Tools for Modeling and Control of Freeway Networks

Tools for modeling and control of freeway networks by Ajith Muralidharan Doctor of Philosophy in Engineering Mechanical Engineering University of California, Berkeley Professor Roberto Horowitz, Chair This dissertation presents algorithmic tools that are useful to transportation engineers for freeway traffic modeling and control. A modeling framework that utilizes the link-node cell transmission model (LN-CTM) to simulate traffic dynamics on a chosen freeway network is presented here. A data driven approach, which utilizes available detector measurements on the freeway network to calibrate and specify the model is also illustrated. Flow measurements in ramps, which are needed to specify demands and routing characteristics for the freeway, are usually not available. Two novel imputation algorithms which estimate the missing ramp flows in the freeway network are presented. These algorithms employ a model based estimation procedure, that calculates the unknown on-ramp flows and off-ramp split ratios which can be fed into the model to match the observed mainline density and flow measurements. A detailed analysis of the convergence of these algorithms is presented, along with the advantages of these individual approaches. The final model, specified with the imputed ramp flows is able to replicate the traffic dynamics with good accuracy, as seen by error rates around 5-8% for density/flows contours, and the accurate replication of the bottleneck locations. These imputation algorithms, used within our modeling framework, enables a user to build a freeway model simulating multiple days of freeway behavior, within a week. A model based optimal predictive controller for freeway congestion control, which utilizes the LN-CTM as its underlying model is also presented. The approach searches for solutions represented by a combination of ramp metering and variable speed limits. The optimization problem corresponding to the optimal control problem based on the LN-CTM is non-convex and non-linear. A relaxation method is presented to solve this problem efficiently using an equivalent linear program, before generating the solution to the original problem using a new mapping algorithm. The predictive controller is also extended to cover situations when ramp weaving and/or capacity drop exists in the freeway network. In this case, a set of heuristics are presented and the optimal control problem is solved using a sequence of linear programs, before mapping the solutions back to the original problem.