Estimation and application of dynamic speed-density relations by using transfer function models

Deployment of intelligent transportation systems (ITS) and availability of a vast amount of online data are opening new opportunities for researchers and practitioners. Many of the previously established methods and applications must be revisited in light of the availability of real-time data. Traffic flow models, particularly speed-density relations, lie at the core of a wide range of applications in almost all areas of traffic engineering and control. In simulation applications and continuum traffic flow models, first-order models use a steady-state or static speed-density relation, whereas higher-order models, with additional terms and parameters, are usually driven by the deviation of speed from this steady-state value. In calibrating speed-density relations using time series data, the existence of serial correlation and other dynamic effects in the data has largely been ignored in previous studies. In this study, transfer function methods (bivariate time series models) are used to specify and estimate dynamic speed-density relations from typical detector data from an advanced traffic management system control center. First the deviation of speed from an equilibrium static relation is estimated, and later the method is extended to directly estimate speed without explicit specification of an equilibrium speed-density relation. The robustness of the model temporally and spatially is investigated. In all cases considered, the method exhibits good performance and robustness in application. Furthermore, since the method is based on the use of online information, it has the capability of being adaptive and adjusting its parameters online.