Publication: Random versus deterministic 2-dimensional traffic flow models
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1995-02
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Abstract
Deterministic and stochastic cellular automata models available to study two-dimensional traffic fIow are compared in this paper. It is shown that a connection between them can be made only when the infinite time and infinite system limits are taken in the appropriate order. We also stress the crucial importance of the choice of boundary conditions in the deterministic model to obtain bulk properties.
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©1995 The American Physical Society. We want to thank A. Sánchez for a critical reading of the manuscript. We also acknowledge financial support from the Dirección General de Investigación Científica y Técnica (Spain) through Project No. PB92-0248 (F.C.M. and J.M.M.) and Project No. PB91-0378 (J.A.C. and R.B.). R. B. also acknowledges financial support from the Ministerio de Educación y Ciencia (Spain).
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[1]K. Nagel and M. Schreckenberg, J. Phys. (France) I, 2, 2221 (1992); K. Nagel and H. J. Herrmann, Physica A 199/2, 254 (1993); A. Schadschneider and M. Schreckenberg, J. Phys. A 26, L679 (1993).
[2] O. Biham, A. A. Middleton, and D. Levine, Phys. Rev. A 46, R6124 (1992).
[3] J. A. Cuesta, F. C. Martínez, J. M. Molera, and A. Sánchez, Phys. Rev. E 48, R4175 (1993).
[4] J. M. Molera, F. C. Martínez, J. A. Cuesta, and R. Brito, Phys. Rev. E 51, 175 (1995).
[5] Actually, for finite size simulations, the value of the correlations is ~(N/2) [(N/2) —1]L = (n /4) —(n/2L ), so for small n (of the order 1/L ), deviations of the value n /4 are noticeable, as can be seen in Fig. 1.
[6] Anyhow, Eq. (4) seems to be an overall good approximation for υ(n) in the freely moving phase (see Ref. [4] for more details). The reason is that, although the difference between a function and an approximation to it may be small, the difference between their derivatives will almost certainly be amplified.