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Cellular Automata Models for Transportation
Applications
Kai Nagel
Institute for Scientific Computing, Swiss Federal Institute of Technology Zurich (ETHZ),
8092 Zurich, Switzerland
Abstract.
This paper gives an overview of the use of CA modes for transportation
applications. In transportation applications, the CA dynamics is embedded within
several other concepts, such as the fact that the dynamics unfolds on a graph
instead of on flat 2d space, or multi-agent modeling. The paper also discusses the
the limits of the CA technology in traffic.
1
Introduction
Cellular automata methods have their applications primarily in areas of spatio-temporal
dynamics. Transportation simulations, with travelers and vehicles moving through cities,
fall into that category. There are however also important differences between a “stan-
dard” CA simulation and those used in traffic. These differences are that in traffic, the
dynamics is normally considered as unfolding on a graph instead of on flat space, and that
particles in transportation simulations are better characterized as “intelligent agents”.
These aspects will be discussed in Secs. 3 and 4. This is followed by a discussion of the
limits of the CA technology and relations to other methods (Sec. 5), and a short outlook
on a simulation of “all of Switzerland” (Sec. 6). The paper is concluded by a summary.
2
CA Rules for Traffic
In CA models for traffic, space is typically coarse-grained to the length a car occupies in
a jam (
m), and time typically to one second (which can be justified
by reaction-time arguments [1]). One of the side-effects of this convention is that space
can be measured in “cells” and time in “time steps”, and usually these units are assumed
implicitly and thus left out of the equations. A speed of, say,
=1
/ρ
jam
≈
7
.
5
, means that the
vehicle travels five cells per time step, or 37.5 m/s, or 135 km/h, or approx. 85 mph.
v
=5
Deterministic Traffic CA.
Typical CA for traffic represent the single-lane road as a
1-dimensional array of cells of length
, each cell either empty or occupied by a single
vehicle. Vehicles have integer velocities between zero and
v
max
. A possible update rule
is [2]
Car following:
v
t
+1
= min
{g, v
t
+1
,v
max
}
x
t
+1
=
x
t
+
v
t
+1
The first rule describes deterministic car-following: try to accelerate by one velocity unit
except when the gap is too small or when the maximum velocity is reached.
Movement:
g
is the gap,
