The fact that traffic congestion upstream of a bottleneck causes a reduction in the discharge flow rate through the bottleneck has been well documented in several empirical studies. However, what has been missing is an understanding of the causes of these empirically observed flow reductions. An identification of these causes is important in order to develop various mitigation schemes through the use of emerging technology. The concept of capacity drop can be introduced at time-independent bottlenecks (e.g. freeways) as well as time-dependent bottlenecks (e.g. signalized intersections). While to the author's knowledge no one has attempted to link these phenomena, the research presented in this thesis serves as a first step in doing so. The research uses the INTEGRATION simulation software, after demonstrating its validity against empirical data, to simulate time-independent and time-dependent bottlenecks in an attempt to characterize and understand the contributing factors to these flow reductions. Initially, the INTEGRATION simulation software is validated by comparing its results to empirically observed traffic stream behavior. This thesis demonstrates that the discharge flow rate is reduced at stationary bottlenecks at the onset of congestion. These reductions at stationary bottlenecks are not recovered as the traffic stream propagates downstream. Furthermore, these reductions are not impacted by the level of vehicle acceleration. Alternatively, the drop in the discharge flow rate caused by time-dependent bottleneck is recoverable and is dependent on the level of acceleration. The difference in behavior is attributed to the fact that in the case of a stationary bottleneck the delay in vehicle headways exceeds the losses caused by vehicle accelerations and thus is not recoverable. In the case of vehicles discharging from a backward recovery wave the dominant factor is the delay caused by vehicle acceleration and this can be recuperated as the traffic stream travels downstream. / Master of Science

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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. / Ph. D.

Microscopic simulation software use car-following models to capture the interaction of a vehicle and the preceding vehicle traveling in the same lane. In the literature, much research has been carried out in the field of car-following and traffic stream modeling. Microscopic car-following models have been characterized by using the relationship between a vehicle's desired speed and the distance headway (h) between the lead and follower vehicles. On the other hand, macroscopic traffic stream models describe the motion of a traffic stream by approximating for the flow of a continuous compressible fluid. This research work develops and compares three different formulations of car-following models — speed formulation, molecular acceleration, and fluid acceleration formulation. First, four state-of-the-art car-following models namely, Van Aerde, Greenshields, Greenberg and Pipes models, are selected for developing the three aforementioned formulations. Then a comprehensive car-following behavior encompassing steady-state conditions and two constraints — acceleration and collision avoidance — is presented. Specifically, the variable power vehicle dynamics model proposed by Rakha and Lucic (2002) is utilized for the acceleration constraint. Subsequently, the thesis describes the issues associated with car-following formulations. Recognizing that many different traffic flow conditions exist, three distinct scenarios are selected for comparison purposes. The results demonstrate that the speed formulation ensures that vehicles typically revert to steady-state conditions when vehicles experience a perturbation from steady-state conditions. On the other hand, both acceleration formulations are unable to converge to steady-state conditions when the system experiences a perturbation from a steady-state. The thesis also attempts to address the question of capacity drop associated with vehicles accelerating from congested conditions. Specifically, the capacity drop proposition is analyzed for the case of a backward recovery (typical of a signalized intersection) and stationary shockwave (typical of a capacity drop on a freeway). In the case of the backward recovery shockwave, the acceleration constraint results in a temporally and spatially confined capacity drop as vehicles accelerate to their desired steady-state speed. This temporally and spatially confined capacity drop results in what is typically termed the start loss of a signalized phase. Subsequently, vehicles attain steady-state conditions, in the case of the speed and molecular acceleration formulations, at the traffic signal stop bar after the initial five vehicle departures. The analysis also demonstrates that after attaining steady-state conditions the capacity may drop for the initial vehicle departures as a result of traffic stream dispersion. This traffic dispersion capacity drop increases as vehicles travel further downstream. Alternatively, in the case of a stationary bottleneck the aggressiveness of vehicle accelerations plays a major role in defining the capacity drop downstream of a bottleneck. The study demonstrates that any temporal headways that may be lost while vehicles accelerate to steady-state conditions may not be recuperated and thus result in capacity drops downstream of a bottleneck. A typical example of this scenario is the traffic stream flow rate downstream of a stop sign, which is significantly less than the roadway capacity. The reduction in capacity is caused by losses in temporal headways between successive vehicles which are not recuperated. The study also demonstrates that the ability to model such a capacity drop does not require the use of a dual-regime traffic stream model as is proposed in the Highway Capacity Manual (HCM). Instead, the use of a single-regime model captures the observed capacity with the introduction of an acceleration constraint to the car-following system of equations. / Master of Science