This paper presents an aproach for modeling travel time variability and reliability that accounts for time-of-day effects on travel time variations. The conditional probability density functions of travel time in each specific period play a fundamental role in the modeling of time-varying variability and reliability. Nonparametric kernel density estimation is applied to travel time data, which enhances the flexibility and accuracy in accommodating travel time distributions under various complex traffic conditions. The proposed functional travel time density model (FTTDM) uses functional principal component analysis in kernel density function estimates for modeling and depicting time-varying variability through the dependence on the departure time of day. The resulting quantile estimates are used to obtain time-varying reliability, which considers the addition of extra time to the average or the median for an on-time arrival. This study uses linked travel time data of an electronic toll collection system to estimate route travel times in the Taiwan Freeway system. As illustrated in the data applications, the FTTDM effectively captures the time-varying feature of travel time variability and reliability, and the reliability indicators identify the unreliable departure time of day of a route.
IEEE Transctions on Intelligent Transportation Systems p.1-10