A Physics-Inspired Distributed Energy Equation for Macroscopic Traffic Flow Models

This paper presents a distributed, physics-based energy equation to be used with macroscopic traffic flow models. The proposed macroscopic energy equation is derived starting from the road load equation and it is then integrated with the Aw-Rascle-Zhang model. Results are compared against the energy output of microscopic car-following models, namely the Improved Intelligent Driver Model and the Extended Intelligent Driver Model. To enable the comparison between macroscopic and microscopic model variables, kernel density estimation is used. This allows individual vehicle positions, speeds, and energy usage obtained from the ordinary differential equations to be converted to distributed quantities. The proposed macroscopic energy equation is evaluated on three different traffic scenarios: free flow, congested traffic, and mixed traffic. It is shown that the proposed energy model can calculate the energy output within ±4% in free flow traffic, ±11% in congested traffic, and ±8% in mixed traffic.

I. Introduction

In the United States, transportation accounts for a large portion of total energy use. In fact, roughly 27% of energy usage comes from the transportation sector [1]. Traffic congestion plays a large role in this energy usage. In the United States, up to 3.5 billion gallons of fuel are wasted yearly as a result of congestion [2]. Because of this, much effort has been made to assess the impact of traffic on both highways and urban networks through modeling and simulation [3], [4], [5], [6].