Modeling and Analysis of Pedestrian Flows

According to the Traveler Opinion and Perception Survey of 2005, about 107.4 million Americans regularly use walking as a mode of transport during their commute, which amounts for 51% of the total American population. In 2009, 4092 pedestrian fatalities were reported nationwide, out of 59,000 pedestrian crashes. This amounts for 12% of the fatalities in the total traffic accidents recorded, and shows an over-representation of pedestrians incidents. Thus, it is imperative to understand the causes behind such statistics, and conduct a comprehensive research on pedestrian walking behavior and their interaction with surroundings. A lot of researches on pedestrian flows have been conducted with respect to crowd dynamics in various situations like evacuation simulations. In this thesis, we investigate the Hughes model for pedestrian flows, which is governed by a coupled system of a scalar conservation law and an eikonal equation. The Hughes model considers the pedestrians as a continuum fluid and describes the motion of pedestrians in adensely crowded region. For the one-dimensional Hughes model with a single turning point (the origin), the governing equation can be be decomposed into two classical conservation laws on two sub-domains around the origin. We study various commonly observed interactions of pedestrian flows for tracking and understanding their movement on a mesoscopic level. In this thesis, the conservation law for pedestrian flows and the Hughes model are introduced in Chapter 2. We then summarize some existing theoretical work on the well posedness and existence of the entropy solutions of the Hughes model in Chapter 3. In Chapter 4, we study the one-dimensional Hughes model with a single turning point (the origin) and the given pedestrian potential which governs pedestrian flow tendency around the origin, and investigate 18 different cases. An interesting phenomena of dual shocks is observed, and remains to be investigated further in the future work