Optimal Evacuation Control in Large Urban Networks With Stochastic Demand

TL;DR

This paper introduces a risk-aware MPC framework for large-scale urban evacuations, optimizing origin gating policies under stochastic demand and spatial risk, with proven monotonicity properties and demonstrated effectiveness in flood scenarios.

Contribution

It develops a novel risk-aware MPC approach using the Generalized Bathtub Model, providing analytical results and practical insights for optimal evacuation control under uncertainty.

Findings

MPC reduces evacuation queues by 27% on average.

Optimal control policies are monotone decreasing and bang-bang under certain conditions.

The framework effectively models flood evacuation scenarios with real data.

Abstract

We develop a risk-aware Model Predictive Control (MPC) framework for large-scale vehicular evacuations. Traffic dynamics are captured by the Generalized Bathtub Model, which describes the network-wide trip completion rate by tracking the time evolution of the distribution of remaining trip distances. We model evacuation inflow as a stochastic inflow process, and employ origin gating as the control policy, implemented through staged departure orders or adaptive ramp metering. A convex objective integrates total evacuation delay with a generic hazard-exposure term which can embed any spatial risk field (e.g., flood depth, fire intensity). We prove that if the residual-distance distribution exhibits non-decreasing hazard rate, then the optimal origin-gating profile is necessarily monotone decreasing and, under an inflow cap, bang-bang (single switch). This result supplies a closed-form seed for numerical optimizations and clarifies why early heavy release followed by throttling is optimal. Furthermore, we demonstrate that the assumption of a non-decreasing hazard rate is always satisfied when the origins of evacuation movements are uniformly distributed over a convexly bounded evacuation zone-a property that is fulfilled in the vast majority of real evacuation scenarios, at least approximately. The framework is demonstrated through a flood evacuation scenario on Amager Island, a densely populated area of Copenhagen that faces significant flood risk due to its low elevation and coastal exposure. The Generalized Bathtub evacuation model is coupled with a lightweight shallow-water model parameterized using real bathymetric and topographic data from Amager Island. Across 10,000 stochastic demand scenarios, the MPC policy reduces the expected area-under-queue by an average of 27% compared to a no-control scenario.