Abstract
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.
Highlights
Modeling travel time distribution is essential for measuring the consistency of the traffic performance of a highway system
This study develops a nonparametric Bayesian model to estimate the travel time distribution for freeways
The model is based on Dirichlet process distribution with an extension of a hierarchical structure to account for the mixture/multistate characteristics of a given dataset
Summary
Modeling travel time distribution is essential for measuring the consistency of the traffic performance of a highway system. The distribution of the travel time is useful in simulation and theoretical derivations regarding different traffic performance measures such as travel time reliability and variability. The accurate estimation and prediction of travel time are essential for traffic operators, planners, and traveler information systems [1]. This study develops a nonparametric Bayesian model to estimate the travel time distribution for freeways. This model does not require specifying the true number of components; instead, the number of components grows with the dataset, which is automatically inferred using the Bayesian posterior inference framework. The discussion of the dataset and a method used to estimate the travel time is presented. The results and model evaluation using simulated data with known parameters is displayed, after which conclusions and recommendations for possible future research are made
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