# Statistical Analysis and Modeling for Optical Networks
## 2 Literature Review on Statistical Analysis and Modeling for Networks
### Statistics for Networks  
The indispensable role of statistics in network analysis and design stems from its capacity to decipher and optimize complex interconnected systems [34; 35; 36; 37]. In the realm of network analysis, statistical methodologies are fundamental for characterizing network topology, discerning inherent patterns, and extracting actionable insights from extensive datasets. Descriptive statistics, for instance, quantify critical network properties, like degree distributions, clustering coefficients, and path lengths, thereby illuminating underlying organizational structures, such as small-world and scale-free networks. The evolution of statistical applications in network analysis and design parallels the progression of network theory and data analysis [34; 35; 36; 37; 38]. Initially, statistical methods were deployed in social network analysis to describe and quantify interpersonal relationships [35]. Sociological pioneers, starting with [PERSON] and continuing through sociometry in the 1930s, utilized statistical tools to map social interactions [36]. The mid-20 th century witnessed the rise of graph theory, providing a mathematical scaffold for network analysis, with statistical techniques employed to assess network connectivity and structure [8; 34]. The advent of computer networks in the latter half of the 20 th century necessitated the use of statistical methods for analyzing network traffic, performance, and reliability. Optical networks became mainstream beginning in the 1990s, and their role became global. Optical communication techniques became popular, and all the core networks became optical [38; 39; 40; 41; 42]. Queueing theory, a probabilistic discipline, was applied to model network congestion and optimize resource allocation [29]. The internet's exponential growth, coupled with the availability of vast network datasets in the late 20 th and early 21 st centuries, spurred the development of advanced statistical models, including exponential random graph models and stochastic block models, to capture intricate network structures and dynamics [12; 15; 43; 44]. Statistical modeling, encompassing these techniques, facilitates the understanding of network formation mechanisms and the identification of community structures [15; 19; 20; 21; 22; 23]. In network design, statistical analysis informs pivotal decisions regarding resource allocation, routing optimization, and network resilience [3]. By analyzing traffic patterns, connection probabilities, and network performance metrics, designers can enhance network efficiency and robustness. Moreover, statistical methods are crucial for predicting network behavior under varying conditions, enabling proactive strategies to mitigate congestion, failures, and security threats [44]. Overall, statistics provides the quantitative foundation for informed decision-making across all facets of modern network analysis and design. Statistics for Network Analysis, Estimation and Dimensioning  
In early-stage planning and dimensioning of optical networks, engineers often work with incomplete or partial information [3; 30; 31; 32; 33]. Typically, only basic parameters, such as coverage area and node count, are available. In such cases, statistical modeling becomes essential for network planning and design, enabling fast estimations even with limited data [4; 31]. These models help predict compensation techniques at the receiving end, repeater and amplifier placements, and total fiber length requirements. A reliable statistical model of link lengths is crucial for making accurate optical network estimations with minimal information [31; 32; 33]. To ensure practical applicability, the model must be highly accurate so that its predictions remain trustworthy for real-world deployments. Therefore, rigorous testing on existing optical networks is necessary to validate its performance and reliability [25; 45]. Statistical analysis of optical networks must integrate the characteristic behaviors observed in these systems [46].