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G-2026-03

Numerical evaluation of distributed wireless networks at scale

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Large-scale distributed wireless networks offer infrastructure-free and cost-effective connectivity. Recent theoretical work has shown that scalability critically depends on underlying user interaction patterns; however, a fundamental gap remains between asymptotic feasibility results and concrete, numerically grounded performance metrics. This paper presents a comprehensive numerical evaluation of very large-scale distributed wireless networks by decomposing the cross-layer P2P capacity analysis into two tightly coupled components: the expected hop count \(\mathbf{E}(h)\) and the effective single-hop transmission capacity \(\mathbf{E}(C_{\mathrm{eff}})\). Leveraging network symmetry and geometric partitioning, we transform the discrete hop-count problem into a continuous formulation and derive a closed-form integral upper bound on \(\mathbf{E}(h)\) using convex optimization. This enables efficient numerical evaluation even for networks with millions of nodes and reveals that, despite network diameters spanning hundreds of kilometers, typical communication paths traverse only a small fraction of this extent under real-world interaction patterns. To quantify \(\mathbf{E}(C_{\mathrm{eff}})\), we develop a cross-layer wireless model with full spatial reuse and derive a closed-form upper bound on aggregate interference, allowing optimization of the resource-sharing parameter that maximizes per-node throughput. Combining both components yields explicit numerical bounds on link-level capacity, end-to-end P2P throughput, delay, spectral efficiency, and energy consumption. The results demonstrate that large-scale distributed networks can sustain substantial per-user data volumes while operating with limited spectrum and ultra-low transmit power. Short-range links enable aggressive spatial reuse and high energy efficiency, and naturally align with millimeter-wave technologies that provide large bandwidths. Overall, this work shows that large-scale distributed wireless networks are not only theoretically scalable but also practically competitive with infrastructure-based systems.

, 48 pages

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