Set-theoretic analysis of the isolated ramp metering problem

Abstract

Summary Analysis of ramp metering, as an effective freeway traffic control solution, is focused in the paper. The studied traffic control problem is discussed in a set-theoretic context in order to quantitatively characterize its effectivenes. The notions of maximal robust controlled invariant set, as well as t-step robust controllable set are defined and used for analyzing the ramp metering problem independently of the control policy applied. Algorithms are developed to compute these sets, with special attention to their practical interpretations. Numerical examples with graphical representation of the proposed methodology are given to examine local ramp metering and conclude implications to control strategies.