Dynamic reconfiguration strategies for managing shelter and road congestion in urban emergency evacuations Dec. 10, 2024 The University of Tokyo Satoki Masuda Eiji Hato Session F4: Emergency and Crisis Response Management re-evacuation shelter shelter 

Background In disaster situations, congestion in roads and shelters is a big problem. → failure to evacuate before a disaster, stopping evacuation 2 2019.10.13 https://www.nikkei.com/article/DGXMZO64877960S0A011C2CC1000/ Typhoon Hagibis (2019) https://www.sankei.com/article/20200630-WCE42MYYPZPB7IZ3E2ABIL766Y/ Road congestion Shelter congestion More vehicles → more evacuees to shelters More evacuees in shelters → less chance of finding a vacant shelter → more cruising vehicles on roads There is an interaction between congestion in roads and shelters. 

Review: Evacuation road traffic management InFO (Innermost First Out) policy = achieves maximum number of evacuees and minimum total travel time 3 High risk Low risk ramp inflow 𝑟! (𝑡) 1OD, multi-bottleneck 𝑞!"# (𝑡) 𝑖 = 𝐼 𝑖 = 𝐼 − 1 𝑖 = 0 So & Daganzo (2010) Optimal inflow volume = (bottleneck capacity downstream) – (flow from upstream) → Prioritizing the upstream, high-risk areas. = fundamental evacuation strategy to avoid shadow evacuation Shadow evacuation Evacuation traffic from low-risk areas hinders that from high-risk areas. Zhao et al. (2020), Dow and Cutter (2002) Zhao Zhang, Nelida Herrera, Efe Tuncer, Scott Parr, Mohammad Shapouri, and Brian Wolshon. Effects of shadow evacuation on megaregion evacuations. Transportation Research Part D: Transport and Environment, 83:102295, 6 2020. Kirstin Dow and Susan L Cutter. Emerging hurricane evacuation issues: hurricane Floyd and South Carolina. Natural hazards review, 3(1):12–18, 2002. Stella K. So and Carlos F. Daganzo. Managing evacuation routes. Transportation Research Part B: Methodological, 44:514–520, 2010. 

# vehicle time Inflow at UE Outflow at UE an evacuee delay time Shadow evacuation + destination congestion Congestion on the destination shelter propagates to the bottleneck. 4 O D 1OD, 1 bottleneck High risk Shelter × Evacuees who delay their departure time may fail to evacuate. × Congestion on one shelter and bottleneck may affect other bottlenecks. Need to model and control system-wide congestion propagation, considering destination congestion. # vehicle time Inflow at UE Outflow at UE delay time an evacuee 

Research objectives 1. Modeling the interaction between destination and road congestion to analyze the system-wide congestion propagation. 2. Deriving the optimal dispatching strategy that minimizes evacuation time and maximizes successful evacuees. 5 re-evacuation shelter shelter MFD MFD Macroscopic model to predict and control system-wide congestion. Region A Region B #vehicle Trip comp. rate z 

Macroscopic traffic modeling 6 𝑚 (internal) : Moving in region 𝑖 with a destination inside 𝑖 𝑜 (external) : Moving in region 𝑖 with a destination outside 𝑖 𝑠 (searching) : Cruising and searching for a shelter in region 𝑖 𝑒 (evacuated) : Successfully evacuated to region 𝑖 𝑑 (dispatched) : Dispatched to assigned shelters in other regions re-evacuation shelter shelter hazard risk level search 

re-evacuation shelter shelter Macroscopic traffic modeling State transition dynamics of 𝑜 (external) 7 evacuation demand inflow from neighboring regions outflow to neighboring regions trip completion rate accumulation MFD of each region search 

re-evacuation shelter shelter Macroscopic traffic modeling 8 State transition dynamics of 𝑚 (internal) evacuation demand inflow from neighboring regions transition to searching state 𝑠 Trip completion rate calculated with MFD search 

re-evacuation shelter shelter Macroscopic traffic modeling 9 State transition dynamics of 𝑠 (searching) transition from state 𝑚 Matching success function between shelters and evacuees # searching vehicles shelter vacancy network mean speed interaction between road congestion 𝑁! and shelter congestion 𝑁" search 

re-evacuation shelter shelter Macroscopic traffic modeling 10 State transition dynamics of 𝑒 (evacuated) Matching success function dispatched vehicles from other regions dispatched vehicles to other regions inflow outflow MFD of each region search 

Optimal control of vehicle dispatching 11 Calculate vehicle dispatching 𝜔 to minimize total evacuation travel time s.t. state transition dynamics Direct multiple shooting method: state and control variables are simultaneously optimized Tradeoff Dispatching too many vehicles → Road congestion due to dispatched vehicles Dispatching not enough vehicles → Shelter congestion 

Case study in Tokyo Koto City, Tokyo = densely populated urban area 12 10km 6km 540,000 people Koto City 

Case study in Tokyo Flood risk: The inundation depth and duration could exceed 10 meters and two weeks. 13 Arakawa river Koto City 

Case study in Tokyo • Koto City, Tokyo • Calculation time for one run (878,260 agents, 5528 nodes, 12799 links) Microscopic simulation: > 1 hours Zone-based traffic flow model: 1.2 [sec] 14 Arakawa river Koto City The network is divided into 9 sub-networks. 

Accumulation dynamics without control 15 𝑁! (internal) 𝑁" (searching) 𝑁# (evacuated) 1. Evacuated people in zone 6 approaching its shelter capacity around 𝑡 = 30. 2. The matching success rate begins to decrease due to shelter congestion after 𝑡 = 30. → Accumulation of searching vehicle 𝑁$ in zone 6 increases 3. Congestion of searching vehicle hinders vehicle travel inside zone 6. time time time ① ② ③ 

Accumulation dynamics without control 16 Spatially unbalanced shelter capacity → Spatially unbalanced congestion zone 6 zone 2 zone 5 zone 4 zone 1 

Results of optimal control of vehicle dispatching 17 𝑁# (evacuated) optimal control no control Re-evacuating evacuees from zone 5, 6 (low shelter capacity) to zone 4, 7 (high shelter capacity). 𝑁" (searching) time time Searching vehicles in zone 6 decrease due to dispatching. → Evacuation success rate increase. 

Results of optimal control of vehicle dispatching 18 𝑁! (internal) optimal control no control Dispatching is conducted without significant congestion → Solve the tradeoff b/w dispatched vehicle congestion and shelter congestion. 𝑁$ (external) 

Conclusion • We model the interaction of road and shelter congestion with macroscopic traffic models. • The transition dynamics of different states of evacuees are represented. • The interaction is captured in the evacuation success rate function. 19 • The proposed model can represent the decreasing evacuation success rate as road congestion worsens. • Optimal control of vehicle dispatching effectively reduces road congestion and increases the number of successful evacuees. ◼ Future work • Incorporating perimeter control to mitigate road congestion. • Developing efficient solution algorithms for optimal control problems. • Considering the uncertainty of model parameters and demand.