  Highway capacity is often subject to stochastic perturbations due to the
combined effects of weather, traffic mixture, driver behavior, etc. This paper
is motivated by the need of a systematic approach to traffic control with
performance guarantees in the face of such perturbations. We develop a novel
control-theoretic method for designing perturbation-resilient ramp metering. We
consider a cell-transmission model with 1) Markovian cell capacities and 2)
buffers representing on-ramps and upstream mainline. Using this model, we
analyze the stability of on-ramp queues by constructing piecewise Lyapunov
functions that consider the nature of nonlinear traffic dynamics. Then, we
design ramp controllers that guarantee bounds for throughput and queue sizes.
We also formulate the problem of coordinated ramp metering as a bi-level
optimization with non-convex inner sub-problems. To address the computational
issue in solving this problem, we also consider localized and partially
coordinated reformulations. A case study of a 18.1-km highway in Los Angeles,
USA indicates a 8.3\% (resp. 9.9\%) reduction of vehicle-hours-traveled
obtained by the localized (resp. partially coordinated) control, both
outperforming the classical ALINEA and METALINE controllers.
