Bayesian Mixture Modeling Approach to Account for Heterogeneity in Speed Data

Speed is one of the most important parameters describing the condition of the traffic flow. Many analytical models related to traffic flow either produce speed as a performance measure, or use speed to determine other measures such as travel time, delay, and the level of service. Mathematical models or distributions used to describe speed characteristics are very useful, especially when they are utilized in the context of simulation and theoretical derivations. Traditionally, normal, log-normal and composite distributions have been the usual mathematical distributions to characterize speed data. These traditional distributions, however, often fail to produce an adequate goodness-of-fit when the empirical distribution of speed data exhibits bimodality (or multimodality), skewness, or excess kurtosis (peakness). This often occurs when the speed data are generated from several different sub-populations, for example, mixed traffic flow conditions or mixed vehicle compositions. The traditional modeling approach also lacks the ability to explain the underlying factors that lead to different speed distribution curves. The objective of this paper is to explore the applicability of the finite mixture of normal (Gaussian) distributions to capture the heterogeneity in vehicle speed data, and thereby explaining the aforementioned special characteristics. For the parameter estimation, Bayesian estimation method via Markov Chain Monte Carlo (MCMC) sampling is adopted. The field data collected on IH-35 in Texas are used to evaluate the proposed models. The results of this study show that the finite mixture of normal distributions can very effectively describe the heterogeneous speed data, and provide richer information usually not available from the traditional models. The finite mixture modeling produces an excellent fit to the multimodal speed distribution curve. Moreover, the causes of different speed distributions can be identified through investigating the components.