synthesizing agents and relationships for land use / transportation modelling
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Synthesizing Agents and Relationships for Land Use / Transportation Modelling. Lecture Outline. Introduction Previous Work Data New Methods Results. Introduction. How would land use, transportation patterns and emissions react to... High congestion charge? Greenbelt policy? - PowerPoint PPT PresentationTRANSCRIPT
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David PritchardCivil Engineering, University of Toronto
September 12, 2008
Synthesizing Agents and Relationships for Land Use / Transportation
Modelling
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Lecture Outline
● Introduction● Previous Work● Data● New Methods● Results
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Introduction
● How would land use, transportation patterns and emissions react to...
● High congestion charge?● Greenbelt policy?● “Do nothing” while population grows ● Major transportation projects
● Major extrapolations from current behaviour● Too hard to predict conventionally
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Introduction
Traditional 4-stage
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Introduction
Integrated Land Use/Transportation Environment (ILUTE) model
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Introduction
● We can’t build such a complicated model using conventional methods
● Instead, preferred approach is microsimulation model
● What is microsimulation?
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Introduction
Conventional Model
Simulation Model
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Introduction
● Microsimulation = Simulation + Agents● Models the state of agents● Combined behaviour of agents yields
system state● 1. Begin with initial population in start year● 2. Update population, year by year
● age persons, change family structures● change jobs, move homes● use this to predict annual travel patterns
● 3. Obtain travel patterns in forecast year
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Introduction
● Need an initial population in the start year● List of agents and their attributes - e.g.,
● Number of persons, and their ages● Number of vehicles● Type of dwelling● etc.
● But - complete list is unknown● “Population Synthesis” used instead
● Use known data to create initial agents● Result has known statistical properties● Best estimate from limited data
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Introduction
My results:Improved method for population synthesis
Allows more attributes for each agentNew method for relationship synthesis
Allows correct set of agents and correct set of relationships
Created a synthetic population for ILUTE Persons, families, households and dwellings Complete 1986 population for GTHA
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Previous Work
Two representations of set of agents List of agents and their attributes (as categories) Contingency table
One cell for each combination of attributes Cell contains count of number of agents
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Previous Work
Data Limitations Patchwork of partial data Mostly, we have one-way margins Break down of a single attribute into a few
categoriesExample: look at how we can use one-way margins
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Previous Work
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Previous Work
Iterative Proportional Fitting
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Previous Work
Iterative Proportional Fitting
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Previous Work
Iterative Proportional Fitting e.g., “Biproportional Updating” of O/D tables
Exactly satisfies target marginsAlso minimizes discrimination information relative to source population
Information theory: maximum entropyResulting PDF satisfies the constraints without assuming any information we do not possess
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Previous Work
Many options for margins in 3D
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Previous Work
Beckman, Baggerley & McKay (1996)State-of-the-art application of IPF for census Geography attribute gets special treatment
Due to nature of data in PUMS and census tablesTwo approaches: zone-by-zone, or all zones at once
Treats final table as a PMF Monte Carlo draws used to integerize Hurts fit to target margins
Limited number of attributes
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Previous Work
Williamson, Birkin and Rees (1998)Not IPF: “Combinatorial Optimisation”List-based, instead of tablesPros:
good fit to target margins may handle more attributes
Cons: no guarantees about relationship with source
sample not entropy maximizing slow
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Data
Summary Tables Usually one attribute, by zone (2D margin) Contingency table Large sample: 20% or 100% Sometimes 2-3 attributes by zone Used as Target Margins
Public Use Microdata Sample (PUMS) List; almost all attributes, except zones Small sample (1-2%) Canada: defined for each large Census
Metropolitan Area (CMA) Used as Source Sample
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Data
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Data
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Data
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Data
Canadian Census includes three PUMS Persons Census families Households & Dwellings
Also summary tables related to each
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New Methods: Sparsity
Beckman et al.’s approach doesn’t work well with many attributes
Computation becomes hard Huge memory requirement Slow
Thirteen attributes on family agent: Beckman Zone-by-Zone needs 1.4 GB memory Beckman Multizone needs 1,036 GB memory
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New Methods: Sparsity
Number of cells in multiway table grows exponentially with number of attributes (dimensions)
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New Methods: Sparsity
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New Methods: Sparsity
Large number of binsMost bins are zeroNumber of bins is larger than sample!
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New Methods: Sparsity
Is it meaningful to use many attributes? Tentatively, yes Not a meaningful 13-way distribution But, a link between many statistically valid low-
order distributions (e.g., 3-way) If acceptable, can we do better than standard IPF?
Yes - use a sparse data structure instead of a complete array to represent table
Store only non-zero cells in table
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New Methods: Sparsity
Same representation as Williamson’s “Combinatorial Optimisation”
But, uses IPF algorithmMaximum entropy guarantee; fastCan implement either zone-by-zone or multizone IPF using sparse data structure
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New Methods: Relationships
Land use/transportation models have more types of agents Agents: Persons, families,
households, business establishments
Objects: Vehicles, dwellings
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New Methods: Relationships
Need to synthesize correct relationshipsExamples:
Which persons are married? Opposite sex, similar ages - usually
Which household owns/rents a given dwelling? Number of rooms and number of persons should
be correlatedEarlier methods could guarantee correct PDF for one agent type, but not all simultaneously
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New Methods: Relationships
Family PUMS contains information about persons in family husband/wife ages; child ages
Can synthesize “family” agent Include some “person” attributes in family
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New Methods: Relationships
Then, conditionally synthesize persons on family attributes IPF result is a joint probability mass function
P(AGE, EDU, INCOME, OCCUP, SEX, ...)
Can convert to a conditional PMF
P(EDU, INCOME, OCCUP, ... | AGE, SEX)
Synthesize, repeating for husband, wife, children
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New Methods: Relationships
Guarantees good fit for both agent types Correct Family PDF Correct Person PDF
Simple, data-driven No rules No special data sources, models
Provided that attributes can be aligned between agents
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Results
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Results
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Results
Programmed in R A statistical programming platform Dynamic language, fast prototyping Good support for categorical data, contingency
tablesToronto CMA: 1.1 million households, 1.0 million families, 3.3 million persons
Run time: 2 hours, 7 minutes on older 1.5GHz computer
Repeated for Hamilton and Oshawa CMAs
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Results
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Results
Experiment Is there value in using really rich input data? Or does PUMS + 1D tables give enough?
Calculated fit against all available dataSRMSE and G2 information theoretic statistics
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Results
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Results
Improvement of result with additional data evident However, no statistical tests possible
Monte Carlo stage causes some errorMy conditional synthesis introduces small amount of additional error
Little difference between zone-by-zone and multizone methods
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Questions?