Linear chaos for the Quick-Thinking-Driver model
- 301 Downloads
In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car). Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.
KeywordsDeath model Birth-and-death problem Car-following Quick-Thinking-Driver Devaney chaos Distributional chaos \(C_0\)-semigroups
The authors were supported by a grant from the FPU program of MEC and MEC Project MTM2013-47093-P.
- 2.Banasiak, J., Lachowicz, M.: Chaos for a class of linear kinetic models. C. R. Acad. Sci. Paris Série II 329, 439–444 (2001)Google Scholar
- 8.Barrachina, X., Conejero, J.A.: Devaney chaos and distributional chaos in the solution of certain partial differential equations. Abstr. Appl. Anal. 457,019, 11 (2012)Google Scholar
- 13.Chung, C.C., Gartner, N.: Acceleration noise as a measure of effectiveness in the operation of traffic control systems. Operations Research Center. Massachusetts Institute of Technology. Cambridge (1973)Google Scholar
- 14.CNN (2014) Driverless car tech gets serious at CES. http://edition.cnn.com/2014/01/09/tech/innovation/self-driving-cars-ces/. Accessed 7 Apr 2014
- 16.DARPA Grand Challenge. http://en.wikipedia.org/wiki/2005_DARPA_Grand_Challenge#2005_Grand_Challenge
- 22.Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics, vol. 194. Springer, New York, 2000. With contributions by Brendle S., Campiti M., Hahn T., Metafune G., Nickel G., Pallara D., Perazzoli C., Rhandi A., Romanelli S., and Schnaubelt RGoogle Scholar
- 24.Greenshields, B.D.: The photographic method of studying traffic behavior. In: Proceedings of the 13th Annual Meeting of the Highway Research Board, pp. 382–399 (1934)Google Scholar
- 25.Greenshields, B.D.: A study of traffic capacity. In: Proceedings of the 14th Annual Meeting of the Highway Research Board, pp. 448–477 (1935)Google Scholar
- 28.Helly, W.: Simulation of Bottleneckes in Single-Lane Traffic Flow. Research Laboratories, General Motors. Elsevier, New York (1953)Google Scholar