Related Publication: Vahid, Moosavi and Ludger Hovestadt. “Modeling urban traffic dynamics in coexistence with urban data streams.” Proceedings of the 2nd ACM SIGKDD International Workshop on Urban Computing. ACM, 2013.

1. svm@arch.ethz.ch
SEC
Markovian Modeling of Urban Traffic Flows in Coexistence
With Urban Data Streams
Vahid Moosavi
Simulation platform, Future Cities Lab, ETHZ
Supervisor: Professor Ludger Hovestadt
Chair for Computer Aided Architectural Design, Department for Architecture, ETH Zürich
26 April 2013
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2. Multi-layer modeling and the curse of dimensionality…
2
We take different layers (dimensions) and want to
mimic the behavior.
For example in Traffic modeling:
• Shortest Path and rationality??!!
• Traffic congestions?!
• Traffic Lights?!!
• Lots of other unknown elements that we don’t
know yet and in fact manipulate.
…Curse of Dimensionality
…Complicated models, but not complex

3. 3

4. 4

5. 5
Rational (Specific )
Models
Complex (Pre-specific )
Models
Properties of the system for modeling
PossibleRelations
(typesandnumbers)
Multi-Agent
Systems
Urban Cellular
automata
Urban Dynamics
Basic Statistics
(Hypothesis Testing)
Urban Metabolism
Natural
(Deterministic)
Models
Urban Scaling
Social Physics
Fractal Models
Complexity and the Limits of Model-ability in Rational Way
It is not about more data or
more computing power, we
need an abstraction from
the concept of rational
modeling.

6. An inversion in the concept of modeling
6
X Y
X Y
Model
Reality
Analysis
Synthesis Model
Reality
Celebration of Computation
Celebration of Connectedness
Celebration of Analysis
If not then,

7. An inversion in the concept of modeling
7
X Y X Y
Celebration of Computation Celebration of Connectedness
Celebration of Analysis
If not then,
Logic or rationale
Or (descriptive
theories)
ObservationsObservations
Celebration of Computation
supports

8. An example From Language modeling…
Problems
• Sentiment Analysis
• Translation
• Communication
• …
8
Approaches for dealing
with these problems
1. Based on Grammar, Logic
and Model of the language.
(Noam Chomsky)
2. Based on data-driven
probabilistic models.
(Originally by Markov and
now in Google Translate)
… And maybe be a dialectical
approach too...
On Chomsky and the Two Cultures of Statistical Learning: http://norvig.com/chomsky.html

9. Relational Model
Classic SpaceSyntax, London
“The social logic of space,(1984)”
33,000+ taxicabs
GPS Trajectory of Taxicabs,
Beijing, 2012
Inversion in
Modeling
9
Rational Model
X Y X Y
Celebration of Computation Celebration of Connectedness

10. Video
10

11. An Experiment : Markovian Models in coexistence with data
streams (using Taxi cabs GPS trajectories)
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• Each Taxi produces a sequence of
symbols. …It is telling its own story.
• Symbols could be road names, units of
space, district names,…
• Sequence can be based on any time
resolution.
… we can construct a Markov Network
encapsulating the transitions between
states (symbols)
• Remark: The Markov network construction
can be based on a specific time period (e.g.
rush hours, weekends,…) or specific part of
the city.
Possible functions
• Simulation of traffic flow
• Stationary distribution of cars
• Road clustering
• Road Engineering and scenario planning
– Finding critical roads
– Road network sensitivity analysis
– …
– As an opposing or complementary view to
Chomsky, Linell presented interactionism:
The sense-making ability of humans is
rooted in social interaction; the mind is
interactive, dialogical, social, shared,
extended, distributed, etc.

12. Video : A sample Sequence
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13. Experiment : Markovian Models in coexistence with data
streams
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0 0.5 0.5 0 0 0 0
0.5 0 0.5 0 0 0 0
0.450.45 0 0.1 0 0 0
0 0 0.5 0 0.5 0 0
0 0 0 0.1 0 0.45 0.45
0 0 0 0 0.5 0 0.5
0 0 0 0 0.5 0.5 0
CarID,Date,Lon,Lat,Symbol
100,2008-02-02 21:22:11,116.36263,39.93097,374
100,2008-02-02 21:24:56,116.36708,39.92274,405
100,2008-02-02 21:29:57,116.34696,39.92226,403
100,2008-02-02 21:32:14,116.34557,39.91717,403
100,2008-02-02 21:34:59,116.33843,39.92169,402
100,2008-02-02 21:37:16,116.32875,39.92175,401
100,2008-02-02 21:40:01,116.31468,39.9225,400
100,2008-02-02 21:42:18,116.29511,39.92328,398
100,2008-02-02 21:45:02,116.29542,39.9306,368
…,374,405,403,403,402,401,400,398,368,…
A sample stream of the
data
A row stochastic
Markov Matrix
1 2 3 4 5 6 7
1
2
3
4
5
6
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14. Some Properties of Markov Chain in Urban road network
Quantity / Markov Network Trafic Network
Perron Eigenvector (dual) Vehicular density in the city network
Mean First Passage Times Average travel times for a pair of origin/destination
Kemeny constant Average travel time for a random trip
Perron Eigenvector (primal) Congested junctions in the network
Second Eigenvector (dual) Associates nodes to traffic sub-communities
141.Crisostomi, E., Kirkland, S., Shorten, R. (2011), A Google-like model of road network dynamics and its application to regulation and control. International Journal of Control

15. Future Steps
• Time series prediction for individuals
• MCMC for multi-agent based simulation if needed : Data-Driven
Simulation no more direct theory or logic, but in principle we no
longer need simulation but just analysis on top of data-driven models.
For example, there is no need to be able mimicking the behavior of
one day of a city, with urban data streams, we can watch it. We should
go back to the history of simulation as a numerical approximation to
Analytical models, which was the celebration of computing power, but
now the issue is not about the computing power, it is about the limit
of the thing (model based on theories) which are being computed. It is
a limit of model-ability. Then, urban data streams brings a new
capability for us.
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16. • Markov Modeling of Singapore Ezlink Data
• Based on important link in the Kemeny Analysis, run again the steady state
probability without that area.
• Validation: Use power k of Markov and then compare with the result in K
steps based on empirical data
• Predicting the future states by power of Markov Chain
• Caclulating and visualizing the other network measures
• Accessibility analysis using Mean first passage time: one measure can be just
a an average and deviation
• Use SOM to compare different features such as Kemeny constant effect, First
Eig, Average Mean First Paassage time, Other features such closeness,
betweenness, other network features
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17. Results
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18. Thanks!
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19. Urban Data Streams Planning Interventions
Markov Chain (MC)
Construction
Updating MC periodically
Urban Segments
Regional Scale
Transition Time
Selected Time Period Traffic Community Detection
Real Time Traffic Flow
Road network Engineering
Expected Empirical Travel Times
Network Analytics
City
Mining and Analysis
Modeling

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