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.