Optimal Ramp Metering of Freeway Corridors

Abstract

Ramp meters have been used for congestion management on freeways since the 1960s to maximize freeway capacity by controlling on-ramp flows. Traditionally, the focus has been to develop rule-based algorithms and optimal control case studies. This led to a host of algorithms and methods which cannot be proven to provide an optimal control and the case studies does not provide a systematic understanding of the characteristics of optimal control and its influence on traffic dynamics. Moreover, optimal is not easy to achieve in practice due to the limited storage on the on-ramps. Towards this end, this dissertation systematically studies the optimality conditions for the case of unlimited storage and spatiotemporal evolution of control and its corresponding traffic dynamics on freeway and ramps under queue constraint, carefully taking the traffic dynamics into account. A Kinematic Wave model of the freeway-ramps system is optimized for minimal total delay. The optimality conditions for the case of unlimited ramp storage are studied using Moskowitz functions that provide several interesting insights for different scenarios, including the case of limited storage. This dissertation shows that the current problem posed as a nonlinear coupled PDE system with a nonlinear merge model cannot be solved analytically. This study also shows that the discrete-time nonlinear formulation solved with simulation-based optimization does not converge in reasonable time. To overcome this, the problem is reposed as a LP formulation that includes capacity drop. For discrete formulation, this study develops an error-free solution to the KW model with a source term that enhanced the quality of the numerical solution. This study identifies four distinct regions in the state surface with distinct metering patterns. Explicit modeling of ramps enabled correlating the initialization and termination times of the metering patterns with the evolution of traffic dynamics on the freeways and ramps. Using these results, this dissertation presents a hybrid isolated ramp metering algorithm that outperforms existing methods.