Abstract
There has been significant progress in modelling complex systems by using cellular automata (CA) [1, 2]; such complex systems include, for example vehicular traffic [3] and biological systems [4,5]. In most cases, particle-hopping CA models have been used to study the spatio-temporal organization in systems of interacting particles driven far from equilibrium [2,3]. In traffic systems, vehicles are represented by particles while their mutual influence is captured by the inter-particle interactions. Generically, these inter-particle interactions tend to hinder their motions which leads a monotonic decrease of the average speed as function of the particle density [6,7].
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References
S. Wolfram, Theory and Applications of Cellular Automata (World Scientific, Singapore, 1986)
B. Chopard, M. Droz, Cellular Automata Modelling of Physical Systems (Cambridge University Press, 1998)
D. Chowdhury, L. Santen, A. Schadschneider, Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329, 199–329 (2000)
D. Chowdhury, K. Nishinari, A. Schadschneider, Self-organized patterns and traffic flow in colonies of organisms: From bacteria and social insects to vertebrates. Phase Transit. 77, 601–624 (2004)
D. Chowdhury, K. Nishinari, A. Schadschneider, Physics of transport and traffic phenomena in biology: From molecular motors and cells to organisms. Phys. Life Rev. 2, 318 (2005)
D. Chowdhury, V. Guttal, K. Nishinari, A. Schadschneider, A cellular-automata model of flow in ant trails: Non-monotonic variation of speed with density. J. Phys. A: Math. Gen. 35, L573–L577 (2002)
K. Nishinari, D. Chowdhury, A. Schadschneider, Cluster formation and anomalous fundamental diagram in an ant trail model. Phys. Rev. E 67, 036120 (2003)
D. Helbing, Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067 (2001)
B. Kerner: The Physics of Traffic (Springer, Heidelberg, 2004)
B. Hölldobler, E.O. Wilson, The Ants (Belknap, Cambridge, 1990)
B. Hölldobler, E.O. Wilson: The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies (W.W. Norton, New York, 2008)
A. John, A. Schadschneider, D. Chowdhury, K. Nishinari, Trafficlike collective movement of ants on trails: Absence of jammed phase. Phys. Rev. Lett. 102, 108001 (2009)
M. Burd, D. Archer, N. Aranwela, D.J. Stradling, Traffic dynamics of the leaf cutting ant. American Natur. 159, 283 (2002)
F. Schweitzer, Brownian Agents and Active Particles, Springer Series in Synergetics (Springer, Heidelberg, 2003)
S. Camazine, J.L. Deneubourg, N.R. Franks, J. Sneyd, G. Theraulaz, E. Bonabeau, Self-organization in Biological Systems (Princeton University Press, Princeton, 2001)
A.S. Mikhailov, V. Calenbuhr, From Cells to Societies (Springer, Berlin, 2002)
B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process. Phys. Rep. 301, 65 (1998)
B. Derrida, M.R. Evans, in: Nonequilibrium Statistical Mechanics in One Dimension, ed. by V. Privman (Cambridge University Press, Cambridge, 1997)
G.M. Schütz, Exactly solvable models for many-body systems far from equilibrium, ed. by C. Domb, J.L. Lebowitz, Phase Transitions and Critical Phenomena, Vol. 19, (Academic Press, London, UK, 2000)
R.A. Blythe, M.R. Evans, Nonequilibrium steady states of matrix product form: a solver’s guide. J. Phys. A 40, R333 (2007)
A. Kunwar, A. John, K. Nishinari, A. Schadschneider, D. Chowdhury, Collective traffic-like movement of ants on a trail – dynamical phases and phase transitions. J. Phys. Soc. Jpn. 73, 2979 (2004)
K. Nishinari, D. Takahashi, Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton. J. Phys. A: Math. Gen. 31, 5439 (1998)
O.J. O’Loan, M.R. Evans, M.E. Cates, Jamming transition in a homogeneous one-dimensional system: The bus route model. Phys. Rev. E 58, 1404 (1998)
D. Chowdhury, R.C. Desai, Steady-states and kinetics of ordering in bus-route models: Connection with the Nagel-Schreckenberg model. Eur. Phys. J. B 15, 375 (2000)
F. Spitzer, Interaction of Markov processes. Adv. Math. 5, 246–290 (1970)
M.R. Evans, Phase transitions in one-dimensional nonequilibrium systems. Braz. J. Phys. 30, 42 (2000)
M.R. Evans, T. Hanney, Nonequilibrium statistical mechanics of the zero-range process and related models. J. Phys. A 38, R195 (2005)
M.R. Evans, Exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics. J. Phys. A 30, 5669 (1997)
A.B. Kolomeisky, G. Schütz, E.B. Kolomeisky, J.P. Straley, Phase diagram of one-dimensional driven lattice gases with open boundaries. J. Phys. A 31, 6911 (1998)
V. Popkov, G. Schütz, Steady-state selection in driven diffusive systems with open boundaries. Europhys. Lett. 48, 257 (1999)
K. Nishinari, K. Sugawara, T. Kazama, A. Schadschneider, D. Chowdhury, Modelling of self-driven particles: Foraging ants and pedestrians. Physica A 372, 132 (2006)
A. John, A. Schadschneider, D. Chowdhury, K. Nishinari, Collective effects in traffic on bi-directional ant trails. J. Theor. Biol. 231, 279 (2004)
R. Beckers, J.L. Deneubourg, S. Goss, Trails and U-turns in the selection of a path by the ant Lasius niger. J. Theor. Biol. 159, 397 (1992)
I.D. Couzin, N.R. Franks, Self-organized lane formation and optimized traffic flow in army ants. Proc. Roy Soc. London B 270, 139 (2003)
S.A. Janowsky, J.L. Lebowitz, Finite-size effects and shock fluctuations in the asymmetric simple-exclusion process. Phys. Rev. A 45, 618 (1992)
G. Tripathy, M. Barma, Steady state and dynamics of driven diffusive systems with quenched disorder. Phys. Rev. Lett. 78, 3039 (1997)
A. Kunwar, D. Chowdhury, A. Schadschneider, K. Nishinari, Competition of coarsening and shredding of clusters in a driven diffusive lattice gas. J. Stat. Mech. (2006) P06012
M. Burd, N. Aranwela, Head-on encounter rates and walking speed of foragers in leaf-cutting ant traffic. Insect. Sociaux 50, 3 (2003)
P. F. Arndt, T. Heinzel, V. Rittenberg, Spontaneous breaking of translational invariance in one-dimensional stationary states on a ring. J. Phys. A 31, L45 (1998); J. Stat. Phys. 97, 1 (1999)
N. Rajewsky, T. Sasamoto, E.R. Speer, Spatial particle condensation for an exclusion process on a ring. Physica A 279, 123 (2000)
K. Johnson, L.F. Rossi, A mathematical and experimental study of ant foraging trail dynamics. J. Theor. Biol. 241, 360 (2006)
A. Dussutour, J.L. Deneubourg, V. Fourcassié, Temporal organization of bi-directional traffic in the ant Lasius niger (L.), Jrl. Exp. Biol. 208, 2903 (2005)
A. John, A. Schadschneider, D. Chowdhury, K. Nishinari, Characteristics of ant-inspired traffic flow – Applying the social insect metaphor to traffic models. Swarm Intelligence 3, 199 (2008)
A. John, Physics of Traffic on Ant Trails and Related Systems, Doctoral Thesis, (Universität zu Köln, Cologne, Germany, 2006)
P. Chakroborty, A. Das, Principles of Transportation Engineering (Prentice Hall of India, Englewood Cliffs, NJ, 2003)
A.D. May, Traffic Flow Fundamentals (Prentice Hall Englewood Cliffs, NJ, 1990)
C. Burstedde, K. Klauck, A. Schadschneider, J. Zittartz, Simulation of pedestrian dynamics using a 2-dimensional cellular automaton. Physica A 295, 507 (2001)
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Chowdhury, D., Nishinari, K., Schadschneider, A. (2010). CA Modeling of Ant-Traffic on Trails. In: Kroc, J., Sloot, P., Hoekstra, A. (eds) Simulating Complex Systems by Cellular Automata. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12203-3_12
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