In recent years, traffic congestion in transportation networks has grown rapidly and has become an acute problem. The impetus for studying this problem has been further strengthened due to the fast growing field of Intelligent Vehicle Highway Systems (IVHS). Therefore, it is critical to investigate and understand its nature and address questions of the type: how are traffic patterns formed? and how can traffic congestion be alleviated? Understanding drivers' travel times is key behind this problem. In this paper, we present macroscopic models for determining analytical forms for travel times. We take a fluid dynamics approach by noticing that traffic macroscopically behaves like a fluid. Our contributions in this work are the following: (i) We propose two second-order non-separable macroscopic models for analytically estimating travel time functions: the Polynomial Travel Time (PTT) Model and the Exponential Travel Time (ETT) Model. These models generalize the models proposed by Kachani and Perakis as they incorporate second-order effects such as reaction of drivers to upstream and downstream congestion as well as second-order link interaction effects. (ii) Based on piecewise linear and piecewise quadratic approximations of the departure flow rates, we propose different classes of travel time functions for the first-order separable PTT and ETT models, and present the relationship between these functions. (iii) We show how the analysis of the first-order separable PTT Model extends to the second-order model with non-separable velocity functions for acyclic networks. (iv) Finally, we analyze the second-order separable ETT model where the queue propagation term - corresponding to the reaction of drivers to upstream congestion or decongestion - is not neglected. We are able to reduce the analysis to a Burgers equation and then to the more tractable heat equation. / Singapore-MIT Alliance (SMA)

The purpose of this research is to develop methodologies for applying traffic flow theories to various ITS categories through the utilization of evolving surveillance technologies. This integration of theory, measurement and application has been overlooked since the advent of ITS because of the number of disciplines involved. In this context, the following illustrative methodologies are selected, developed and presented in this study: - a methodology for automatic measurement of major spatial traffic variables for the present and the future implementation of various ITS functional areas, in general; and - a methodology for real-time link and incident specific freeway diversion in conjunction with freeway incident management, in particular. The first methodology includes the development of a dynamic flow model based on stochastic queuing theory and the principle of conservation of vehicles. An inductive modeling approach adapted here utilizes geometric interpretations of cumulative arrival-departure diagrams which have been drawn directly from surveillance data. The advantages of this model are real-time applicability and transportability as well as ease of use. Analysis results show that the estimates are in qualitative and quantitative agreement with the empirical data measured at 30-second intervals. The analytical expression for link travel times satisfies traffic dynamics where the new form of the equation of conservation of vehicles has been derived. This methodology has potential applicable to automatic traffic control and automatic incident detection. The methodology is then applied to freeway diversion in real-time in conjunction with freeway incident management. The proposed new form of the equation of conservation of vehicles is applied to detect recurring or non-recurring congestion analytically. The principle of conservation of vehicles is applied to develop the concept of progression and retrogression of incident domain, which turns out to be compatible with traditional shock wave traffic mechanism during incidents. The link and incident specific diversion methodology is achieved by using a delay diagram and volume-travel time curves, which can be plotted per link per incident. The use of such graphic aids makes problem solving much easier and clearer. The dynamic traffic flow model developed here can also be applied to estimate travel times during incidents as a function of time. The development of a computer program for freeway diversion concludes this research. / Ph. D.