Abstract
Three-dimensional networks-on-chip (3-D NoCs) provide high inter-layer bandwidth but expose routing to through-silicon-via failures, thermal gradients, congestion, and topology changes. This paper proposes ESDAR-3D, an epoch-safe diversity-adaptive routing method for worm-hole-switched 3-D meshes and partially connected vertical topologies. The adaptive plane admits every healthy neighbor that remains connected to the destination and ranks candidates using residual distance, queue pressure, observed link risk, vertical thermal/wear cost, onward path diversity, and a packet-local revisit penalty. A bounded adaptive phase can irreversibly enter an epoch-specific escape virtual channel routed on a breadth-first spanning tree. A channel ranking proves that the escape dependency graph is acyclic; bounded adaptive residence and fair arbitration establish livelock freedom. A banked epoch protocol prevents old and new escape trees from sharing a virtual channel during reconfiguration. Exhaustive structural validation covers 46,938 fault configurations of an 18-router mesh and 26,290 configurations of a 27-router mesh, with zero escape-rank or connected-pair delivery violations. Seeded Monte Carlo tests on a 4 x 4 x 4 mesh likewise found no structural violation. The reported results validate safety and reachability only; cycle-accurate latency, throughput, area, and power evaluation remain necessary before silicon-oriented claims can be made.