The Role of Fractal Dimension in Wireless Mesh Network Performance

TL;DR

A novel algorithm is presented that constructs WMN topologies with tunable fractal dimensions, allowing precise control over spatial self-similarity, and demonstrates the potential of fractal geometry as a design paradigm for scalable and efficient WMN architectures.

Abstract

Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement, which inadequately represent the complex, hierarchical spatial patterns observed in practical deployments. In this study, we present a novel algorithm that constructs WMN topologies with tunable fractal dimensions, allowing precise control over spatial self-similarity. By systematically varying the fractal dimension, the algorithm generates network layouts spanning a continuum of spatial complexities, ranging from sparse fragmented clusters to dense, cohesive structures. Through NS-3 simulations, Key performance metrics including throughput, latency, jitter, and packet delivery ratio were evaluated across a range of fractal dimensions. Comparative evaluations against classical random, small-world, scale-free, grid and hierarchical tree networks models reveal that high-dimensional fractal topologies achieve enhanced resilience and throughput under equivalent conditions. These findings demonstrate the potential of fractal geometry as a design paradigm for scalable and efficient WMN architectures.

Figures (9)

• Figure 1: Network topologies generated with fractal dimensions from $D = 1$ to $D = 9$. Low-dimensional networks exhibit fragmented, sparse structures, whereas higher-dimensional embeddings result in denser and more uniformly connected graphs. Node color indicates the average link capacity per node, reflecting its local connectivity.
• Figure 2: Fractal dimension validation and dependence of performance metrics. Left: Box-counting estimation of fractal dimension across spatial configurations with $N = 10^5$ nodes. The solid line($D_{\text{BC}}$), denotes measured values, while the dotted line ($D_{\text{target}}$) marks the ideal identity line, confirming the accuracy of the embedding algorithm. Right: Pearson correlation matrix among performance metrics. Throughput and PDR exhibit moderate positive correlation, whereas delay and jitter are largely uncorrelated with other metrics, indicating low redundancy across evaluation dimensions.
• Figure 3: Global efficiency, algebraic connectivity, and average edge-disjoint paths (EDP) versus fractal dimension $D = 1$ to $D = 10$. Unweighted networks show higher efficiency but lower connectivity, and EDP is shown for unweighted networks only
• Figure 4: Pairwise relationships between key performance metrics across fractal dimensions. Each point represents a network configuration; marker shapes indicate low ($D < 5$, triangles) and high ($D\geq5$, circles) fractal dimensions.Higher-dimensional networks consistently show better performance across all metric combinations.
• Figure 5: Comparative performance analysis of fractal and baseline networks. Quality-of-service (QoS) metrics—including throughput, packet delivery ratio (PDR), end-to-end delay, and jitter are evaluated across fractal, scale-free (BA), small-world (WS), random (ER), grid and hierarchical tree topologies under the same simulation conditions.