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Street Traffic Simulation
Charles Erwin
CS 521 Computational Science
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Topics to Cover
What is involved in Traffic Simulation?
Value/Usefulness of Traffic Models
Examples of Current Traffic Models
References
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Traffic Simulation
Traffic Simulators are a type of Traffic study. There are three types of
traffic flow studies, differing in scope:
• microscopic scale: at a first level, every vehicle is considered as an
individual, so an equation is written for everyone, usually an ODE.
• macroscopic scale: in analogy with fluid dynamics models, it is
something more useful to write a system of (PDE) balance laws for some
gross quantities of interest, e.g the density of vehicles or their mean
velocity.
• mesoscopic (kinetic) scale: a third, intermediate, possibility, is to define a
function f(t,x,V) which expresses the probability of having a vehicle at
time t in position x which runs with velocity V. This function, following
methods of statistical mechanics, can be computed solving an integrodifferential equation, like the Boltzmann Equation.
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Traffic Simulation (cont)
Even though Traffic Flow has been studied as
early as the 1950s, there still isn’t one general
theory applied in real flow conditions.
Traffic is very difficult to simulate because not
only are the elements mechanical, the reactions
and behaviours of human drivers must also be
accurately predicted.
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Usefulness of Traffic Models
Modeling traffic is useful to engineers and city planners.
Simulate control measures available:
•
•
•
•
Speed Limits
Vehicle specific limitations (trucks)
Lane changing restrictions
Flow control at ramps
Simulate Infrastructure before it is bought.
Introduce new parameters such as cruise control and see
the effects.
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Specific Example: IDM
The Intelligent Driver Model (IDM) is a "car-following
model", i.e., the traffic state at a given time is characterized
by the positions, velocities, and the lane index of all
vehicles. The decision of any driver to accelerate or to
brake depends only on his own velocity, and on the "front
vehicle" immediately ahead of him.
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IDM (cont)
Lane-changing decisions, however,
depend on all neighboring vehicles.
Specifically, the acceleration dv/dt
of a given driver depends on his
velocity v, on the distance s to the
front vehicle, and on the velocity
difference Delta v (positive when
approaching).
where
v0
Desired velocity on free
road.
T
Desired safety headway
following other
vehicles.
a
Acceleration in every
day traffic.
b
Comfortable braking
deceleration.
s0
Minimum bumper-tobumper distance to
front of vehicle.
Δ
Acceleration exponent.
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IDM (cont)
In general, every "drivervehicle unit" can have its
individual parameter set.
• Trucks are characterized by low
values of v0, a, and b.
• Careful drivers drive at a high
safety time headway T.
• Aggressive ("pushy") drivers are
characterized by a low T in
connection with high values of v0,
a, and b.
Parameter
Car
Truck
v0
120 km/H
80 km/H
T
1.5 s
1.7 s
s0
2.0
2.0
a
0.3m/s^2
0.3m/s^2
b
3.0 m/s^2
2.0 m/s^2
Here are some Values in General:
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IDM (cont)
IDM is only a “Longitudinal Traffic model”, in
that it only takes into account traffic in a world
where there is only ever one lane. This of course
is not very useful by itself.
To fully utilize IDM, another traffic model is
necessary to allow for multiple lanes. The
example utilised here used “MOBIL.”
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MOBIL: Lane Change Model
MOBIL = Minimizing Overall Braking
decelerations Induced by Lane changes
Lane changes takes place, if
• the potential new target lane is more attractive, i.e., the "incentive
criterion" is satisfied,
• and the change can be performed safely, i.e., the "safety criterion"
is satisfied.
Introduce new parameter p: Politeness factor.
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MOBIL (cont)
While other lane-change models typically assume
purely egoistic behaviour, i.e., p=0, MOBIL can
model different behaviours by varying this factor:
• p > 1 => a very altruistic behaviour.
• p є [0, 0.5] => a realistic behaviour: Advantages of other drivers
have a lower priority, but are not neglected: Notice that this feature
means that yielding to "pushy" is included into MOBIL.
• p=0 => a purely selfish behaviour. Notice that also selfish drivers
do not ignore the safety criterion!
• p<0 => a malicious personality who takes pleasure in thwarting
other drivers even at the cost of own disadvantages. This may have
some interesting game-theoretic consequences. Of course, even
those mischief makers do obey the safety criterion.
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Microsimulation of Road Traffic
Online Applet
http://vwisb7.vkw.tu-dresden.de/~treiber/MicroApplet/index.html
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Traffic Model: Dresden 3d Model
Instance: Driver notices that traffic suddenly stops for no
apparent reason.
• After some time, vehicles begin to move again.
• Modeled in a traffic microsimulation by Dirk Hellbing
of Dresden University of Technology.
• Presented with the idea of allowing a driver to see what
the cause of the traffic jam really is instead of just
stopping.
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Dresden 3d Model (cont)
Example of the “Phantom Traffic Jam”
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Dresden 3d Model (cont)
Traffic with Environmental Conditions
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A Famous Traffic Model: SimCity
SimCity’s Traffic
Generation Model
• Traffic has been a major part of
SimCity since the very first version
of the game.
• Generating reasonable routes for a
City’s inhabitants is handled via
trip generation, where a Sim
attempts to find a way from one
destination to another via the road
network.
• The programmers wanted to
capture intent in transportation
simulation.
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SimCity (cont)
SimCity’s Traffic Generation Model
• The solution to how a Sim finds a route between two destinations
is solved using A* search.
• Instead of using distance as a heuristic, which would prevent
things like mass transit or walking from being likely options,
SimCity’s search routine uses time as the parameter to minimize.
• Travel time is calculated by a number of factors. Each form of
transportation can move over each different kind of tile at a
different speed. Pedestrians can travel over all types of roads at a
fixed rate, but cars and busses can go faster on main roads than on
residential streets. In addition, they can go really fast on highways,
which are forbidden to pedestrians by the laws of the city.
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SimCity (cont)
SimCity’s Traffic Generation Model
• Most forms of transportation are affected by how much traffic has
previously traveled over a tile. Each type of road has a different capacity
for traffic, and once a tile reaches capacity traffic slows down. A very
congested tile can be extremely slow, causing Sims to investigate other
paths first.
However, there are major flaws in the SimCity model.
• The suggested solution to most congestion in SimCity is to add more
routes for Sims to choose from. An alternative solution I independently
discovered was adding multiple toll booths along congested paths. The
engine allows for as many booths as can fit and therefore you can
maximize transportation profit as well as minimize congestion along
routes, a very unlikely solution in real life.
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References
Basics of Traffic Flow http://en.wikipedia.org/wiki/Traffic_flow
Traffic Simulation applet designed and written by Martin Treiber.
"TU Dresden 3d traffic simulator" at www.mtreiber.de
SimCity 4’s Traffic Model
http://simcity.ea.com/about/inside_scoop/traffic.php
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