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
these?
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
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
…
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 11
2
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 21
2
4
5
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 31
2
4
5
4
4
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 41
2
4
4
Eliminate
5 >= 4
4
5
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 51
2
4
4
4 10
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 61
2
4
4
4 10
6
7Eliminate
7 >= 6
7
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 71
2
4
4
4 10
6
Eliminate8 >= 7
8
7
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 81
2
4
4
4 10
7
6
10
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 91
2
4
4
4 10
7
6
10
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 101
2
4
4
4 10
7
6
10Eliminate
10 >= 7
10
Eliminate
10 >= 10
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 111
2
4
4
4 10
7
6
10
10
8
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 121
2
4
4
4 10
7
6
10
8
9
910
Eliminate 10 > 9
Eliminate
10 >= 9
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 131
2
4
4
4
7
6
10
8
9
9
12 12
Eliminate
12 >= 10
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
631
232
334
444
132 1
132 1
242 1
STEP 141
2
4
4
4
7
6
10
8
9
9
12 10
Eliminate
12 >= 10
7
8
6
1 2 3 4
5 6 7 8
9 10 11 12
14 15 1613
FINAL1
2
4
4
4
7
6
10
8
9
9
10
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.