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Beskrivelse
This book introduces an integer linear program called the Minimum Cost Flow with Congestion Assignment (MCFCA) model. MCF-CA is a multi-period evacuation model that uses a novel approach called congestion assignment to analyze clearing times during mass evacuations. Congestion assignment discretizes the nonlinear relationship between the number of vehicles on a road segment and the maximum speed at which those vehicles can travel. MCF-CA selects among three congestion levels (none, moderate, and high) for each road segment in each time epoch. Depending on the congestion level selected, MCF-CA limits the number of vehicles that are able to traverse the road segment and uses Ak elik's Time-Dependent Speed-Flow Function (Ak elik 2003) to determine the average travel speed of the vehicles for that time period. As a result, we are able to determine approximate evacuation clearing times under nonlinear congestion effects by solving an integer linear program. We limit residents' prior knowledge of traffic conditions by implementing MCF-CA in a rolling horizon fashion and book the impact of this limited knowledge on evacuation patterns. We also model the impact of sub-optimal routing decisions on the part of residents by artificially shifting residents toward their own shortest paths rather than a "socially optimal" route. Mass evacuation can more than double the clearing times of individual county evacuations. However, during both county and mass evacuations, resident routing choices significantly impact clearing times. As more residents choose suboptimal routes, clearing times are prolonged. Lastly, we find that more than 50% of residents will experience congestion at some point during the evacuation horizon. However, allowing some congestion improves evacuation clearing times by 20-36% over not congesting. Although congestion decreases vehicle travel speed by 70-80%, over 50% more residents are able to start or continue evacuating during each time epoch.
