A cellular automaton

A cellular automaton - J. Phys. I France 2 (1992) 2221-2229...

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Unformatted text preview: J. Phys. I France 2 (1992) 2221-2229 DECEMBER 1992, PAGE 2221 aassification Physics Abstracts 02.50 02.70 o3AoG A cellular automaton model for freeway traffic Kai Nagel(~) and Michael Schreckenberg(~) (~) Mathematisches Institut, Universitit zu I~6ln, Weyertal 86-90, W-sore I~6ln 41, Germany (~) Institut fir Theoretische Physik, Universitit zu K61n, Zfilpicher Str. 77, W-sore I~6ln 41, Germany (Received 3 September 1992, accepted 10 September 1992) Abstract. We introduce a stochastic discrete automaton model to simulate freeway traffic. Monte-Carlo simulations of the model show a transition from laminar traffic flow to start-stop- waves with increasing vehicle density, as is observed in real freeway traffic. For special cases analytical results can be obtained. 1. Introduction. Fluid-dynamical approaches to traffic flow have been developed since the 1950's [ii. In recent times, the methods of nonlinear dynamics were succesfully applied to these models, stressing the notion of a phase transition from laininar flow to start-stop-waves with increasing car density [2]. Automatic detection of stronger fluctuations near this critical point has already been used to install better traffic control systems in Germany [3]. On the other hand, boolean stimulation models for freeway traffic have been developed [4, 5]. For lattice gas automata, it is well known that boolean models can simulate fluids [6]. We show that indeed our boolean model for traffic flow has a transition from laminar to turbulent behavior, and our simulation results indicate that the system reaches a possibly critical state by itself in a bottleneck situation (reminiscent of self organizing criticality [7]). This point together with an extension to multi-lane traffic will be the subject of further investigations [12]. The outline of this paper is as follows: At the beginning, we describe our model (Sect. 2) and discuss its phenomenological behavior, especially the transition (Sect. 3). In section 4 results for the bottleneck situation are presented. Section 5 contains a discussion of the results and compares them to values in reality. Sections 6 and 7 give a short conflusion/outlook. A preliminary account of the model is given in [8]. 2222 JOURNAL DE PHYSIQUE I N°12 2. The model. Our computational model is defined on a one-dimensional array of L sites and with open or periodic boundary conditions. Each site may either be occupied by one vehicle, or it may be empty. Each vehicle has an integer velocity with values between zero and vmax. For an arbitrary configuration, one update of the system consists of the following four consecutive steps, which are performed in parallel for all vehicles: I) Acceleration: if the velocity v of a vehicle is lower than vmax and if the distance to the next car ahead is larger than v + I, the speed is advanced by one [v- v +11. 2) Slowing down (due to other cars): if a vehicle at site I sees the next vehicle at site I + j (with j < v), it reduces its speed to...
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A cellular automaton - J. Phys. I France 2 (1992) 2221-2229...

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