A novel approach for vehicle travel time distribution: copula-based dependent discrete convolution

Travel time reliability is considered as one of the key indicators for the performance of transportation systems. The majority of studies concerning estimating arterial travel time distribution commonly assume that the path travel time follows a certain distribution without considering segment correlation. Therefore, convolution is used. However, the assumption of independence of travel times on successive segments may not be appropriate. Recent studies showed that copulas are able to capture segment correlation. These copula models, however, are unfeasible in real-world applications. This paper proposes a novel approach using dependent discrete convolution. Path-level travel time distribution is estimated by aggregating segment-level travel time distributions using copula-based discrete convolution. This estimation is compared to the estimation of traditional convolution, a state-of-the art copula model, and the empirical distribution. It is shown that the proposed methodology produces accurate results within feasible computational time, thus, making it eligible for real-world applications.