Theoretical investigation of traffic flow : inhomogeneity induced emergence : a dissertation presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science at Massey University, Auckland, New Zealand

Abstract

This research work is focused on understanding the effects of inhomogeneity on traffic flow by theoretical analysis and computer simulations. Traffic has been observed at almost all levels of natural and manmade systems (e.g., from microscopic protein motors to macroscopic objects like cars). For these various traffic, basic and emer- gent phenomena, modelling methods, theoretical analysis and physical meanings are normally concerned. Inhomogeneity like bottlenecks may cause traffic congestions or motor protein crowding. The crowded protein motors may lead to some human diseases. The congested traffic patterns have not been understood well so far. The modelling method in this research is based on totally asymmetric simple exclusion process (TASEP). The following TASEP models are developed: TASEP with single inhomogeneity, TASEP with zoned inhomogeneity, TASEP with junction, TASEP with site sharing and different boundary conditions. These models are motivated by vehicular traffic, pedestrian trafficc, ant traffic, protein motor traffic and/or Internet traffic. Theoretical solutions for the proposed models are obtained and verified by Monte Carlo simulations. These theoretical results can be used as a base for further developments. The emergent properties such as phase transitions, phase separations and spontaneous symmetry breaking are observed and discussed. This study has contributed to a deeper understanding of generic traffic dynamics, particularly, in the presence of inhomogeneity, and has important implications for explanation or guidance of future traffic studies.