Optimal evacuation control in large urban networks with stochastic demand
The study develops a risk-aware Model Predictive Control framework for large-scale vehicular evacuations using the Generalized Bathtub Model to track network-wide trip completion rates. The control policy uses origin gating, such as staged departures or adaptive ramp metering, to minimize a convex objective combining evacuation delay and spatial hazard exposure. Tested on a simulated flood evacuation of Amager Island in Copenhagen using a coupled shallow-water model, the policy reduced the expected area-under-queue by an average of 27% across 10,000 stochastic demand scenarios.
Why it matters — It provides a mathematical proof that the optimal origin-gating profile is monotone decreasing and follows a single-switch bang-bang structure under uniform spatial demand, explaining why early heavy release followed by throttling is mathematically optimal. This theoretical result offers a closed-form seed that significantly simplifies and speeds up numerical optimization for real-time emergency management.
Caveat: The framework's optimal control proof relies on the assumption of a non-decreasing hazard rate in the residual-distance distribution, which may not hold in highly irregular or non-convex evacuation zones.