Exact results for deterministic cellular automata traffic models

Abstract

We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow can be expressed in terms of generalized hypergeometric function. We show that the steady state limit agrees with previously published results.

13 pages, 4 figures

References in corpus (4)

• A Simplified Cellular Automaton Model for City Traffic
• Solution of the Density Classification Problem with Two Cellular Automata Rules
• Cellular automaton rules conserving the number of active sites
• Analytical Results For The Steady State Of Traffic Flow Models With Stochastic Delay

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• Probabilistic cellular automata with conserved quantities
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• Critical behavior of a cellular automaton highway traffic model
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• Asymptotic expansions of the hypergeometric function with two large parameters $-$ application to the partition function of a lattice gas in a field of traps
• Hysteresis phenomenon in deterministic traffic flows
• Convergence to equilibrium in a class of interacting particle systems evolving in discrete time
• A slow-to-start traffic model related to a M/M/1 queue
• On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow
• Critical behavior of number-conserving cellular automata with nonlinear fundamental diagrams
• Exact stationary state for a deterministic high speed traffic model with open boundaries
• Variational principles in the analysis of traffic flows. (Why it is worth to go against the flow.)
• Catalan numbers and power laws in cellular automaton rule 14
• Second order additive invariants in elementary cellular automata
• Approximating dynamics of a number-conserving cellular automaton by a finite-dimensional dynamical system
• Structure and dynamics in the low-density phase of a two-dimensional cellular automaton model of traffic flow
• Analytic Proof of the Attractors of a Class of Cellular Automaton
• Dynamics of traffic jams: order and chaos
• First-passage processes in a deterministic one-dimensional cellular automaton model of traffic flow
• Dynamics of the Cellular Automaton Rule 142
• Ergodic properties of a simple deterministic traffic flow model re(al)visited
• Exact limiting solutions for certain deterministic traffic rules