Reliability evaluation and multi-stage performance analysis of multi-state air-ground cooperative networks for city aviation and railway infrastructure

Dynamic assessment of stable operation capability and performance efficiency for air-ground cooperative networks under various shock scenarios, such as adverse weather and equipment failures, is critical for ensuring network reliability. This paper proposes a multi-state air-ground cooperative network reliability evaluation and multi-stage performance analysis approach for city aviation and railway infrastructure. First, a comprehensive network architecture is established that incorporates aviation and railway passenger transport systems along with their operational interdependencies. Subsequently, a multi-state failure-recovery process model is developed to characterize network reliability under different shock scenarios. Next, a three-tier cost analysis framework is introduced to quantify revenue losses, image losses, and operational costs under various shock scenarios. A multi-stage performance model is then proposed, integrating resistive, degraded, recovery, and comprehensive performance efficiency indicators to capture dynamic network behavior throughout the entire disruption cycle. The primary advantage of this framework lies in its capability to systematically assess network reliability while providing actionable insights for performance optimization through targeted improvement strategies. Experimental validation using air-ground cooperative networks from three adjacent provinces in China demonstrates the effectiveness of the proposed approach. For the Air-Dominant and Rail-Supplementary (ADRS) and Bilayer Air-Rail Parallel (BARP) network modes, after implementing improvement strategies, the comprehensive performance efficiency improved by 0.0154 and 0.0872 respectively under general failure scenarios, and by 0.0563 and 0.0542 respectively under extreme failure scenarios.