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Journal of Advanced Transportation
Volume 2017 (2017), Article ID 5069824, 9 pages
Research Article

Bayesian Nonparametric Model for Estimating Multistate Travel Time Distribution

1Department of Civil and Environmental Engineering, FAMU-FSU College of Engineering, Tallahassee, FL, USA
2School of Engineering, University of North Florida, Jacksonville, FL, USA

Correspondence should be addressed to Emmanuel Kidando

Received 15 October 2016; Revised 18 December 2016; Accepted 28 December 2016; Published 20 February 2017

Academic Editor: Yuchuan Du

Copyright © 2017 Emmanuel Kidando et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Multistate models, that is, models with more than two distributions, are preferred over single-state probability models in modeling the distribution of travel time. Literature review indicated that the finite multistate modeling of travel time using lognormal distribution is superior to other probability functions. In this study, we extend the finite multistate lognormal model of estimating the travel time distribution to unbounded lognormal distribution. In particular, a nonparametric Dirichlet Process Mixture Model (DPMM) with stick-breaking process representation was used. The strength of the DPMM is that it can choose the number of components dynamically as part of the algorithm during parameter estimation. To reduce computational complexity, the modeling process was limited to a maximum of six components. Then, the Markov Chain Monte Carlo (MCMC) sampling technique was employed to estimate the parameters’ posterior distribution. Speed data from nine links of a freeway corridor, aggregated on a 5-minute basis, were used to calculate the corridor travel time. The results demonstrated that this model offers significant flexibility in modeling to account for complex mixture distributions of the travel time without specifying the number of components. The DPMM modeling further revealed that freeway travel time is characterized by multistate or single-state models depending on the inclusion of onset and offset of congestion periods.