arXiv subjects

Randy Machemehl

Publications and source records attributed to Randy Machemehl.

2 recordsLinked to original sources

arXiv2021

Robust Traffic Control Using a First Order Macroscopic Traffic Flow Model

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.

math.OC↗

arXiv2021

A Robust Traffic Control Model Considering Uncertainties in Turning Ratios

The effects of model parameter uncertainty on traffic flow control problems have recently drawn research attention. While the uncertainty in fundamental diagram related parameters has been investigated in the past, few articles have focused on network parameters uncertainty, including turning ratio uncertainty. To fill this gap, this article proposes a robust control model to deal with the uncertainties in the turning ratio by using distributionally robust chance constraints. The model allows one to compute the optimal control action that maximizes some objective, under all possible distributions of network parameters. We then apply this robust control framework to both a freeway network and an urban network, and evaluate the impact of uncertainty on optimal control inputs, over the test networks. The case studies show that compared to non-robust control, the proposed robust model can reduce congestion brought by the uncertainties and improve the overall throughput.

math.OC↗