Information Technology Reference
In-Depth Information
......4.....1..2.....3...2....3..........5..........5....
..5.......2..1...2......1..2.....4............4..........
.......3....1.2....2.....1...2.......4............4......
..........1..1..3....2....1....2.........5............4..
.4.........1..2....2...3...2.....3............4..........
.....5......2...2....3....1..3......4.............5......
..........3...3...3.....1..1....4.......4..............5.
4............3...2...3...2..1.......5.......4............
....4...........2..2....1..1.1...........4......5........
........4.........1..2...2..1.2..............5.......4...
..4.........4......2...3...1.1..2.................4......
......5.........4....2....1.0.2...2...................4..
...........5........2..3...01...2...2....................
5...............4.....2...00.1....3...3..................
.....4..............2...0.01..2......3...3...............
.5.......4............1.0.0.1...3.......3...3............
......5......5.........00.1..2.....3.......3...4.........
...........5......3....00..1...3......3.......4....4.....
................4....0.01...1.....4......4........4....5.
....................01.0.1...2........4......5........4..
....................1.00..1....3..........4.......4......
.....................000...2......3...........5.......4..
....5................000.....3.......3.............5.....
..4......5...........001........3.......4...............5
......5.......4......00.1..........3........5............
5..........5......1..01..2............3..........5.......
.....5..........2..1.0.2...3.............3............5..
...4......4.......1.00...2....3.............3............
.......4......3....001.....2.....3.............3.........
...........5.....1.00.1......3......4.............4......
..4.............1.000..1........3.......5.............5..
Fundamental Diagram for 1−lane Circle simulation
2000
1500
1000
Circle = 1000
P_Brake = 0.2
V_MAX = 5
500
0
0
10
20
30
40
50
60
70
80
90
100
Density [v/km/lane]
Fig. 2.
Stochastic CA. LEFT: Jam out of nowhere leading to congested traffic. RIGHT: One-
lane fundamental diagram as obtained with the standard cellular automata model for traffic using
p
noise
=0
.
2
; from [6].
(ii) over-reactions at braking and car-following, and (iii) randomness during acceleration
periods.
This makes the dynamics of the model significantly more realistic (Fig. 2).
p
noise
=
0
.
5
is more realistic
with respect to the resulting value for maximum flow (capacity), see Fig. 2 (right) [6].
is a standard choice for theoretical work (e.g. [5]);
p
noise
=0
.
2
Slow-to-Start (S2s) Rules/Velocity-Dependent Randomization (VDR).
Real traffic has
a strong hysteresis effect near maximum flow: When coming from low densities, traffic
stays laminar and fast up to a certain density
. Above that, traffic “breaks down” into
start-stop traffic. When lowering the density again, however, it does not become laminar
again until
ρ
2
, up to 30% [7,8]. This effect
can be included into the above rules by making acceleration out of stopped traffic weaker
than acceleration at all other speeds, for example by making the probability
ρ<ρ
1
, which is significantly smaller than
ρ
2
p
n
in the
STCA velocity-dependent: If
, then the speed reduction through
the randomization step is more often applied to vehicles with speed zero than to other
vehicles. Such rules are called “slow-to-start” rules [9,10].
p
n
(
v
=0)
>p
n
(
v≥
1)
Time-Oriented CA (TOCA).
A modification to make the STCA more realistic is the so-
called time-oriented CA (TOCA) [11]. The motivation is to introduce a higher amount
of elasticity in the car following, that is, vehicles should accelerate and decelerate at
larger distances to the vehicle ahead than in the STCA, and resort to emergency braking
only if they get too close. The rule set is easier to write in algorithmic notation, where
v
:=
v
+1
is increased by one at this line of the program.
For the TOCA velocity update, the following operations need to be done in sequence for
each car:
means that the variable
v
1. if (
g>v· τ
H
) then, with probability
p
ac
:
v
:= min
{v
+1
,v
max
}
;
2.
v
:= min
{v, g}
3. if (
g<v· τ
H
) then, with probability
p
dc
:
v
:= max
{v −
1
,
0
} .
