Stacked Intelligent Metasurfaces-Aided eVTOL Delay Sensitive Communications

With rapid urbanization, ground transportation is increasingly strained, motivating the development of Advanced Air Mobility (AAM) to exploit low-altitude airspace for three-dimensional transportation. A key enabler of AAM is the electric Vertical Take-off and Landing (eVTOL) Aircraft, valued for its flexibility and efficiency. However, the immaturity of Ultra Reliable Low Latency Communication (URLLC) technologies poses critical challenges to safety-sensitive operations. In particular, existing Stacked Intelligent Metasurface (SIM)-assisted eVTOL systems lack rigorous mathematical frameworks to characterize probabilistic delay bounds under dynamic air traffic, which are essential for collision avoidance and airspace management. To bridge this gap, we employ network calculus tools to derive the probabilistic upper bound on communication delay in the AAM system for the first time. Furthermore, we formulate a complex non-convex optimization problem that jointly minimizes the probabilistic delay bound and the propagation delay threshold. To solve this problem efficiently, we propose a solution based on the Block Coordinate Descent (BCD) algorithm and Semidefinite Relaxation (SDR) method. In addition, we conduct a comprehensive analysis of how various factors impact regret and transmission rate, and explore the influence of varying load intensity and total delay on the probabilistic delay bound. Under identical meta-atom settings, simulation results indicate that the proposed method achieves a 26.85% average improvement in transmission rate over the low-complexity Alternating Optimization (AO) algorithm. This work provides a theoretical foundation and technical reference for future delay performance optimization and safety assurance in AAM systems.