A Cost Potential Cellular Automata Model For Pedestrian Flow Based On Mathematical And Physical Analysis

In this thesis, we propose a cost potential field (CPF) cellular automata (CA) modelfor pedestrian flow. The formulation follows those basic rules that are applied in the well-known floor field (FF) CA model, which read:(1) a cell is empty or occupied by just anindividual;(2) a pedestrian moves to all eight neighboring cells or keep still with certainprobabilities; and (3) the probability for moving to an occupied cell is always zero. Here,determination of all nine probabilities helps to navigate a pedestrian’s movement to thedestination, which is kernel of the formulation.We establish a cost potential field for the navigation, thus our formulation difersfrom that in the FFCA model, which adopts a floor field as is so named, and which hasbeen dominating for a decade in the study field. The cost from a cell to the destination isreflected by two major factors:(1) the arrival time; and (2) the discomfort that increaseswith the density in the journey. By assuming that a pedestrian is able to minimize hisor her expected cost to the destination, he or she will choose an empty neighboringcell moving to which helps reduce his or her current cost potential to the greatest extent.Here, the arrival time and discomfort considered in the potential field function are similarto the static and dynamic fields in the floor field CA model, respectively. To modeltwo pedestrian groups with diferent origin-destination paths, we introduce a formulato reflect the interaction between pedestrians having diferent directions of motion, bywhich the lane formation in pedestrian counter flow is reproduced.We also extend the CPFCA model to describe a walking facility in which the sightis obscure and pedestrians adopt a perceived cost potential to choose the path. To re-evaluate the cost potential, we introduce a concept of visibility whose value is between0and1, equals to1under normal circumstances, and equals to0when the pedestrian iscompletely screened from the destination. Moreover, an aggregated force is defined tomodel the pushing behavior that is due to low visibility and high density. The resultantmodels, i.e., the perceived CPFCA model and perceived CPFCA model with aggregatedforce field, reproduce the pedestrian flow in walking domains with bottlenecks and turn-around paths. In summary, the major contributions of the thesis are as follows:1Proposition of the cost potential field, which directly gives rise to the CPFCAmodel for the description of one pedestrian group with the same origin-destination path,and which helps reproduce such typical phenomena as evacuation.2Formulation of the intersection between two streams of pedestrians, which isefcient in modeling two pedestrian groups with diferent origin-destination paths, andwhich typically reproduce the lane formation in pedestrian counter flow.3Extension of the CPFCA model to a perceived CPFCA model with aggregateforce field, which helps improve the cost potential by introducing a parameter to describevisibility and a force to describe the pushing behavior, and which reasonably reproducepedestrian flows in waking domains with turn-around paths and bottlenecks.