Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 99508

99508 - Augmenting the Aw-Rascle-Zhang Traffic Flow Model With a Distributed Energy Equation 

Traffic congestion has a significant impact on travel time, idling operation, and overall transportation energy demand. In 2019, it was reported that in the United States, due to stop and go conditions, drivers spent an additional 8.7 billion hours on the road, consumed an additional 3.5 billion gallons of fuel, and emitted 36 million tons of excess greenhouse gases. Controlling vehicles using boundary control (via ramp metering) or in-domain control (via vehicle platooning) has been explored to reduce traffic jams. However, to design effective control algorithms for the traffic flow, a model that accurately describes traffic must be developed. Two forms of traffic models exist, microscopic, which take the form of ordinary differential equations (ODEs) and macroscopic, which take the form of partial differential equations (PDEs). Microscopic models describe the individual position and acceleration of vehicles while macroscopic models describe locally aggregated quantities such as vehicle density, flow, and mean speed. Because microscopic models describe the movement of each individual vehicle, their implementation becomes computationally intensive when simulating a large system, such as a highway that can be up to several miles long. To this end, it is beneficial to use macroscopic models when simulating large stretches of road. But, while energy optimization problems that utilize microscopic models are well studied, the use of macroscopic models for energy optimization has not yet been explored.

Currently, macroscopic models are used in control problems that seek to control traffic density to a desired setpoint or to control the location of traffic shockwaves, or traffic jams, so that they do not propagate upstream. While controlling the density along a road may lead to reduced energy usage, no studies in literature have proven that it results in the minimal energy usage. Unlike microscopic car-following models that calculate the forces acting against each individual vehicle and evaluate the energy at the wheel via the road load equation, there is no description of energy use in macroscopic models. Therefore, a macroscopic model that includes a distributed energy equation is needed. It is postulated that, by formulating an energy minimization problem using a macroscopic traffic model with a distributed energy equation, it is possible to develop strategies for controlling traffic flow that not only reduce traffic jams, but also minimize energy usage all while being less computationally intensive over large stretches of road.

This research is focused on the creation of a distributed road load equation that characterizes the energy usage along a stretch of road so that the above energy minimization problem can be solved. The base macroscopic model, which is to be augmented with the distributed energy equation, is the Aw-Rascle-Zhang (ARZ) model. The ARZ model consists of a hyperbolic system of PDEs which include a continuity equation and a momentum equation. The ARZ model is used, as opposed to the Lighthill-Whitham-Richards (LWR) and Payne-Whitham (PW) models, because these models suffer from the fact that they rely on a predefined equilibrium speed equation or can result in the ability of vehicles to have negative velocities, respectively. The energy output of the augmented ARZ model is then validated against two microscopic car-following models. The microscopic models used are the Improved Intelligent Driver Model (IIDM) and the Extended Intelligent Driver Model (EIDM), which is an extension of the IIDM implemented in the program Simulation of Urban Mobility (SUMO). SUMO, and the EIDM, is used as a benchmark as it is a proven traffic simulation software. The outcome of this research is a distributed, macroscopic description of energy usage that can be used for energy optimization over large stretches of road.

Presenting Author: Brian Block The Ohio State University

Presenting Author Biography: Brian Block graduated with his Bachelor of Science in Mechanical Engineering from the Schreyer Honors College at The Pennsylvania State University in 2019. He is currently pursuing his PhD in Mechanical Engineering at The Ohio State University. He received the NSF Graduate Research Fellowship in 2020.

Authors:

Brian Block The Ohio State University
Xiaoling Chen The Ohio State University
Stephanie Stockar The Ohio State University