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

Trip Distribution

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




Trip Distribution Models

1.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


• The Fratar formula can be written as


Example: Fratar MethodAn 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

a

b

c

4

6

10

20Given:



Solution:







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.


• The gravity model is expressed as


• 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.

Single Constrained vs. Doubly Constrained model


• For a doubly constrained gravity model, the adjusted attraction factors are computed according to the formula

Gravity Model Example


Solution:

Iteration 1 :








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


Three items are used as input to the gravity model for calibration:

1.Production-attraction trip table for each purpose

2.Travel times for all zone pairs, including intrazonal times

3. 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.


The Calibration Process1.Use the gravity model to distribute trips based on initial inputs.2.Total trip attractions at all zones j, as calculated by the model, are compared to those obtained from the input “observed” trip table.3.If this comparison shows significant differences, the attraction Aj is adjusted for each zone, where a difference is observed.4.The model is rerun until the calculated and observed attractions are reasonably balanced.5.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.


Figure 11-7 shows the results of four iterations comparing travel-time frequency.Transportation Engineering (CIVTREN)

notes of AM Fillone, DLSU-Manila


• 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.

Figure 11-9 Smoothed Adjusted Factors, Calibration 2


• 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.


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


SUMMARY OUTPUT

Regression StatisticsMultiple R 0.995749R Square 0.991516Adjusted R Square 0.988688Standard Error 0.02602

Observations 5

ANOVA

df SS MS F Significance F

Regression 1 0.237369 0.237369 350.5919 0.000333Residual 3 0.002031 0.000677Total 4 0.2394

CoefficientsStandard

Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -2.73218 0.05194 -52.6023 1.51E-05 -2.89748 -2.56689 -2.89748 -2.56689lnw -0.461 0.024621 -18.7241 0.000333 -0.53935 -0.38265 -0.53935 -0.38265


Since, ln A = -2.73218, A = e^(-2.73218) A = .065and c = - (-.461) c = 0.461

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