1. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Trip Distribution
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

2. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

3. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

4. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Trip Distribution Models
GrowthFactor/Fratar Method
A simple method to distribute trips in a study area.
Assumptions of the model
a. the distribution of future trips from a given origin zone is proportional to the present trip distribution
b. this future distribution is modified by the growth factor of the zone to which these trips are attached
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

5. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
The Fratar formula can be written as
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

6. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Example: Fratar Method
An origin zone i with 20 base-year trips going to zones a, b, and c numbering 4, 6, and 10, respectively, has growth rates of 2, 3, 4, and 5 for i, a, b, and c, respectively. Determine the future trips from i to a, b, and c in the future year. i 20
Given: 4 10 a 6 c b
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

7. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

8. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

9. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Solution:
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

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14. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
The Gravity Model
The most widely used trip distribution model
The model states that the number of trips between two zones is directly proportional to the number of trip attractions generated by the zone of destination and inversely proportional to a function of time of travel between the two zones.
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

15. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
The gravity model is expressed as
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

16. Single Constrained vs. Doubly Constrained model
Singly Constrained model – when information is available about the expected growth trips originating in each zone only or the other way, trips attracted to each zone only
Doubly Constrained model – when information is available on the future number of trips originating and terminating in each zone.
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

17. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
For a doubly constrained gravity model, the adjusted attraction factors are computed according to the formula
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

18. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Gravity Model Example
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19. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Solution:
Iteration 1 :
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25. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

26. Calibrating a Gravity Model
Calibrating of a gravity model is accomplished by developing friction factors and developing socioeconomic adjustment factors
Friction factors reflect the effect travel time of impedance has on trip making
A trial-and-error adjustment process is generally adopted
One other way is to use the factors from a past study in a similar urban area
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

27. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Three items are used as input to the gravity model for calibration:
Production-attraction trip table for each purpose
Travel times for all zone pairs, including intrazonal times
Initial friction factors for each increment of travel time
The calibration process involves adjusting the friction factor parameter until the planner is satisfied that the model adequately reproduces the trip distribution as represented by the input trip table – from the survey data such as the trip-time frequency distribution and the average trip time.
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

28. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
The Calibration Process
Use the gravity model to distribute trips based on initial inputs.
Total trip attractions at all zones j, as calculated by the model, are compared to those obtained from the input “observed” trip table.
If this comparison shows significant differences, the attraction Aj is adjusted for each zone, where a difference is observed.
The model is rerun until the calculated and observed attractions are reasonably balanced.
The model’s trip table and the input travel time table can be used for two comparisons: the trip-time frequency distribution and the average trip time. If there are significant differences, the process begins again.
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

29. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Figure 11-7 shows the results of four iterations comparing travel-time frequency.

30. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

31. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Figure 11-9 Smoothed Adjusted Factors, Calibration 2
An example of smoothed values of F factors in Figure 11-9.
In general, values of F decreases as travel time increases, and may take the form F varies as t-1, t-2, or e-t.
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

32. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
A more general term used for representing travel time (or a measure of separation between zones) is impedance, and the relationship between a set of impedance (W) and friction factors (F) can be written as:
Example:
A gravity model was calibrated with the following results:
Impedance (travel time, mins), W 4 6 8 11 15
Friction factors, F
.035
.029
.025
.021
.019
Using the f as the dependent variable, calculate parameter A and c of the equation.
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

33. Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila
Solution:
The equation can be written as
ln F = ln A – c ln W
ln W
1.39
1.79
2.08
2.40
2.71
ln F
-3.35
-3.54
-3.69
-3.86
-3.96
These figures yield the following values of A = .07 and c = .48.
Hence, F = 0.07/W0.48
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila

34. Since, ln A = -2.73218, A = e^(-2.73218) A = .065 and c = - (-.461)
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 5
ANOVA df SS MS F
Significance F
Regression 1
Residual 3
Total 4
0.2394
Coefficients
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
1.51E-05
lnw
-0.461
Since, ln A = ,
A = e^( )
A = .065
and
c = - (-.461)
c = 0.461
Transportation Engineering (CIVTREN) notes of AM Fillone, DLSU-Manila