A copula-based approach to accommodate the dependence among microscopic traffic variables

Developing microscopic traffic simulation models requires the knowledge of probability distributions of microscopic traffic variables. Although previous studies have proposed extensive mathematical distributions for describing traffic variables (e.g., speed, headway, vehicle length, etc.), these studies usually consider microscopic traffic observations to be independent variables and distributions for these variables are investigated separately. As a result, some traditional approaches consider microscopic traffic variables as independent inputs to the traffic simulation process and these methods may ignore the possible dependence among different traffic variables.The objectives of this paper are to investigate the dependence structure among microscopic traffic variables and to examine the applicability of the copula approach to the joint modeling of these variables. Copulas are functions that relate multivariate distribution functions of random variables to their one-dimensional marginal distribution functions. The concept of copulas has been well recognized in the statistics field and recently has been introduced in transportation studies. The proposed copula approach is applied to the 24-h traffic data collected on IH-35 in Austin, Texas. The preliminary data analysis indicates that there exists dependence among microscopic traffic variables. Moreover, the modeling and simulation results suggest that copula models can adequately accommodate and accurately reproduce the dependence structure revealed by the traffic observations. Overall, the findings in this paper provide a framework for generating multiple microscopic traffic variables simultaneously by considering their dependence.