Real-time navigation services, such as Google Maps and Waze, are widely used in daily life. These services provide rich data resources in real-time traffic conditions and travel time predictions; however, they have not been fully applied in transportation modeling. This paper aims to use traffic data from Google Maps and applying cutting-edge technologies in maximum likelihood estimation to model traffic networks and travel time reliability. This paper integrates Google Maps travel time data for routes and traffic condition data for links to model the complexities of traffic networks. We then formulate the Fisher information matrix and apply the asymptotic normality to obtain the probability distribution of the travel time estimates for a random route within the network of interest. We also derive the travel time reliability by considering two levels of uncertainties, i.e., the uncertainty of the route's travel time and the uncertainty of its travel time estimates. The proposed method could provide a more realistic and precise travel time reliability estimate. The methodology is applied to a small network in the downtown Baltimore area, where we propose a link data collection strategy and provide empirical evidence to show data independence by following this strategy. We also show results for maximum likelihood estimates and travel time reliability measures for different routes within the network. Furthermore, we use the historical data from a different network to validate this approach, showing our method provides a more accurate and precise estimate compared to the sample mean of the empirical data.