Copula-Based Dependence Modeling for Resilient 6G Multi-Hop Wireless Networks
Reliable operation of multi-hop wireless networks requires accounting for statistical dependence among link failures caused by common propagation conditions and shared network components. This paper develops a copula-based framework for modeling node-induced dependence among link-level signal-to-noise ratios and quantifying its effect on end-to-end outage. By separating marginal fading distributions from the dependence structure, the framework captures nonlinear and tail-dependent coupling beyond conventional correlation-based models. Exact outage expressions are derived for primary-backup configurations involving edge-disjoint paths and paths with shared links. We then characterize the conditional outage probability of each candidate backup path given a primary-path failure, jointly accounting for node-induced dependence and shared-link failures. In high-reliability regimes, we derive a first-order score that decomposes conditional outage into terms associated with marginal path outage, shared links, and node-induced dependence, enabling efficient dependence-aware backup-path selection. We also establish sufficient conditions under which the first-order and exact selection rules identify the same backup path. Numerical results validate the analysis and show that copula families with the same Kendall's $τ$ can yield markedly different outage behavior because of their different tail-dependence properties. In particular, lower-tail dependence and path overlap can substantially reduce redundancy gains and reverse rankings based only on marginal outage probability.