This research explored the idea of unifying the deterministic and stochastic process approaches together, and developing a generalised framework of dynamic traffic assignment models to include day-to-day and within day variations in traffic flow. The framework of models is also aimed at capturing individual drivers’ adaptation of route choices based on the route costs experienced through suitable driver learning models. In this thesis, the route flows within a day in a given departure period are modelled as random variables, and their evolution over a period of time (a number of days) is modelled as stochastic processes based on the laws of probability. The interactions among the route flows from various departure periods over the network links in space and time, are modelled through dynamic link loading procedures. Stochastic processes under certain mild conditions admit a unique stationary probability distribution which can be modelled by using simulation techniques. Alternatively, the moments (e.g., mean and variance) of the equilibrium (stationary) probability distribution can also be estimated. This research has advanced the idea of estimating the properties of equilibrium probability distribution by making a particular contribution in formulating the methodology for computing the Jacobians of route travel times with respect to the route inflows in a doubly dynamic assignment context using an analytical procedure, which are necessary for estimating the variance-covariance matrices of stationary route flows. In this modelling framework, there are three modules - the first one is a day-to-day route choice model defined as a discrete time stochastic process, the second is a continuous time dynamic network loading of the route flows considering the complete spatio-temporal effects of the traffic flows that use the road links at the same time, and the third is the drivers’ learning and adjusting model based on a linear filter. The main idea of estimating the properties of stationary probability distribution in this research builds on two earlier results: firstly, when the demand is sufficiently large, the equilibrium probability distribution converges approximately to a Multivariate Normal distribution and its mean coincides with the SUE flows; secondly, the variance can be estimated by an approximation procedure. The equilibrium probability distribution can also be worked out using the commonly followed Monte Carlo simulation technique, which involves simulating the route choice process as a multinomial probability distribution over a number of days, and then summarising the properties e.g., the mean and the variance of the stationary probability distribution. This procedure though simple, is time consuming and the main difficulty lies in detecting the stationarity of the process. Based on the necessary conditions, simple and practically useable tests for identifying the stationarity of a stochastic process have been introduced. These tests involve analysing autocorrelations and computing large lag standard errors in autocorrelations. The stationary variance-covariance of route flows obtained by the variance approximation model, was compared with that computed by the simulation procedure. Overall, the variance approximation model performs satisfactorily. Variance-covariance of route flows has been found sensitive primarily to the input logit choice parameter, which defines the boundaries of the validity of the variance approximation model. Variance-covariance is also affected by the memory length with the shorter memory systems essentially producing highly variant systems. Similarly, the variance-covariance of route flows is also sensitive to the memory weight, and the lower memory weight (0 < memory weight « 1) produces the same effect as that of shorter memory systems. The Jacobians of the travel times worked out in this thesis have much wider applicability, and a few possible situations have been listed here among many others. Firstly, the optimisation based user equilibrium programs can be speeded up by defining the descent direction with the help of the Jacobians. Secondly, the Jacobians may be found very useful in defining the dynamic road user pricing problems. Finally, the sensitivity analysis of user equilibrium problems requires the computation of the Jacobians
