Fundamentals of Transportation/Trip Generation/Solution

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TProblem
Problem:

Planners have estimated the following models for the AM Peak Hour


T_i = 1.5*H_i
\,\!


T_j = (1.5*E_{off,j}) + (1*E_{oth,j}) + (0.5*E_{ret,j}) 
\,\!

Where:

T_i\,\! = Person Trips Originating in Zone i\,\!

T_j\,\! = Person Trips Destined for Zone j\,\!

H_i\,\! = Number of Households in Zone i\,\!

You are also given the following data

Data
Variable Dakotopolis New Fargo
H 10000 15000
E_{off} 8000 10000
E_{oth} 3000 5000
E_{ret} 2000 1500

A. What are the number of person trips originating in and destined for each city?

B. Normalize the number of person trips so that the number of person trip origins = the number of person trip destinations. Assume the model for person trip origins is more accurate.

Example
Solution:

A. What are the number of person trips originating in and destined for each city?

Solution to Trip Generation Problem Part A
Households (H_i) Office Employees (E_{off}) Other Employees (E_{oth}) Retail Employees (E_{ret}) Origins T_i = 1.5*H_i Destinations T_j = (1.5*E_{off,j}) + (1*E_{oth,j}) + (0.5*E_{ret,j})
Dakotopolis 10000 8000 3000 2000 15000 16000
New Fargo 15000 10000 5000 1500 22500 20750
Total 25000 18000 8000 3000 37500 36750

B. Normalize the number of person trips so that the number of person trip origins = the number of person trip destinations. Assume the model for person trip origins is more accurate.

Use: 
\quad T_j^'  = T_j \frac{{\sum\limits_{i = 1}^I {T_i } }}{{\sum\limits_{j = 1}^J {T_j } }} =  > T_j \frac{{37500}}{{36750}} = T_j *1.0204
\,\!

Solution to Trip Generation Problem Part B
Origins (T_i) Destinations (T_j) Adjustment Factor Normalized Destinations (T_j') Rounded
Dakotopolis 15000 16000 1.0204 16326.53 16327
New Fargo 22500 20750 1.0204 21173.47 21173
Total 37500 36750 1.0204 37500 37500