Information Technology Reference
In-Depth Information
.....5.....5.....5....................5.....5..
..........5.....5.....5....................5...
...............5.....5.....5...................
....................5.....5.....5..............
.5.....3...00001.2..3...3...2..3...4....1.01.1.
5.....3...00001.2..3...3...2..3...4....1.01.1.2
.....3...00001.2..3...3...2..3...4....1.01.1.2.
....3...00001.2..3...3...2..3...4....1.01.1.2..
...3...00001.2..3...3...2..3...4....1.01.1.2..3
..3...00001.2..3...3...2..3...4....1.01.1.2..3.
.3...00001.2..3...3...2..3...4....1.01.1.2..3..
3...00001.2..3...3...2..3...4....1.01.1.2..3...
...00001.2..3...3...2..3...4....1.01.1.2..3...4
..00001.2..3...3...2..3...4....1.01.1.2..3...4.
Fig. 1.
Sequence of configurations of CA 184. Lines show configurations of a segment of road in
second-by-second time steps; traffic is from left to right. Integer numbers denote the velocities
of the cars. For example, a vehicle with speed “3” will move three sites (dots) forward. Via this
mechanism, one can follow the movement of vehicles from left to right, as indicated by some
example trajectories. TOP: Uncongested traffic. BOTTOM: Congested traffic.
i.e. the number of empty cells between the vehicle under consideration and the vehicle
ahead, and
is measured in “cells per time step”.
This rule is similar to the CA rule 184 in the Wolfram classification [3]; indeed,
v
for
it is identical. This model has some important features of traffic, such as
start-stop waves, but it is unrealistically “stiff” in its dynamics.
For this CA, it turns out that, after transients have died out, there are two regimes,
depending on the system-wide density
v
max
=1
ρ
L
(Fig. 1):
-
Laminar traffic. All vehicles have gaps of
v
max
or larger, and speed
v
max
. Flow in
.
-
Congested traffic. All vehicles have gaps of
consequence is
q
=
ρv
max
v
max
or smaller. It turns out that their
speed is always equal to their gap. This means that
v
i
=
g
i
=
N
veh
×g
.
Since density
ρ
=1
/
(
g
+1)
, this leads to
q
=
ρv
=1
− ρ.
The two regimes meet at
ρ
c
=1
/
(
v
max
+1)
and
q
c
=
v
max
/
(
v
max
+1);
this is also
the point of maximum flow.
Stochastic Traffic CA (STCA).
One can add noise to the CA model by adding a
randomization term [4]:
Car following:
v
t
+
2
= min
{v
t
+1
,g
t
,v
max
}
max
{v
t
+
2
−
1
,
0
}
with probability
p
n
Randomization:
v
t
+1
=
v
t
+
2
else
Moving:
x
t
+1
=
x
t
+
v
t
+1
t
+
2
t
and
t
+1
refer to the actual time-steps of the simulation;
denotes an intermediate
result used during the computation.
With probability
, a vehicle ends up being slower than calculated deterministically.
This parameter simultaneously models effects of (i) speed fluctuations at free driving,
p
n
