Street Traffic Simulation

Street Traffic Simulation - Transcript

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 CS 521 Computational Science 5

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

v0 T a b

Desired velocity on free road Desired safety headway following other vehicles Acceleration in every day traffic Comfortable braking deceleration Minimum bumper tobumper distance to front of vehicle Acceleration exponent

where

s0



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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 v0 T s0 a b Car 120 km H 1 5 s 2 0 0 3m s 2 3 0 m s 2 Truck 80 km H 1 7 s 2 0 0 3m 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 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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