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

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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?

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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

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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

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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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Spatial Distribution of Employees

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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

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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?