Polynomial Approach and Non-linear Analysis for a Traffic Fundamental Diagram
Abstract
Vehicular traffic can be modelled as a dynamic discrete form. As in many dynamic systems, the parameters modelling traffic can produce a number of different trajectories or orbits, and it is possible to depict different flow situations, including chaotic ones. In this paper, an approach to the wellknown density-flow fundamental diagram is suggested, using an analytical polynomial technique, in which coefficients are taken from significant values acting as the parameters of the traffic model. Depending on the values of these parameters, it can be seen how the traffic flow changes from stable endpoints to chaotic trajectories, with proper analysis in their stability features.References
Institute of Transportation Engineers (ITE) Traffic Engineering Handbook 6th ed. Washington DC, 2009.
Payne H., Models of freeway traffic and control, in Mathematic Models of Public Systems. Smulation Council, 1971;28(1):51–61.
Daganzo C. F., Fundamentals of Transportation and Traffic Operations, Pergamon, Elsevier.
Marušić S., Fluid Models in the Traffic Flow Theory, Promet - Traffic & Transportation, 2000;12(1):7-14.
Chapra S. and Canale R., Numerical Methods for Engineers, 6th Ed. McGraw-Hill, 2009.
Lo S.-C. and Cho H.-J., Chaos and control of discrete dynamic model, Journal of the Franklin Institute, 2005;342:839–851.
Devaney R. L., An introduction to chaotic dynamical systems, 1987.
Thamizh V. A. and Dhivya G., Measuring heterogeneous traffic density, International Journal of Engineering and Applied Sciences, 2010; 6(3): 144–148.
Kim T. and Zhang H. M., An empirical study on gap time and its relation to the fundamental diagram of traffic flow, in 7th International IEEE Conference on Intelligent Transportation Systems, Washington, D.C., 2004:94–99.
Lighthill M. J. and Whitham G. B., On kinematic waves. I. Flood movement in long rivers, Proc. Royal Soc. A., 1955;229:281–316.
Richards P. I., Shock waves on the highway, Operation research, 1956;4:42–51.
Holmgren, R. A., A first Course in Discrete Dynamical Systems, Springer, N. Y., 1994.
Greenberg, H., An analysis of traffic flow. Operations Research 1959;7:79-85.
Greenshields, B.D. “A study of traffic capacity”. Highway Research Board, 1935;14:448-477.
Ngoc P.H.A., Hieu L.T., On stability of discrete-time systems under nonlinear time-varying perturbations, Advance in Difference Equations 2012;2012:120.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
