Traffic Flow Models and the Evacuation Problem

In our paper, we consider several models for traffic flow. The first, a steady state model, employs a model for car following distance to derive the a traffic flow rate in terms of empirically estimated driving parameters. From this result, we go on to derive a formula for total evacuation time as a function of the number of cars to be evacuated. The steady state model is analytically convenient, but has the drawback that it does not take the variance in the travelling velocities of vehicles into account. To address this problem, we develop a cellular automata model for traffic flow in one and two lanes, and augment our results through simulation. After presenting the steady state model and the cellular automata models, we derive a space-velocity curve that synthesizes these results. The section following this development of the basic models addresses the issue of restricting vehicle types using several tools for analyzing vehicle velocity variance. To assess the problem of two lanes converging into one and traffic merging, the next sections address optimal flow issues and explain how congestion occurs. Finally, we bring the collective theory of our assorted models to bear on the five evacuation strategies in question in the section titled “Parallel Paths, and Applications to Evacuation Strategy.” Lastly, we present a newspaper article/conclusion summarizing our results clearly and without going into a high level of mathematical detail.