Machine Learning and Optimization For Traffic and Emergency ...

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)

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

S-CITI related projects
Optimization of control of distributed systems with discrete and continuous variables: Traffic light control

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

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

Road traffic data
We use PennDOT sensor network 155 sensors for volume and speed every 5 minutes

Models of traffic data
Local interactions
Markov random field
Effects are circular
Solution:
Break the cycles

The all-independent assumption
Unre a listic !

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

Latent variable model
A combination of latent factors represent interactions

Four projects

Optimizations in unreliable transportation networks
Unreliable network – connections (or nodes) may fail
E.g. traffic congestion, power line failure

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

many connections may go down together

parts of the network may become disconnected

Optimizations of resources in unreliable transportation networks
Example: emergency system. Emergency vehicles use the network system to get from one location to the other

One failure here won’t prevent us from reaching the target, though the path taken can be longer

Two failures can get the two nodes disconnected

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

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

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

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

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)

Four projects

Incident detection on dynamic data incident incident no incident

Incident detection algorithms
Incidents detected indirectly through caused congestion
State of the art: California 2 algorithm
If OCC(up) – OCC(down) > T1, next step
If [OCC(up) – OCC(down)]/ OCC(up) > T2, next step
If [OCC(up) – OCC(down)]/ OCC(down) > 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

Incident detection algorithms
Machine Learning approach (ICML 2006)
Use a set of simple feature detectors and learn the classifier from the data
Improved performance
California 2 SVM based model

Four projects
Optimization of control of distributed systems with discrete and continuous variables: Traffic light control

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

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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