Sparse travel time estimation from streaming data

We address two shortcomings in online travel time estimation methods for congested urban traffic. The first shortcoming is related to the determination of the number of mixture modes, which can change dynamically within a day and from day to day. The second shortcoming is the widespread use of Gaussian probability densities as mixture components. Gaussian densities fail to capture the positive skew in travel time distributions, and consequently, large numbers of mixture components are needed for reasonable fitting accuracy when applied as mixture components. They also assign positive probabilities to negative travel times. To address these issues, this paper derives a mixture distribution with Gamma component densities, which are asymmetric and supported on the positive numbers. We use sparse estimation techniques to ensure parsimonious models and propose a generalization of Gamma mixture densities using Mittag-Leffler functions that provides enhanced fitting flexibility and improved parsimony. In order to accommodate within-day variability and allow for online implementation of the proposed methodology (i.e., fast computations on streaming travel time data), we introduce a recursive algorithm that efficiently updates the fitted distribution whenever new data become available. Experimental results using real-world travel time data illustrate the efficacy of the proposed methods.