  A linear programming (LP) model is proposed to improve the performance of a
controlled freeway during an emergency evacuation. Based on reasonable
assumptions, the main relationships among key factors are kept without the
uncertain impact of subordinate factors in this model. Three vital issues
related to optimal freeway control during an emergency evacuation are
addressed. How to properly realize some predetermined priorities assigned to
some on-ramps during an emergency evacuation is analyzed through sensitivity
analysis of objective function coefficients. The time-varying throughput
capacity of freeway mainline and the storage capacities of on-ramps are also
addressed by using sensitivity analysis of the right-hand side (RHS) of
corresponding constraints. The last key issue we focused on is how to deal with
the uncertain demand in a crude form by applying robust optimization. The
methodology presented in this paper can help evacuation managers realize a
coordinated ramp metering with predetermined priorities put on some on-ramps
during an emergency evacuation. The result obtained by analyzing the impact of
time-varying mainline capacity provides the evacuation manager a chance of
using the extra capacity in some segments of mainline to buffer the traffic so
as to reduce the congestion related to upstream on-ramps. To reduce the risk
due to the possible infeasibility of deterministic control approaches in an
uncertain situation, we apply an affinely adjustable robust counterpart (AARC)
approach to deal with uncertain dynamic demands restricted to polyhedral sets.
The preliminary numerical experiments show that the AARC approach provides us
with a promising solution comparing to the sampling based stochastic approach.
