markovian modeling of urban traffic flows in coexistence with urban data streams
TRANSCRIPT
Markovian Modeling of Urban Traffic Flows in Coexistence With Urban Data Streams
Vahid MoosaviSimulation platform, Future Cities Lab, ETHZ
Supervisor: Professor Ludger HovestadtChair for Computer Aided Architectural Design, Department for Architecture, ETH Zürich
26 April 2013
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Multi-layer modeling and the curse of dimensionality…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
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Rational (Specific ) Models
Complex (Pre-specific ) Models
Properties of the system for modeling
Possible Relations (types and num
bers)
Multi-Agent Systems
Urban Cellular automata
Urban Dynamics
Basic Statistics(Hypothesis Testing)
Urban Metabolism
Natural (Deterministic)
Models
Urban ScalingSocial 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.
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An inversion in the concept of modeling
X YX Y
Model
Reality
Analysis
Synthesis Model
Reality
Celebration of ComputationCelebration of Connectedness
Celebration of AnalysisIf not then,
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An inversion in the concept of modeling
X Y X Y
Celebration of Computation Celebration of Connectedness
Celebration of AnalysisIf not then,
Logic or rationale Or (descriptive
theories)
ObservationsObservations
Celebration of Computationsupports
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An example From Language modeling…
Problems• Sentiment Analysis• Translation• Communication• …
Approaches for dealing with these problems1. 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
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Relational Model
Classic SpaceSyntax, London “The social logic of space,(1984)”
33,000+ taxicabs
GPS Trajectory of Taxicabs, Beijing, 2012
Inversion in Modeling
Rational Model
X Y X Y
Celebration of Computation Celebration of Connectedness
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Video
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An Experiment : Markovian Models in coexistence with data streams (using Taxi cabs GPS trajectories)
• 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.
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Video : A sample Sequence
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Experiment : Markovian Models in coexistence with data streams
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 21:22:11,116.36263,39.93097,374100,2008-02-02 21:24:56,116.36708,39.92274,405100,2008-02-02 21:29:57,116.34696,39.92226,403100,2008-02-02 21:32:14,116.34557,39.91717,403100,2008-02-02 21:34:59,116.33843,39.92169,402100,2008-02-02 21:37:16,116.32875,39.92175,401100,2008-02-02 21:40:01,116.31468,39.9225,400100,2008-02-02 21:42:18,116.29511,39.92328,398100,2008-02-02 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
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Some Properties of Markov Chain in Urban road networkQuantity / 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
1.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
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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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• 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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Results
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Thanks!
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 AnalysisModeling
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