  Highway capacity is subject to stochastic perturbations due to weather,
traffic mixture, driver behavior, etc. However, systematic approaches to
traffic control with performance guarantees in the face of such perturbations
are still limited. In this paper, 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
motivated by the nonlinear traffic dynamics. Then, we design ramp controllers
that guarantee bounds for throughput and queue sizes. We formulate the
coordinated ramp metering problem as a bi-level optimization with non-convex
inner problems. To address the computational issue, we also consider a
localized and a partially coordinated reformulation. A case study of a 18.1-km
highway in Los Angeles, USA indicates a 7.6\% (resp. 8.8\%) reduction of
vehicle-hours-traveled obtained by the localized (resp. partially coordinated)
control, both outperforming the 5.4\% reduction obtained by the classical
ALINEA policy.
