Fuks, Henryk; PhD

UNIVERSITY OF ILLINOIS AT CHICAGO, 1997

PHYSICS, GENERAL (0605); COMPUTER SCIENCE (0984); TRANSPORTATION (0709);

ENGINEERING, SYSTEM SCIENCE (0790); OPERATIONS RESEARCH (0796); SOCIOLOGY,
SOCIAL STRUCTURE AND DEVELOPMENT (0700)

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.

Social
Systems Simulation GroupP.O. Box 6904San Diego, CA 92166-0904Roland Werner, PrincipalPhone/FAX (619)
660-1603 |

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