Using frequency domain analysis to elucidate travel time reliability along congested freeway corridors

Travel time reliability (TTR) is an essential measure of service for traffic performance management, especially for congested freeway corridors. This paper proposes a systematic analytical framework to analyze the predictable and unpredictable variations in route TTR in corridor networks. More specifically, the predictable variation in route TTR is estimated with a deterministic fluid-based polynomial arrival queue (PAQ) model, while the unpredictable variation in route TTR is analyzed through the residual induced by the PAQ estimation model. Based on the output of the PAQ estimation model, a frequency-domain approach is proposed to decompose the observed time-domain travel time into underlying unobserved factors in different temporal resolutions. With the discrete-time Fourier transform method and the Butterworth low-pass filtering technique, it is capable of analytically uncovering different temporal scales of predictable variations in TTR, including the trend of day-to-day variations, the dynamics of within-day variations, as well as the stochasticity of within-period variations. Connecting with the unpredictable variations represented by the residual due to the PAQ approximation model, we can comprehensively elucidate TTR for congested freeway corridors. Case studies are conducted to show the effectiveness of the proposed frequency-domain approach in elucidating and measuring different contributing elements in TTR, and more specifically, the four components, i.e., the trend of day-to-day variations, the dynamics of within-day variations, the stochasticity of within-period variations, and the residual induced by the PAQ estimation model, account for 64.9 %, 20.2 %, 1.2 %, 13.7 % of variations in the route travel time, respectively, based on a case study with the PeMS dataset.