  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 day and
from day to day. The second shortcoming is the wide-spread 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, which 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 which
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.
