Machine Learning and Optimization For Traffic and Emergency Resource Management.

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Machine Learning and Optimization For Traffic and
Emergency Resource Management.

• Milos Hauskrecht
• Department of Computer Science
• University of Pittsburgh

Students Branislav Kveton, Tomas Singliar UPitt
collaborators Louise Comfort, JS Lin External
Eli Upfal (Brown), Carlos Guestrin (CMU)
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S-CITI related projects

• Modeling multivariate distributions of traffic
  variables
• Optimization of (emergency) resources over
  unreliable transportation network
• Traffic monitoring and traffic incident detection
• Optimization of distributed systems with discrete
  and continuous variables Traffic light control

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S-CITI related projects

• Modeling multivariate distributions of traffic
  variables
• Optimization of (emergency) resources over
  unreliable transportation network
• Traffic monitoring and traffic incident detection
• Optimization of control of distributed systems
  with discrete and continuous variables Traffic
  light control

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Traffic network

• Traffic network systems are
• stochastic (things happen at random)
• distributed (at many places concurrently)
• Modeling and computational challenges
• Very complex structure
• Involved interactions
• High dimensionality

PITTSBURGH
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Challenges

• Modeling the behavior of a large stochastic
  system
• Represent relations between traffic variables
• Inference (Answer queries about model)
• Estimate congestion in unobserved area using
  limited information
• Useful for a variety of optimization tasks
• Learning (Discovering the model automatically)
• Interaction patterns not known
• Expert knowledge difficult to elicit
• Use Data

Our solutions probabilistic graphical models,
statistical Machine learning methods
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Road traffic data

• We use PennDOT sensor network155 sensors for
  volume and speed every 5 minutes

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Models of traffic data

• Local interactions
• Markov random field
• Effects are circular
• Solution
• Break the cycles

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The all-independent assumption

• Unrealistic!

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Mixture of trees

• A tree structure retains many dependencies but
  still loses some
• Have many trees to represent interactions

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Latent variable model

• A combination of latent factors represent
  interactions

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Four projects

• Modeling multivariate distributions of traffic
  variables
• Optimization of (emergency) resources over
  unreliable transportation network
• Traffic monitoring and traffic incident detection
• Optimization of distributed systems with discrete
  and continuous variables Traffic light control

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Optimizations in unreliable transportation
networks

• Unreliable network connections (or nodes) may
  fail
• E.g. traffic congestion, power line failure

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Optimizations in unreliable transportation
networks

• Unreliable network connections (nodes) may fail
• more than one connection may go down to

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Optimizations in unreliable transportation
networks

• Unreliable network connections (nodes) may fail
• many connections may go down together

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Optimizations in unreliable transportation
networks

• Unreliable network connections (nodes) may fail
• parts of the network may become disconnected

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Optimizations of resources in unreliable
transportation networks

• Example emergency system. Emergency vehicles
  use the network system to get from one location
  to the other

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Optimizations of resources in unreliable
transportation networks

• One failure here wont prevent us from reaching
  the target, though the path taken can be longer

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Optimizations of resources in unreliable
transportation networks

• Two failures can get the two nodes disconnected

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Optimizations of resources in unreliable
transportation networks

• Emergencies can occur at different locations and
  they can come with different priorities

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Optimizations of resources in unreliable
transportation networks

• considering all possible emergencies, it may be
  better to change the initial location of the
  vehicle to get a better coverage

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Optimizations of resources in unreliable
transportation networks

• If emergencies are concurrent and/or some
  connections are very unreliable it may be better
  to use two vehicles

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Optimizations of resources in unreliable
transportation networks

• where to place the vehicles and how many of them
  to achieve the coverage with the best expected
  cost-benefit tradeoff

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Solving the problem

• A two stage stochastic program with recourse
• Problem stages
• Find optimal allocations of resources (em.
  vehicles)
• Match (repeatedly) emergency demands with
  allocated vehicles after failures occur
• Curse of dimensionality many possible failure
  configurations in the second stage
• Our solution Stochastic (MC) approximations
• (UAI-2001, UAI-2003)
• Current
• adapt to continuous random quantities (congestion
  rates,traffic flows and their relations)

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Four projects

• Modeling multivariate distributions of traffic
  variables
• Optimization of (emergency) resources over
  unreliable transportation network
• Traffic monitoring and traffic incident detection
• Optimization of distributed systems with discrete
  and continuous variables Traffic light control

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Incident detection on dynamic data
incident
no incident
incident
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Incident detection algorithms

• Incidents detected indirectly through caused
  congestion
• State of the art California 2 algorithm
• If OCC(up) OCC(down) gt T1, next step
• If OCC(up) OCC(down)/ OCC(up) gt T2, next step
• If OCC(up) OCC(down)/ OCC(down) gt T3,
  possible accident
• If previous condition persists for another time
  step, sound alarm
• Hand-calibrated for the specific section of the
  road

Occupancy spikes
Occupancy falls
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Incident detection algorithms

• Machine Learning approach (ICML 2006)
• Use a set of simple feature detectors and learn
  the classifier from the data
• Improved performance

SVM based model
California 2
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Four projects

• Modeling multivariate distributions of traffic
  variables
• Optimization of (emergency) resources over
  unreliable transportation network
• Traffic monitoring and traffic incident detection
• Optimization of control of distributed systems
  with discrete and continuous variables Traffic
  light control

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Dynamic traffic management

• A set of intersections
• A set of connection (roads) in between
  intersections
• Traffic lights regulating the traffic flow on
  roads
• Traffic lights are controlled independently
• Objective coordinate traffic lights to minimize
  congestions and maximize the throughput

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Solutions

• Problems
• how to model the dynamic behavior of the system
• how to optimize the plans
• Our solutions (NIPS 03,ICAPS 04, UAI 04, IJCAI
  05, ICAPS 06, AAAI 06)
• Model Factored hybrid Markov decision processes
  
• continuous and discrete variables
• Optimization
• Hybrid Approximate Linear Programming
• optimizations over 30 dimensional continuous
  state spaces and 25 dimensional action spaces
• Goals hundreds of state and action variables

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Thank you

• Questions