Centralized exit allocation framework for system optimal evacuation in underground stations

Underground stations represent high-risk environments where fires can result in mass casualties due to limited access points and enclosed spatial configurations. This study proposes a two-phase centralized evacuation guidance model structured sequentially around user equilibrium and system optimum, and comparatively analyzes the performance of the A* algorithm and Dijkstra's algorithm under both conditions. A virtual three-basement-level station was modeled as a node-link graph with dynamic weights reflecting congestion levels and fire spread, and simulations were conducted across ten fire scenarios. Exit allocation ratios were explored at 1% increments to dynamically identify optimal distributions. Under the Phase 1 user equilibrium condition, the A* algorithm demonstrated approximately 4.5 times greater computational efficiency than Dijkstra's algorithm and consistently achieved lower maximum evacuation times; however, bottlenecks arising from the concentration of evacuees at specific exits were observed. The inefficiency gap between user equilibrium and system optimum was quantified using the Price of Anarchy, which averaged 1.10 and 1.14 for the A* and Dijkstra's algorithms, respectively. Under the Phase 2 system optimum condition, adjustments to exit allocation consistently reduced maximum evacuation times across all cases, and in bottleneck-free environments, Dijkstra's algorithm outperformed in certain cases. The findings of this study suggest that exit allocation strategy at the system level should be prioritized over algorithmic performance optimization in the design of evacuation guidance systems.