Optimal Evacuation Control in Large Urban Networks With Stochastic Demand
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908483555688448 |
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| author | Hammerl, Alexander Jin, Wenlong Seshadri, Ravi Rasmusssen, Thomas Kjær Nielsen, Otoo Anker |
| author_facet | Hammerl, Alexander Jin, Wenlong Seshadri, Ravi Rasmusssen, Thomas Kjær Nielsen, Otoo Anker |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Evacuation Control in Large Urban Networks With Stochastic Demand Hammerl, Alexander Jin, Wenlong Seshadri, Ravi Rasmusssen, Thomas Kjær Nielsen, Otoo Anker Optimization and Control 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. |
| title | Optimal Evacuation Control in Large Urban Networks With Stochastic Demand |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.06797 |