A min-plus derivation of the fundamental car-traffic law

IEEE Transactions on Automatic Control

Volumn 50, Issue 5, 2005, Pages 699-705

  Lotito, Pablo A ^a   Mancinelli, Elina M ^b,c   Quadrat, Jean Pierre ^b  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b INRIA   (France)

^c CONICET ^*  (Argentina)

Author keywords

Cellular automata; Fundamental diagram; Lyapunov exponent; Max plus algebra

Indexed keywords

AUTOMATA THEORY; EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; TRAFFIC CONTROL;

CELLULAR AUTOMATA; FUNDAMENTAL DIAGRAM; LYAPUNOV EXPONENT; MAX-PLUS ALGEBRA;

STOCHASTIC CONTROL SYSTEMS;

EID: 20344394667     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.848336     Document Type: Article

References (14)

1. C. Appert and L. Santen, "Modélization du trafic routier par des automates cellulaires," Actes INRETS 91, 2002. Modélization du trafic.
2. F. Baccelli, G. Cohen, G. J. Olsder, and J.-P. Quadrat, Synchronization and Linearity. An Algebra for Discrete Event Systems. New York: Wiley, 1992.
3. M. Blank, "Variational principles in the analysis of traffic flows. (Why it is worth to go against the flow)," Markov Process. Related Fields, vol. 7, no. 3, pp. 287-305, 2000.
4. S. Benjaafar, K. Dooley, and W. Setyawan, "Cellular automata for traffic flow modeling,", citeseer.nj.nec.com/380458.html.
5. B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier et al., "A matrix method of solving an asymmetric exclusion model with open boundaries," in Cellular Automata and Cooperative Systems, N. Boccara et al., Eds. Les Houches, France: Kluwer, Jun. 1992, 1993, pp. 121-133.
6. B. Derrida, M. R. Evans, V. Hakim, and V. Pasquier et al., "Exact results for the one dimensional exclusion model," in Proc. Physica A200, 25-33 4th Bar Ilan Conf. Frontiers in Condensed Matter Physics, 1993, pp. 25-33.
7. B. Derrida and M. R. Evans, "Exact steady state properties of the one dimensional asymmetric exclusion model," in Probability and Phase Transition, G. Grimmett, Ed. Norwell, MA: Kluwer, 1994, pp. 1-16.
8. M. Fukui and Y. Ishibashi, "Traffic flow in 1D cellular automaton model including cars moving with high speed," J. Phys. Soc. Jpn., vol. 65, no. 6, pp. 1868-1870, 1996.
9. S. Gaubert, "Performance evaluation of (max, +) automata," IEEE Trans. Autom. Control, vol. 40, no. 12, pp. 2014-2025, Dec. 1995.
10. S. Gaubert and D. Hong, "Series expansions of Lyapunov exponents of monotone homogeneous maps, and forgetful monoids," INRIA, RR-3971, 2000.
11. K. Nagel and H. J. Herrman, "Deterministic models for traffic jams," Physica A, vol. 199, pp. 254-269, 1993.
12. K. Nagel and M. Schreckenberg, "A cellular automaton model for free way traffic." J. Physique I, vol. 2. no. 12, pp. 2221-2229, 1992.
13. B.-H. Wang, L. Wang, P. M. Hui, and B. Hu, "The asymptotic steady states of deterministic one-dimensional traffic flow models," Physica. B, vol. 279, no. 1-3, pp. 237-239, 2000.
14. Scilab [Online]. Available: http://www-rocq.inria.fr/scilab