Optimal Evacuation Plans for Network Flows over Time Considering Congestion
This dissertation seeks to advance the modeling of network flows over time for the purposes of improving evacuation planning. The devastation created by Hurricanes Katrina and Rita along the Gulf Coast of the United States in 2005 have recently emphasized the need to improve evacuation modeling and planning. The lessons learned from these events, and similar past emergencies, have highlighted the problem of congestion on the interstate and freeways during an evacuation. The intent of this research is to develop evacuation demand management strategies that can reduce congestion, delay, and ultimately save lives during regional evacuations. The primary focus of this research will concern short-notice evacuations, such as hurricane evacuations, conducted by automobiles. Additionally, this dissertation addresses some traffic flow and optimization deficiencies concerning the modeling of congested network flows.
This dissertation is a compilation of three manuscripts. Chapters 3 and 4 examine modeling network flows over time with congestion. Chapter 3 demonstrates the effects of congestion on flows using a microscopic traffic simulation software package, INTEGRATION. The flow reductions from the simulation are consistent with those found in several empirical studies. The simulation allows for the examination of the various contributing factors to the flow reductions caused by congestion, including level of demand, roadway geometry and capacity, vehicle dynamics, traffic stream composition, and lane changing behavior. Chapter 4 addresses some of the modeling and implementation issues encountered in evacuation planning and presents an improved modeling framework that reduces network flows due to congestion. The framework uses a cell-based linear traffic flow model within a mixed integer linear program (MILP) to model network flows over time in order to produce sets of decisions for use within an evacuation plan. The traffic flow model is an improvement based upon the Cell Transmission Model (CTM) introduced in Daganzo (1994) and Daganzo (1995) by reducing network flows due to congestion. The flow reductions are calibrated according to the traffic simulation studies conducted in Chapter 3. The MILP is based upon the linear program developed in Ziliaskopoulos (2000); however, it eliminates the "traffic holding" phenomenon where it cannot be implemented realistically within a transportation network. This phenomenon is commonly found in mathematical programs used for dynamic traffic assignment where the traffic is unrealistically held back in order to determine an optimum solution. Lastly, we propose additional constraints for the MILP that improve the computational performance by over 90%. These constraints exploit the relation of the binary variables based on the network topology. Chapter 5 applies the improved modeling framework developed in Chapter 4 to implement a demand management strategy called group-level staging -- the practice of evacuating different groups of evacuees at different times in order to reduce the evacuation duration. This chapter evaluates the benefits of group-level staging, as compared to the current practice of simultaneous evacuation, and explores the behavior of the modeling framework under various objective functions.