The estimation of discovery duration in fully connected mesh-networks under non-zero bit error rates

This is the authors' abstract. We don't add key points for this paper.

Neighbor discovery is a fundamental step in establishing wireless mesh-networks, but its completion time is strongly affected by channel interference. Since route construction in self-organizing wireless networks relies on prior neighbor detection, any delays at this stage directly impact overall network setup time. In practical radio environments, packet losses further prolong the discovery process. In this work, we study how the packet error rate (PER) influences the average time required to discover all neighbors in a complete-graph topology. We reformulate this problem as a variant of the coupon collector problem, which leads to a closed-form analytical expression relating the mean discovery time to PER. The accuracy of the derived formula is verified through simulation. The proposed model allows network designers to quantitatively estimate initialization delays during the planning phase, eliminating the need for experimental measurements. The results offer a practical means to forecast mesh-network deployment timelines already at the radio-coverage calculation stage.