Design-Stage Modeling of Health-Risk-Induced Egress Delay in Stadium Stands Using Reproducible Queue Networks

Stadium stands combine high occupant density, steep seating geometry, and constrained egress routes, yet design-stage egress calculations usually represent spectators through aggregate flow rates and do not explicitly account for health-related stair-use tolerance. This study proposes a reproducible queue-based workflow for estimating health-risk-induced egress delay in independent stadium-stand units and for supporting early-stage design screening. A deterministic capacity–flow baseline is first computed for each stand and translated into an auditable GraphML queue network. A Nursing-Based Health Score (NBHS), derived from riser height, tread depth, and stair pitch, is used as a geometry-based tolerance proxy rather than a clinical diagnostic score. NBHS risk is then propagated through vulnerable-profile headway multipliers at constrained gangway-to-vomitory bottleneck edges, and stand-level delay is estimated using grouped Monte Carlo queue processing. The queue baseline remained close to the deterministic reference (mean Tqueue0/Tdet = 0.980), supporting interpretation of subsequent delays as controlled perturbations. Delay increased monotonically with headway sensitivity, and stand-level variation was explained by GraphML-derived bottleneck service-rate properties. These findings provide a practical design-stage reference for identifying stand configurations where stair geometry and egress bottleneck capacity jointly amplify delay for vulnerable spectators.