This paper proposes a double time-scale model to capture the day-to-day evolution along with the within-day variability of travel time. The proposed model can be used to evaluate short-term to long-term effects of new transport policies and construction of critical infrastructures, and to analyze the resilience of road networks under disruptions. The within-day travel time variability is modeled using the functional data analysis, in which the effects of road traffic congestion and noise of traffic data are considered explicitly. The within-day process is then regarded as the local volatility (or the noise process) to drive the day-to-day process while the latter is described by a modified geometric Brownian motion (GBM). Then, the day-to-day travel time process is obtained by the statistics of the modified GBM. The model probabilistically captures the evolution of day-to-day and within-day travel time processes analytically. Moreover, an efficient method based on the cross-entropy method is developed for calibrating the model parameters. A lasso-like regularization is employed to guarantee a small bias between the model estimations and the measurement counterparts. Finally, two empirical studies are carried out to validate the proposed model at different scales with different traffic scenarios, i.e., a case study on the Guangzhou Airport Expressway (link to path scale) under traffic accident conditions and a case study in New York City (city-scale) to analyze the network resilience under Hurricane Sandy. Both case studies adopted probe vehicle data but with different configurations (fine versus coarse, small versus big data). The empirical studies confirm that the proposed model can accommodate the inherent variability in traffic conditions and data meanwhile being computationally tractable. The numerical results illustrate the applicability of the proposed model as a powerful tool in practice for analyzing the short-term and long-term impacts of disruptions and systematic changes in the performance of road networks.