Microscopic Driver Behaviour Models
? PTV AG 2006
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We consider:
A single vehicle ?kinematics“
x(t), v(t), a(t)
dx(t), dv(t)
Two vehicles ?Car Following“
q(t), k(t), v(t)
Many vehicles ?Traffic Flow“
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Kinematics of a single vehicle
position speed acceleration
t
x (t) v(t) a (t)
space
x (t ) = x 0 + v (τ )dτ
0
time
1 x(t ) = x0 + v0 ? t + ? a ? t 2 2
for constant a
2 v2 ? v12 braking distance formula: dx = 2a
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Interaction of two vehicles: car following
Distance Time headway Relative speed dx [m] dt [s] dv [m/s]
reaction time [s]
absolutely safe distance: assumes immediate stopping of the preceeding vehicle relatively safe distance: considers that the vehicle in front also has to decelerate
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Microscopic Modelling of Traffic Flow
v (t), dx(t), dv(t)
Many models available; lots of research done Range from very simple to very complicated models Which model can explain most traffic flow phenomena?
dx
Free
Perception threshold for approaching
...
Approaching
Upper following distance
Following Danger
safety distance
dv
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Car-Following Models GM models (Herman, Gazis)
Vn (t)m [Vn?1(t ?T) ?Vn (t ?T)] an (t) =α l [?x(t)]
an (t ) : acceleration of vehicle n at time t α, l, m: parameters
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Car-following and Traffic Stream Models
m
Vn (t)m an (t) =α ?V(t ?T) l [?x(t)]
Under steady-state, single lane conditions integration of carfollowing models results in traffic stream models
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Cellular Automata Model
> space-discrete: Road divided in cells of the length of a car > typically time step 1 second > speeds discrete as well: 1,2,3,... cells per second
> simple movement rules:
1. 2. 3. 4.
if speed below maximum speed, increase speed by 1 if leading car less than speed cells away, reduce speed to distance – 1 with probability p: reduce speed by 1 move vehicle according to speed
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One timestep in a CA model
Situation at time t
Step 1: Accelerate (max speed = 5)
Step 2: Brake to avoid collision
Step 3: random slowdown
Step 4: Move to situation at time t+1
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Resulting trajectories of a CA model
http://rcswww.urz.tu-dresden.de/~helbing/RoadApplet/
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The Psycho-Physical Car-Following Model
v dx, dv
Psycho: Physical:
- desired speeds - desired safety distances - perception limits - imperfect vehicle control
α
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Basic driving modes in Wiedemann‘s model
dx
Free
Perception threshold for approaching
Approaching
Upper following distance
Following
safety distance
Danger (slower than leader) (faster than leader) dv
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Car-Following Process
dx[m] 60
dx[m] 60
measured
55 50 45 40 35 30 25 20 15 10 5
simulated
55 50 45 40 35 30 25 20 15 10 5
-dv[m/s] -6 -5 -4 -3 -2 -1
0 0 1 2 3 4
+dv[m/s] 5 6
-dv[m/s] -6 -5 -4 -3 -2 -1
0 0 1 2 3 4
+dv[m/s] 5 6
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Stochastic Noise in Car-Following
dx[m] 60
dx[m] 60
high noise
55 50 45 40 35 30 25 20 15 10 5
low noise
55 50 45 40 35 30 25 20 15 10
-dv[m/s] -6 -5 -4 -3 -2 -1
0 0 1 2 3 4
+dv[m/s] 5 6
-dv[m/s] -6 -5 -4 -3 -2 -1
5 0 0 1 2 3
+dv[m/s] 4 5 6
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? PTV AG 2006
Lane Changing Models
> Traditionally more or less independend from car-following > Typically structured in 3 decision steps:
1. Is the situation on the current lane ok? 2. Is the situation on a neighbour lane better? 3. Does the traffic situation allow a change?
> Step 3 typically implements a gap acceptance model. > There are mandatory and discretionary lane changes:
> mandatory: getting off the current lane in order to continue
on the desired path (e.g. exiting), or to avoid lane closure > discretionary: attempting to achieve desired speed, avoid following trucks, avoid merging traffic, etc.
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Improvements of he traditional approaches
Merging and Weaving > cooperation between drivers needed > requires ?tactical“ driving, i.e. the driver needs a plan > even more sophisticated models for congested merging > Interaction of lane changing and car-following model needed Lane Selection > compare not only adjacent lanes but all lanes
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Non lane based traffic: Pedestrian modeling
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Pedestrians in traffic engineering
> Pedestrians have always been
an important aspect in junction control > However, a model of their real movement was not needed
> pedestrian flows play a more
> > > > >
important role in other situations:
bus terminals railway and underground stations airports buildings sports stadiums
> Areas of interest:
> capacity of infratructure > efficient operation > emergency situations, evacuation
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Pedestrian flow: Empirical data
> Measurement technique: video analysis
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Pedestrian flow: Empirical data
> Measurement technique: automated video tracking of pedestrians
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