ce 326 f2013 lecture 4-5 trip generation
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CE 326: Transportation PlanningTRIP GENERATION
Travel Demand
Most transportation trips are derived demand Trips are a function of the activities that they serve
Some recreational transportation trips may not be derived demand
Demand can be induced when changes to infrastructure or services reduce the cost of transportation
The Four Step Model
Trip Generation Determine the number of person or vehicle trips to and from different land uses
in an analysis zone
Trip Distribution Predict origin-destination flows from zone to zone
Mode Choice Predict the share of users who will choose to travel using each available mode
Trip Assignment Allocate trips to specific routes
Modeling Challenges
Future conditions predicted from historic data Land Use
Transportation network
Traffic
Steps are iterative
http://www.mwcog.org/transportation/images/4step.gif
Trip Generation
• FOUR STEP MODEL BASICS
• ESTIMATING PRODUCTIONS• Household Surveys
• Minimum Sample Size
• Cross Classification
• Linear Regression
• ESTIMATING ATTRACTIONS• Trip Rate Analysis
• CONVERTING PRODUCTIONS AND ATTRACTIONS TO ORIGINS AND DESTINATIONS
Trip Ends: Productions and Attractions
A production is a trip-end connected with a residential land use in a zone Estimated as a function of socieconomic characteristics of a zone or household
An attraction is a trip-end connected to a non-residential land use in a zone Estimated as a function of the availability and intensity of non-residential opportunities in
a zone
Household Survey Trip Rates
Demographic Data
Productions
Workplace/Special Generator Surveys
Trip Rates
Land Use Data
Attractions
Estimating Productions
• HOUSEHOLD SURVEYS
• MINIMUM SAMPLE SIZE
• CROSS CLASSIFICATION
• LINEAR REGRESSION
Household Surveys
Household surveys results are used to estimate trip rates as a function of household characteristics National Household Travel Survey
Regional Household Surveys
Household Surveys Performed about every 10 years
Trips Frequencies
Distances
Household characteristics Demographics
Vehicle Ownership
Normal Distribution
Normal distribution is symmetric about the mean
For a two-tailed distribution: 1 std. dev. : 68.3% of values
1.96 std. dev. : 95.0% of values
3 std. dev. : 99.7% of values
Z is the number of standard deviations corresponding to a specific confidence level
Estimated vs. True Value
The values calculated using sample data provide only an estimate of the true mean and standard deviation
Central Limit Theorem
For a large sample size, has approximately a normal distribution regardless of the shape of the distribution
Standard Error of the Mean
The std. dev. of the sample mean (or standard error) is given by:
where N is the population size, n is the sample size, and σ2 is the population variance
For a single sample, the best estimate of the population variance is the sample variance
For large populations and small sample sizes, (N-n)/N approaches one, so:
Estimating Sample Size
To estimate the required sample size for an infinite population, we rearrange the equation to:
Then, if necessary, we correct for finite population size:
′
′
1 ′
Sample Size Determination
Estimating sample size for a population parameter is a function of 3 variables Variability
Desired degree of precision
Population size
Sampling error can be reduced by increasing sample size
However, budget constraints may limit sample size
Must assume a best estimate sample variance (standard deviation)
*Except in surveys of very small populations, it is the number of observations in the sample, rather than the sample size as a percentage of the population, which determines the precision of the sample estimates.*
Confidence Level and Confidence Interval
In order to determine the statistical validity of an estimate, we must first define the desired precision level The precision level is the degree of confidence(percent p) that the sampling
error of a produced estimate will fall within a desired range
The confidence level is often defined in terms of the level of significance,
α= (100-p)
We must also define the acceptable range of error of an estimate (x-μ) Absolute: a fixed number
Relative: defined as a percentage of the true value
Standard Normal Distribution
In a standard normal distribution,μ= 0
σ= 1
The sample mean is distributed normally with parameters x and standard error( ).
We can convert this variable to a standard normal variable, z, using the formula:
Replacing x and σ in the z equation, we get:
Data Year: 2009, New York State, MSA > 3 MillionHousehold
Size# Household
VehiclesHouseholds (in
thousands)Person Trips (in
millions)1 0 840.24 985.821 1 484.38 799.211 2 46.14 86.541 3 3.14 4.561 4+ 1.04 1.762 0 469.87 1258.042 1 412.02 1133.132 2 394.28 1205.862 3 58.85 165.812 4+ 24.11 54.223 0 230.85 922.583 1 245.84 1151.813 2 229.96 1028.993 3 140.73 702.473 4+ 24.95 137.284 0 124.35 596.944 1 184.99 1128.84 2 208.61 1317.74 3 83.71 576.724 4+ 53.12 340.375 0 128.59 642.825 1 108.78 891.475 2 98.78 777.465 3 40.91 297.475 4+ 22.91 165.24
National Household Travel Survey Data
Cross-Classification
Trip rates are derived from survey data and “cross-classified” with one or more individual variables to estimate trip rates
Number of categories increases exponentially with the number of variables included
Cross-Classification Example
Linear Regression
Used to estimate trips as a linear function of household, individual, or land use variables
For one independent variable (Y) and one dependent variable (X)
Linear Regression Example
Method of Least Squares
We want to determine the values of a and b that minimize S
At the minimum, the partial derivatives of S with respect to a and b will be equal to zero
Setting the derivatives equal to zero and solving the equations simultaneously yields formulas for a and b
Sum of Squared Residuals
The residual is an error term that accounts for the difference between an observed value and its model estimate
The sum of squared residuals is a measure used in statistics to quantify the fit of a model to an observed dataset
R2
R2 is a measure of how well a model fits the observed data
R2 represents the proportion of variability in a dataset that is accounted for by the model
R2 values range from 0 (no predictive power) to 1 (perfect model)
1
where
Multivariate Linear Regression
Linear regression can also be used to estimate Y as a linear function of multiple variables
Solving for multiple variables manually is extremely tedious Software packages, including Excel, can be used to estimate parameter
values
Estimating Attractions
• TRIP RATE ANALYSIS
Attraction Trip Rate Analysis
Trips estimated as a function of land use characteristics Usually estimated from traffic counts, workplace/special generator surveys
Example
Production-Attraction Matrix vs. Origin-Destination Matrix
• PA VS. OD MATRIX
• CONVERTING FROM PA TO OD
P-A vs. O-D Matrix
Production-Attraction Matrix Used in Trip Distribution stage as input to Gravity or Growth Factor Model
Productiveness and attractiveness of zones will change as a function of demographicsand land use
Origin-Destination Matrix Used in Traffic Assignment stage to determine sources (location where trips created)
and sinks (location where trips are consumed) for trips
Production-Attraction Matrix
For home-based trips, does not indicate directionality
Origin-Destination Matrix
Indicates directionality for all trips
Home Based vs. Non-Home Based Trips
Home-based-trips either begin or end at a residence Will have one production end and one attraction end
Home end is the production end regardless of directionality
Non-home-based trips neither begin nor end at a residence In reality, both ends are attractions
In order to develop a production-attraction matrix, by definition the origin end is defined as the production end
P-A vs. O-D Example (1)
P-A vs. O-D Example (2)
P-A vs. O-D Example (2)