Dynamic network flow optimization for real-time evacuation reroute planning under multiple road disruptions

During the course of an evacuation, evacuees often encounter unexpected incidents interrupting their plans for evacuation. Roads may not be accessible due to flooding, wild-fire propagation, accidents, the collapse of highway structures, and various other reasons. The evolving disturbances to the evacuation plan due to road disruptions may prolong the evacuation process and lead to chaos, injuries, and loss of life unless a quick, efficient recovery plan is implemented. In this work, we aim to provide a rerouting approach for an evacuation network that undergoes road disruptions. Unlike previous studies, it is assumed that incidents can occur on multiple roads and that the time of each occurrence can differ from the time of other occurrences. Flow optimization techniques are used to represent evacuation traffic flow on the transportation network. A dynamic traffic flow rate is considered in which the evacuation flow rate can change over time during the planning horizon. The variation in the flow rates enables a better projection of the traffic dynamics and consequences caused by disturbances. Furthermore, a path-based dynamic network flow optimization formulation is proposed to make the model scalable for large evacuation networks. Two preprocessing algorithms are introduced to calculate specific parameters associated with road disruptions and topology of the evacuation network. The use of these parameters enables us to transform the original optimization model into a linear model to reduce the computational burden. Numerical experiments are made to show the performance of the proposed model. Furthermore, the effects of specific features such as disruption time, disturbance location, and the plan updating time on the evacuation process are investigated. Results indicate that when more incidents occur later or when incident information is received earlier, the magnitude of the rerouting completion time is lessened.