Providing transportation system operators and travelers with accurate travel time information allows them to make more informed decisions, yielding benefits for individual travelers and for the entire transportation system. Most existing advanced traveler information systems (ATIS) and advanced traffic management systems (ATMS) use instantaneous travel time values estimated based on the current measurements, assuming that traffic conditions remain constant in the near future. For more effective applications, it has been proposed that ATIS and ATMS should use travel times predicted for short-term future conditions rather than instantaneous travel times measured or estimated for current conditions. This dissertation research investigates short-term freeway travel time prediction using Dynamic Neural Networks (DNN) based on traffic detector data collected by radar traffic detectors installed along a freeway corridor. DNN comprises a class of neural networks that are particularly suitable for predicting variables like travel time, but has not been adequately investigated for this purpose. Before this investigation, it was necessary to identifying methods for data imputation to account for missing data usually encountered when collecting data using traffic detectors. It was also necessary to identify a method to estimate the travel time on the freeway corridor based on data collected using point traffic detectors. A new travel time estimation method referred to as the Piecewise Constant Acceleration Based (PCAB) method was developed and compared with other methods reported in the literatures. The results show that one of the simple travel time estimation methods (the average speed method) can work as well as the PCAB method, and both of them out-perform other methods. This study also compared the travel time prediction performance of three different DNN topologies with different memory setups. The results show that one DNN topology (the time-delay neural networks) out-performs the other two DNN topologies for the investigated prediction problem. This topology also performs slightly better than the simple multilayer perceptron (MLP) neural network topology that has been used in a number of previous studies for travel time prediction.

Bhom's hydrodynamic formulation (or quantum fluid dynamics) is an attractive approach since, it connects classical and quantum mechanical theories of matter through Hamilton-Jacobi (HJ) theory, and quantum potential. Lopreore and Wyatt derived and implemented one-dimensional quantum trajectory method (QTM), a new wave-packet approach, for solving hydrodynamic equations of motion on serial computing environment. Brook et al. parallelized the QTM on shared memory computing environment using a partially implicit method, and conducted accuracy study of a free particle. These studies exhibited a strange behavior of the relative error for the probability density referred to as the transient effect. In the present work, numerical experiments of Brook et al. were repeated with a view to identify the physical origin of the transient effect and its resolution. The present work used the QTM implemented on a distributed memory computing environment using MPI. The simulation is guided by an explicit scheme.