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passenger cars passed
,
the number of lorries passed
,
the average speed of the pas-
senger cars
, and
the average speed of the lorries
. Our approach to generate the
tra
c state in the whole autobahn network from these locally measured quanti-
ties is to feed the data into an advanced cellular automaton tra
c simulator. The
simulator does not only deliver information about the tra
c states in regions
not covered by measurement, but also delivers reasonable estimates for other
valuable quantities like travel times for routes, a quantity that is not directly
accessible through the measurements of the detectors.
2 Simulation Model
Because data is fed real-time into the simulator it has to be e
cient, that is, at
least real time. Due to their design cellular automata models are very e
cient
in large-scale network simulations [1,2,3,4,5]. Models which reproduce the dy-
namic phases of tra
c are still under debate. For this reason an object-oriented
design of the simulator is advantageous because it allows a flexible use of dif-
ferent cellular automata models through inheritance of classes. The first cellular
automaton model for tra
c flow that was able to reproduce some characteristics
of real tra
c, like jam formation, was suggested by Nagel and Schreckenberg [6]
in 1992. We will give a brief review of their basic model before we describe the
more advanced cellular automaton model used by the simulator, which includes
anticipation, brake-lights, and asymmetric rules for lane changes.
2.1 The Nagel-Schreckenberg Model
In the Nagel-Schreckenberg model the road is represented by a one dimensional
lattice which is subdivided in cells with a length of 7
.
5m. Each cell is either
occupied by one vehicle or is empty. In every time-step
t → t
+ 1 the following
update rules are applied to the cars in the lattice in parallel:
•
Step 1: Acceleration:
v
n
(
t
+
1
3
) := min(
v
n
(
t
)+1
,v
max
)
.
•
Step 2: Braking:
v
n
(
t
+
2
3
) := min(
v
n
(
t
+
1
3
)
,d
n
(
t
)
−
1)
.
•
Step 3: Randomization with probability constant
p ∈
]0
,
1[:
max(
v
n
(
t
+
3
)
−
1
,
0)
,
with probability
p
,
v
n
(
t
+1):=
v
n
(
t
+
3
)
,
default.
•
Step 4: Move (drive):
x
n
(
t
+1):=
x
n
(
t
)+
v
n
(
t
+1)
.
