CE 326 F2013 Lecture 4-5 Trip Generation

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)