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Modelling the Behaviour of Drivers: Bi-objective Traffic Assignment

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Olga Perederieieva

on 18 July 2015

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Transcript of Modelling the Behaviour of Drivers: Bi-objective Traffic Assignment

Bi-objective user equilibrium
Modelling the Behaviour of Drivers: Bi-objective Traffic Assignment
Modelling
Conventional approach
Bi-objective approach
Traffic network
Analyse
Predict impact of projects and policies
Implement better policies
Goals of transportation management:
Models aim to:
Predict how the road users will decide to travel during a given period of time
How to predict what route a particular individual will choose
Make assumptions on how people usually make
their route choices
Wardrop’s first principle or user equilibrium condition (Wardrop, 1952):
The journey times on all the routes actually used are equal, and less than those which would be experienced by a single vehicle on any unused route
How does it work
Congestion modelling
Traffic assignment problem: summary
Transportation
network
Number
of drivers
Their origins
and
destination
Link cost
functions
Traffic assignment model
Assign traffic flows to links of the
road network in such a way that the
user equilibrium condition is satisfied
Example on a small network
Bigger example
https://drive.google.com/file/d/0BxNMF-nz4Xb3cWZsRG1IZm45Umc/edit?usp=sharing
Optimisation formulation
origin
destination
Demand: 4000
Reminder: everyone chooses his/her fastest path
Definition
User equilibrium
Fastest path
Bi-objective user equilibrium
Fast path, but expensive
Cheap path, but slow
Trade-off
Trade-off
dominated
non-dominated
Important: multiple solutions with different trade-offs
Traffic assignment: potentially infinitely many solutions
How to solve: ?
Depending on preferences some people will choose cheap, others fast path
How to model preferences?
Challenges:
still have a nice convex optimisation problem (potentially apply the same algorithms)
by adjusting the parameters of the model we want to be able to find
any bi-objective user equilibrium solution
all trade-offs are taken into account

Idea:
combine two objectives into one
Naive solution:
linear combination of objectives
only some trade-offs are present in the solution
Better solution:
non-linear combination of objectives
Small example
User equilibrium
Non-linear function
5$
5$
5$
5$
5$
5$
5$
5$
Larger instance: ART2
Conclusion
Everything is a trade-off
User equilibrium:

can solve large instances
(detailed complex models)
not flexible
Bi-objective user equilibrium:

can solve small and
medium instances
more flexible
Tolls:
Solution:
https://drive.google.com/file/d/0BxNMF-nz4Xb3Z0kwdDRnTHdDcnM/edit?usp=sharing
https://drive.google.com/file/d/0BxNMF-nz4Xb3angzd3VCbURQeG8/edit?usp=sharing
s
Full transcript