Cellular automata models for diffusion of information and highway traffic flow

                         Fuks, Henryk; PhD

                         UNIVERSITY OF ILLINOIS AT CHICAGO, 1997
                         PHYSICS, GENERAL (0605); COMPUTER SCIENCE (0984); TRANSPORTATION (0709);

                         In the first part of this work we study a family of deterministic models for highway traffic flow which
                         generalize cellular automaton rule 184. This family is parameterized by the speed limit m and another
                         parameter k that represents degree of 'anticipatory driving'. We compare two driving strategies with
                         identical maximum throughput: 'conservative' driving with high speed limit and 'anticipatory' driving with
                         low speed limit. Those two strategies are evaluated in terms of accident probability. We also discuss
                         fundamental diagrams of generalized traffic rules and examine limitations of maximum achievable
                         throughput. Possible modifications of the model are considered. For rule 184, we present exact
                         calculations of the order parameter in a transition from the moving phase to the jammed phase using the
                         method of preimage counting, and use this result to construct a solution to the density classification
                         problem. In the second part we propose a probabilistic cellular automaton model for the spread of
                         innovations, rumors, news, etc., in a social system. We start from simple deterministic models, for which
                         exact expressions for the density of adopters are derived. For a more realistic model, based on
                         probabilistic cellular automata, we study the influence of a range of interaction R on the shape of the
                         adoption curve. When the probability of adoption is proportional to the local density of adopters, and
                         individuals can drop the innovation with some probability p, the system exhibits a second order phase
                         transition. Critical line separating regions of parameter space in which asymptotic density of adopters is
                         positive from the region where it is equal to zero converges toward the mean-field line when the range of
                         the interaction increases. In a region between $R=1$ critical line and the mean-field line asymptotic
                         density of adopters depends on R, becoming zero if R is too small (smaller than some critical value). This
                         result demonstrates the importance of connectivity in diffusion of information. We also define a new class
                         of automata networks which incorporates non-local interactions, and discuss its applicability in modeling
                         of diffusion of innovations.


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