This thesis involves the development of Stochastic Time-Dependent Least-Time Path (STDLTP) algorithms for use by a suitable real-time in-vehicle Route Guidance System (RGS). The algorithms have been developed in the context of Nottingham's urban traffic network for travel by car during peak-times, where saturated conditions are the most likely to occur. The role of real-time information is essential for the estimation and/or prediction of the links' and the paths' traversal times and consequently is necessary for the reliability of the RGS output. The presented work is restricted to SCOOT loop detector data and flow detector data as the only data sources of traffic information. It was found that the current and future links' traversal times are best represented by discrete time-varying probability distributions. Therefore, STDLTP algorithms, based upon different optimization criteria, which accommodate different levels of uncertainty associated with a path's traversal times, were developed. In parallel, several efficient heuristic STDLTP algorithms, based upon the chosen optimization criteria, were also developed. The performance of each of the algorithms was tested, in the context of the Nottingham urban network. Experimental results show that: 1) The computational performance of the implemented STDLTP algorithms was found to be dependent upon the employed optimization criterion. 2) The STDLTP(Weight) algorithm, which sought a trade off between the expected travel time and the uncertainty of a path, was found to provide more informed solutions and routes to the driver. 3) The computationally efficient heuristic STDLTP algorithms led to some plausible but sub-optimal solutions, when alternative optimization criteria to the expected value criterion were employed.