In this thesis, we provide a clear definition and comparison of various descriptions in traffic systems. With the use of the accumulation and flux, defined as a two-point measure, we study the dynamics of the traffic system. We show that a conventional fundamental diagram can be obtained by simply averaging over time. However, through this average, it is assumed that the system is at the steady state, and there is no correlation in between each data point. Instead of considering the steady state, which never exist in reality, we consider the dynamics of traffic congestion. We find that there are two types of dynamics after the break down of the free flow phase, which cannot be distinguished if the data is averaged over time. They can be classified according to the area enclosed...[ Read more ]

In this thesis, we provide a clear definition and comparison of various descriptions in traffic systems. With the use of the accumulation and flux, defined as a two-point measure, we study the dynamics of the traffic system. We show that a conventional fundamental diagram can be obtained by simply averaging over time. However, through this average, it is assumed that the system is at the steady state, and there is no correlation in between each data point. Instead of considering the steady state, which never exist in reality, we consider the dynamics of traffic congestion. We find that there are two types of dynamics after the break down of the free flow phase, which cannot be distinguished if the data is averaged over time. They can be classified according to the area enclosed by their dynamics on the fundamental diagram during congestion. They are referred to as “moderate flow” and “serious congestion” for the area enclosed being small or large respectively. We also show that the area enclosed can reflect the economic loss of the society due to the congestion. With a deeper knowledge between the economic loss and the area enclosed, we illustrate a possibility in identifying the congestion location, which is useful in understanding individual characteristics of various road segments.