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)

In this dissertation, new algorithms that address three traffic problems of major importance are developed. First automatic identification and prediction algorithms are developed to identify and predict the occurrence of traffic congestion. The identification algorithms concoct a model to identify speed thresholds by exploiting historical spatiotemporal speed matrices. We employ the speed model to define a cutoff speed separating free-flow from congested traffic. We further enhance our algorithm by utilizing weather and visibility data. To our knowledge, we are the first to include weather and visibility variables in formulating an automatic congestion identification model. We also approach the congestion prediction problem by adopting an algorithm which employs Adaptive Boosting machine learning classifiers again something novel that has not been done previously. The algorithm is promising where it resulted in a true positive rate slightly higher than 0.99 and false positive rate less than 0.001. We next address the issue of travel time modeling. We propose algorithms to model travel time using various machine learning and statistical learning techniques. We obtain travel time models by employing the historical spatiotemporal speed matrices in conjunction with our algorithms. The algorithms yield pertinent information regarding travel time reliability and prediction of travel times. Our proposed algorithms give better predictions compared to the state of practice algorithms. Finally we consider driver safety at signalized intersections and uncontrolled intersections in a connected vehicles environment. For signalized intersections, we exploit datasets collected from four controlled experiments to model the stop-run behavior of the driver at the onset of the yellow indicator for various roadway surface conditions and multiple vehicle types. We further propose a new variable (predictor) related to driver aggressiveness which we estimate by monitoring how drivers respond to yellow indications. The performance of the stop-run models shows improvements after adding the new aggressiveness predictor. The proposed models are practical and easy to implement in advanced driver assistance systems. For uncontrolled intersections, we present a game theory based algorithm that models the intersection as a chicken game to solve the conflicts between vehicles crossing the intersection. The simulation results show a 49% saving in travel time on average relative to a stop control when the vehicles obey the Nash equilibrium of the game. / Ph. D.