Stochastic geometry analysis of UAV-assisted networks with probabilistic UAV activation

Unmanned aerial vehicles (UAVs) are prominent to modern wireless networks but are severely limited by onboard energy, making continuous operation of a large swarm infeasible. To address this, this paper proposes a probabilistic activation scheme in which UAVs from a larger candidate pool can enter sleep states to conserve energy. Leveraging a tractable probabilistic activation strategy, each UAV is independently switched on with an optimized probability that can be easily derived in closed form. This differentiates our work from earlier heuristic sleep-mode techniques which rely on traffic-threshold rules without analytical guarantees. We thus develop a tractable analytical framework using stochastic geometry to evaluate this scheme, modeling the active UAVs as a 3D Poisson Point Process (PPP) under a probabilistic Line-of-Sight (LoS)/Non Line-of-Sight (NLoS) propagation conditions. Novel analytical expressions are derived for the coverage probability, average achievable rate, and network energy efficiency, with their accuracy rigorously validated by Monte Carlo simulations. Our analysis reveals a fundamental trade-off between network performance and power consumption, demonstrating the existence of an optimal activation probability that maximizes the system performance. This analytical framework enables network operators to optimize activation and transmit power profiles across the entire network. The goal of this optimization is to improve outage probability, ergodic rate, and energy efficiency.