Information Technology Reference
In-Depth Information
v
mi
m
(
t
) := min(
d
m,l
(
t
)
,v
m
(
t
))
−
1
,
where
d
m,l
(
t
) is the number of free cells between the car
m
and its next car in
front
l
, is a lower bound of how far the car
m
will move during this time-step.
Brake lights are a further component of the anticipated driving. They allow
cars to react to disturbances in front earlier by adjusting their speed. Empir-
ical observations suggest [15,16] that drivers react in a temporal- rather than
a spatial-horizon. For this reason the velocity-dependent temporal interaction
horizon
t
n
(
t
) := min(
v
n
(
t
)
,h
)
is introduced to the model. The constant
h
determines the temporal range of
interaction with the brake light
b
m
(
t
) of the next car
m
in front. The car
n
does
only react to
b
m
(
t
) if the time to reach the back of the car
m
, assuming constant
velocity (
v
n
=
const .
) and that the car
m
stands still, is less than
t
n
(
t
), that is,
t
n
(
t
):=
d
n,m
(
t
)
v
n
(
t
)
<t
n
(
t
)
.
In our model we take
h
equal to 7s.
The third modification of the Nagel-Schreckenberg model implemented in the
simulator is a velocity dependent randomization, which means that the probabil-
ity constant
p
is replaced with a probability function dependent on the velocity
of the car. Further, the probability is also a function of the brake light of the
next car in front. In every time-step for every car
n
with car
m
next in front,
the probability that the car
n
brakes is
p
b
,
if
b
m
(
t
)=onand
t
n
(
t
)
<t
n
(
t
),
p
0
,
if
v
n
(
t
) = 0 and (
b
m
(
t
)=offor
t
n
(
t
)
≥ t
n
(
t
)),
p
d
,
default.
p
=
p
(
v
n
(
t
)
,b
m
(
t
)) :=
In our model we take
p
b
equal to 0
.
96,
p
0
equal to 0
.
1, and
p
d
equal to 0
.
01.
To sum up, to move the cars forward in the network the algorithm executes
the following steps in parallel for all cars
n
:
•
Step 0: Initialization:
For car
n
find next car in front
m
. Set
p
:=
p
(
v
n
(
t
)
,b
m
(
t
)) and
b
n
(
t
+1):=off.
•
Step 1: Acceleration:
if
b
n
(
t
)=onor(
b
m
(
t
)=on and
t
n
(
t
)
<t
n
(
t
)),
v
n
(
t
+
1
v
n
(
t
)
,
3
):=
min(
v
n
(
t
)+1
,v
max
)
,
default.
•
Step 2: Braking:
v
n
(
t
+
2
3
) := min(
v
n
(
t
+
1
3
)
,d
e
n,m
(
t
))
.
Turn brake light on if appropriate:
if
v
n
(
t
+
2
3
)
<v
n
(
t
)
,
then
b
n
(
t
):=on
.
