Explicit and implicit numerical methods for solving simple traffic flow continuum models have been studied and efficiently implemented in traffic simulation codes. We studied and implemented explicit and implicit numerical methods for solving high-order flow conservation traffic models. The acceleration and inertia effects of the traffic mass are properly addressed in the new formulations. The high order model does not employ equilibrium flow-density relationships. We wrote an experimental code in C to simulate a freeway (un)congested pipeline and freeway entry/exit traffic flow. Tests with real data collected from the I-35 W freeway in Minneapolis were conducted on a workstation computer. The implicit Euler method gave the same (and in some cases better) accuracy as the explicit Lax method. The implicit Euler method was (about three times) faster than the Lax method.
Bibliographical noteFunding Information:
The first four authors are at the University of Minnesota and the last author is at MN/DOT. A. Chronopoulos is an assistant professor at the Computer Science Dept., A. Lyrintais is an assistant professor at the Dept. of Aerospace Engineering and Mechanics, P. Michalopoulos is a professor at the Civil and Mineral Engineering Dept. C. Fthee is a Master’s student in Computer Science and P. Yi is a researcher at the Minnesota Department of Transportation. This work was supported by the University of Minnesota Center of Transportation Studies.