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A Synthetic Environment to Evaluate Alternative Trip Distribution Models. Xin Ye Wen Cheng Xudong Jia Civil Engineering Department California State Polytechnic University Pomona, CA. 2012 ITE Annual Meeting at Santa Barbara, CA. Alternative Trip Distribution Models. - PowerPoint PPT Presentation
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A Synthetic Environment to Evaluate Alternative Trip
Distribution Models
Xin YeWen ChengXudong Jia
Civil Engineering Department California State Polytechnic University
Pomona, CA
2012 ITE Annual Meeting at Santa Barbara, CA
Alternative Trip Distribution Models Importance of trip distribution models Gravity model (1950’)
Singly- and doubly-constraint Entropy maximization TAZ level
Destination choice model (1970’) Utility maximization Individual level
Cal Poly Pomona Civil Engineering Department
Comparisons of Gravity Model (GM) and Destination Choice Model (DCM)
Similarity: Wilson (1967): destination choice and singly-
constraint gravity models have the same mathematical formula
Then, what is the difference?
Cal Poly Pomona Civil Engineering Department
Difference between GM and DCM TAZ level vs. Individual level Can GM not differentiate market
segments? DCM still applied at TAZ level Trip-end survey for trip attraction
models Is GM a subset of DCM?
Objectives of This Study To provide a better understanding of
difference and similarity between GM and DCM
To introduce the research method of using synthetic environment
To visualize spatial aggregation errors in DCM
Cal Poly Pomona Civil Engineering Department
Research Method [1]:Limitations of Using Real Data
True trip matrices are not known Imperfect indirect measurement (average trip
length, trip length distribution, aggregated trip matrices, etc.)
Imperfect input data for TAZ/Network Survey sampling may not be perfectly random Travelers may not really maximize utility
Cal Poly Pomona Civil Engineering Department
Research Method [2]: Advantages of Synthetic Environment Perfect input data for TAZ/Network Assume travelers to maximize utility Trip matrices are known and can be
aggregated to any spatial levels Survey sampling can be perfectly random
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Synthesized City A city of square shape and its side length is 20
miles Total population is about 500,000 and Total
employees is about 250,000 The city is divided into 200×200 uniform square
cells and each cell’s side length is 0.1 miles Cell is the smallest spatial unit for allocating
trip’s OD, residents’ homes and employees’ jobs Each cell is located by the x-y coordinates of its
geometric center
Transportation Network A grid-like transportation network
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Spatial Distributions of Population and Employees Use probability density functions of mixed
bivariate normal distribution to distribute population/employees
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Spatial Distribution of Population
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X coordinate (miles)
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(mile
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Cal Poly Pomona Civil Engineering Department
Spatial Distribution of Employees
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X coordinate (miles)
Y co
ordi
nate
(mile
s)
Cal Poly Pomona Civil Engineering Department
Travel Synthesis Each person makes one trip from home cell to
another cell Calculate utilities and choose the cell with the
maximum utility as destination cell
Cal Poly Pomona Civil Engineering Department
Model Developments Aggregate cells to TAZs
200 × 200 cells aggregated 20 × 20 TAZs Side length of TAZ is 1 mile
Household travel survey 1% of population are sampled to report their
destination cell (sample size ≈ 5,000) Destination choice model
Develop the model at TAZ level Maximize the log-likelihood function
Gravity model Estimate linear regression model for trip attraction Adjust parameter for friction factors to match the trip
length distribution from the survey
Destination Choice Models
Average trip length of long-distance trip:5.02 Miles
Average trip length of short-distance trip:1.84 Miles
Gravity ModelsShort Trip Long Trip
Comparisons of Model Applications [1]: Trip Matrices
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Comparisons of Model Applications [2]: Trip Attractions
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Conclusions [1] Gravity model:
Linear regression model does not provide consistent coefficients for trip attraction variables
Conventional method to calibrate friction factors can provide consistent coefficient for travel impedance
Destination choice model: When the average trip length is much larger than the
TAZ size, coefficients and estimated trip matrices are reasonable
When the average trip length is closer to TAZ size, coefficients and estimated trip matrices are biased
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Conclusions [2] Observed trip length distribution may not be
perfectly matched in a reasonable trip distribution model at aggregate level
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Thank you for your attention!
Any questions?