Traffic Flow Simulation through Parallel Processing
Abstract
Numerical methods for solving traffic flow continuum models have been studied and efficiently implemented in traffic simulation codes in the past. Explicit and implicit methods have been used in traffic simulation codes in the past. Implicit methods allow a much larger time step size than explicit methods to achieve the same accuracy. However, at each time step a nonlinear system must be solved. The Newton method, coupled with a linear iterative method (Orthomin), is used. The efficient implementation of explicit and implicit numerical methods for solving the high-order flow conservation traffic model on parallel computers was studied. Simulation tests were run with traffic data from an 18-mile freeway section in Minnesota on the nCUBE2 parallel computer. These tests gave the same accuracy as past tests, which were performed on one-processor computers, and the overall execution time was significantly reduced.
Get full access to this article
View all access and purchase options for this article.
References
1. Leo C. J., and Pretty R. L. Numerical Simulation of Macroscopic Continuum Traffic Models. Transportation Research, Vol. 26B, No. 3, 1990, pp. 207–220.
2. Lighthill M. H., and Witham G. B. On Kinematic waves: II A Theory of Traffic Flow on Long Crowded Roads. Proc., Royal Society, London, Series A229, No. 1178, 1955, pp. 317–345.
3. Lyrintzis A. S. et al. Continuum Modeling of Traffic Dynamics. Proc., 2nd International Conference on Applications of Advanced Technologies in Transportation Engineering, ASCE, Minneapolis, Minn., Aug., 1991, pp. 36–40.
4. Michalopoulos P. G., Yi P., and Lyrintzis A. S. Development of an Improved High Order Continuum Traffic Flow Model. In Transportation Research Record 1365, TRB, National Research Council, Washington, D.C., 1992, pp. 125–132.
5. Payne H. J. FREFLO: A Macroscopic Simulation Model of Freeway Traffic. In Transportation Research Record 722, TRB, National Research Council, Washington, D.C., 1979, pp. 68–75.
6. Mikhailov L., and Hanus R. Hierarchical Control of Congested Urban Traffic—Mathematical Modeling and Simulation. Mathematics and Computers in Simulation, Vol. 37, 1994, pp. 183–188.
7. Gerlough D. L., and Huber M. J. Special Report 165: Traffic Flow Theory. TRB, National Research Council, Washington, D.C., 1975.
8. Chronopoulos A. T. et al. Traffic Flow Simulation Through High Order Traffic Modelling. Mathematical Computing Modelling, Vol. 17, No. 8, 1993, pp. 11–22.
9. Kim S. K., and Chronopoulos A. T. A Class of Lanczos-like Algorithms Implemented on Parallel Computers. Parallel Computing, Vol. 17, 1991, pp. 763–778.
10. Chronopoulos A. T., and Pedro C. Iterative Methods for Nonsymmetric Systems in DAEs and Stiff ODEs Codes. Mathematics and Computers in Simulation, Vol. 35, 1993, pp. 211–232.
11. Ortega J. M. Introduction to Parallel and Vector Solution of Linear Systems. Plenum Publishing Company, 1988.
12. McBryan O. A., and Van Der Velde E. F. Matrix and Vector Operations on Hypercube Parallel Processors. Parallel Computing, Vol. 5, 1987, pp. 117–125.
13. Ma S., and Chronopoulos A. T. Implementation of Iterative Methods for Large Sparse Nonsymmetric Systems on Parallel Vector Computers. International Journal of Supercomputer Applications, Vol. 4, 1990, pp. 9–24.
14. Di Brozolo G. R., and Robert Y. Parallel Conjugate Gradient-like Algorithms for Sparse Nonsymmetric Systems on a Vector Multiprocessor. Parallel Computing, Vol. 11, 1989, pp. 223–239.
15. Rodrigue G. Domain Decomposition: A Unified Approach for Solving Fluid Mechanics Problems on Parallel Computers. In Parallel Processing in Computational Mechanics (Adeli H., ed.), Dekker, 1991, pp. 297–330.
16. Meurant G. Domain Decomposition Methods for Solving Large Sparse Linear Systems. In Computer Algorithms for Solving Linear Algebraic Equations: The State of the Art (Spedicato E., ed.), NATO ASI Series, Series F: Computer and Systems Sciences, Vol. 77, Springer-Verlag, 1991, pp. 185–206.
Cite article
Cite article
Cite article
OR
Download to reference manager
If you have citation software installed, you can download article citation data to the citation manager of your choice
Information, rights and permissions
Information
Published In
Article first published: January 1996
Issue published: January 1996
Authors
Metrics and citations
Metrics
Journals metrics
This article was published in Transportation Research Record: Journal of the Transportation Research Board.
VIEW ALL JOURNAL METRICSArticle usage*
Total views and downloads: 14
*Article usage tracking started in December 2016
Altmetric
See the impact this article is making through the number of times it’s been read, and the Altmetric Score.
Learn more about the Altmetric Scores
Articles citing this one
Receive email alerts when this article is cited
Web of Science: 0
Crossref: 1
- Testing high performance numerical simulation programs: experience, le...
Figures and tables
Figures & Media
Tables
View Options
Get access
Access options
If you have access to journal content via a personal subscription, university, library, employer or society, select from the options below:
loading institutional access options
Alternatively, view purchase options below:
Purchase 24 hour online access to view and download content.
Access journal content via a DeepDyve subscription or find out more about this option.
