Explicit numerical methods for solving macroscopic traffic flow continuum models have been studied and efficiently implemented in traffic simulation codes in the past. We studied and implemented implicit numerical methods for solving the flow conservation traffic model. We then wrote an experimental code in C simulating 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 methods gave the same (and in some cases better) accuracy as the Lax method. The implicit methods were (more than twice) faster than the Lax method.
Bibliographical noteFunding Information:
This work was supported by the Univ. of Minnesota Transporation Center and the Army High Performance Computing Research Center. We would like to acknowledge Dr. Eil Kwon (postdoctoral researcher in Civil Engineering at the University of Minnesota) and Ping Yi (graduate student in Civil Engineering at the University of Minnesota) for their comments and useful discussions on this subject.