Title: Throughput-Improving Control of Highways Facing Stochastic Perturbations,
Abstract: In this article, we study the problem of controlling a highway segment facing
stochastic perturbations, such as recurrent incidents and moving bottlenecks.
To model traffic flow under perturbations, we use the cell-transmission model
with Markovian capacities. The control inputs are: (i) the inflows that are
sent to various on-ramps to the highway (for managing traffic demand), and (ii)
the priority levels assigned to the on-ramp traffic relative to the mainline
traffic (for allocating highway capacity). The objective is to maximize the
throughput while ensuring that on-ramp queues remain bounded in the long-run.
We develop a computational approach to solving this stability-constrained,
throughput-maximization problem. Firstly, we use the classical drift condition
in stability analysis of Markov processes to derive a sufficient condition for
boundedness of on-ramp queues. Secondly, we show that our control design
problem can be formulated as a mixed integer program with linear or bilinear
constraints, depending on the complexity of Lyapunov function involved in the
stability condition. Finally, for specific types of capacity perturbations, we
derive intuitive criteria for managing demand and/or selecting priority levels.
These criteria suggest that inflows and priority levels should be determined
simultaneously such that traffic queues are placed at locations that discharge
queues fast. We illustrate the performance benefits of these criteria through a
computational study of a segment on Interstate 210 in California, USA.