Linear programming based evacuation models for a controlled freeway

TL;DR

This paper introduces a linear programming model for controlled freeway evacuation, incorporating sensitivity and robust optimization techniques to improve ramp metering and manage uncertain demand during emergencies.

Contribution

It presents a novel LP-based framework with robust optimization for emergency freeway control, addressing ramp priorities, capacity variations, and demand uncertainty.

Findings

Robust optimization improves control feasibility under demand uncertainty.

Sensitivity analysis aids in prioritizing ramp control and capacity utilization.

Preliminary results favor the affinely adjustable robust approach over stochastic methods.

Abstract

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.