML models learn from real-time and historical operational data, they can provide a holistic view of network health and performance. This includes developing highly accurate statistical models for SNR estimation, predicting the likelihood of link failures based on various environmental and operational parameters, and optimizing power consumption across the network [85]. Furthermore, AI/ML can facilitate the creation of digital twins for optical networks, allowing for the simulation and testing of different network configurations and failure scenarios in a virtual environment before deployment, thereby reducing risks and accelerating innovation.