Travel Demand Forecasting:Trip Distribution

CE331 Transportation Engineering

Land Use and Socio-economic Projections

Trip Generation

Trip Distribution

Modal Split

Traffic Assignment

Transportation System Specifications

Direct User Impacts

Overall Procedure

Trip Distribution

Where to go? Choice may vary with trip purpose

Input Trips generated from and attracted to each

zone (step 1 output) Interzonal transportation cost (travel time,

distance, out-of-pocket cost, …) Output – trip interchange between zones

Presented as Origin-Destination (OD) matrix

Process

Allocate trips originating from each zone to all possible destination zonesAssume destination zones are

competing with each other in attracting trips produced by zone i

Types of Models

Gravity ModelTrips are attracted to a zone as gravity

“attracts” objects Utility Maximization

Assumes that a traveler makes the decision that maximizes his/her utility

Calculating TAZ “Attractiveness”

Gravity Model

K-Factors

• K-factors account for socioeconomic linkages not accounted for by the gravity model

• Common application is for blue-collar workers living near white collar jobs (can you think of another way to do it?)

• K-factors are i-j TAZ specific (but could use a lookup table – how?)

• If i-j pair has too many trips, use K-factor less than 1.0 (& visa-versa)

• Once calibrated, keep constant? for forecast (any problems here???)

• Use dumb K-factors sparingly• Can you design a “smart” k factor? (TTYP)

Gravity Model Example Problem

Input data

How do models compute this? See next pages…

Does this table need to be

symmetrical? Is it usually?

Convert Travel Times into Friction Factors

Yes, but how

did we get

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Find the shortest path from node to all other nodes (from Garber and Hoel)1

Yellow numbers represent link travel times in minutes3

Here’s how

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STEP 11

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STEP 21

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STEP 31

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STEP 41

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Eliminate

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STEP 51

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STEP 61

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7Eliminate

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STEP 71

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Eliminate8 >= 7

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STEP 81

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STEP 91

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STEP 101

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STEP 111

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STEP 121

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910

Eliminate 10 > 9

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STEP 131

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STEP 141

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FINAL1

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Calculate the Attractiveness of Each Zone

Calculate the Relative Attractiveness of Each

Zone

Make sense

?

Distribute Productions to TAZs

First Iteration Distribution

Advanced Concepts – not required for CE331

Comparing and Adjusting Zonal Attractions

• Balanced attractions from trip generation = 76

• The gravity model estimated more attractions to TAZ 3 than estimated by the trip generation model.

• What can we do? (see homework)

Advanced Concepts – not required for CE331

Forecasting for Future Year Assignments

• After successful base year calibration and validation (review … how?)

• Use forecast land use, socioeconomic data, system changes

• Forecasted production and attractions, and future year travel time skims

• Apply gravity model to forecast year• Friction factors remain constant over

time (what to you think?)

In-class exerciseAdvanced Concepts – not required for CE331

A Simple Gravity Model

tij = Pi Tj/(dijn Aj)

Where

Pi – trips generated from zone i;

dij – distance or time;

Tj – trips attracted to zone j;

Aj – balancing factor;

Aj =Σ (Pi /dijn)

n – parameter.

Example – 1

A new theater is expected to attract 700 trips from 2 zones with daily trip productions of 1500 and 3000. The distances to the new theater are 2 and 3 miles, respectively. The factor n is approximately 2. How many trips from each zone will be attracted to the theatre?

Example (cont’d)

A1 = Σ (Pi /dijn) = (1500/22)+ (3000/32)=

708.3

t11=P1T1/(d112A1)=1500(700)/[22(708.3)]=

370.6

t21=P2T1/(d212A1)=3000(700)/

[32(708.3)]=329.4

Utility Maximization

Consider travelers’ choice in trip-making decision

Use utility function (U) to reflect the attractiveness of an alternative (in this case, destination)U = b0 + b1*z1 + b2*z2 + … + bn*zn

• b0, b1, …: parameters

• z1, z2, …: attributes of the alternative

Utility Maximization:Logit Model

j

U

U

j

i

e

ei)Pr(

Pr(i): probability of choosing alternative i over all other alternatives;

Ui: utility value of alternative (destination) i.