  Traffic control is at the core of research in transportation engineering
because it is one of the best practices for reducing traffic congestion. It has
been shown in recent years that the traffic control problem involving
Lighthill-Whitham-Richards (LWR) model can be formulated as a Linear
Programming (LP) problem given that the corresponding initial conditions and
the model parameters in the fundamental diagram are fixed. However, the initial
conditions can be uncertain when studying actual control problems. This paper
presents a stochastic programming formulation of the boundary control problem
involving chance constraints, to capture the uncertainty in the initial
conditions. Different objective functions are explored using this framework,
and case studies for both a single highway link and a small network are
conducted. In addition, the optimal results are validated with Monte Carlo
simulation.
