03 - Trip generation modeling - TDBM

https://www.youtube.com/watch?v=7BenAd8-5_c&nohtml5=False

The first step in Trip Generation modeling is gathering a zoning system: that is a group of TAZ that cover all the area of interest.

Trip generation is the first step in the modeling stage of the classic 4 stage framework.

In terms of an O/D matrix like the following, in this step we try to model the marginal totals: all $P_{i}$ and $A_{j}$ , while the rest of the matrix entries ( $d_{i j}$ ) stay unknown for now.

\begin{matrix} d_{11} & d_{12} & \dots & d_{1 n} & P_{1} \\ d_{21} & d_{22} & \dots & d_{2 n} & P_{2} \\ ⋮ & ⋮ & d_{i j} & ⋮ & ⋮ \\ d_{n 1} & d_{n 2} & \dots & d_{n n} & P_{n} \\ A_{1} & A_{2} & \dots & A_{n} \end{matrix}

where:

$d_{i j} :$ number of trips from TAZ $i$ to TAZ $j$
$P_{i} :$ tot number of trips generated by TAZ $i$
- It's the sum of the colums
$A_{i} :$ tot number of trips attracted by TAZ $j$
- It's the sum of the rows
$n :$ tot number of TAZs

Growth factor

One of the main objective in travel demand modeling is being able to predict future scenarios starting from a current one. In this section, we assume trip generation/attraction per zone is known for the present, and we want to obtain a prediction of it in the future given a change in some variables (population, income, motorization...)

Growth factor - Fratar

growth factor - fratar

One #Growth factor was defined by Fratar in 1954 as:
$F_{i} = \frac{P_{i}^{f} I_{i}^{f} M_{i}^{f}}{P_{i}^{c} I_{i}^{c} M_{i}^{c}}$
where:

$i :$ is the index that identifies the TAZ
$F :$ is the growth factor
$P$ : population
$I :$ income
$M :$ Motorization
$c, f :$ state wether the parameter is referred to the Current or Future scenario respectively

Once the growth factor is obtained, the future trips, $T_{i}^{f}$ , for zone $i$ , are estimated from the current $T_{i}^{c}$ as:

T_{i}^{f} = F_{i} T_{i}^{c}

Growth factor - Cobb-Douglas

growth factor - cobb-douglas

A generalization of the #Growth factor from Fratar is given by Cobb-Douglas production functions. This formula has the same form of the previous one, but can take any parameters the researcher wants to use and also adds an extra parameter, $θ_{k}$ to be calibrated in respect with past situations:
$F_{i} = \prod_{k = 1}^{k = p} {(\frac{X_{k}^{f}}{X_{k}^{c}})}^{θ_{k}}$

Category analysis

In category analysis we don't use the TAZs to describe trip generation. We only use factors that describe the population.

For example, we know how many trips are generated by a household of a certain size with a certain number of workers:

Schermata 2025-04-01 alle 12.43.18.png

For example, the table above shows that a household with 3 people (2 of which are workers) generate 2.661 trips from Home to Work.

It only uses categorical exploratory variables
It is not related to Transport Analysis Zones (at a first stage)

Once the current situation is known, then we will have to apply it to forecast future trip generation (therefore, we will need to refer each generation to a zone).

Here we show an example of category analysis taking into consideration HH income and autos owned.

Schermata 2025-04-01 alle 12.51.31.png|350

20 HH where interviewed and each stated the number of trips produced.

Given the distribution observed, we create 2 factors: one for number of cars, one for income:

Number if cars:
- 0
- 1
- 2 or more
Income:
- $\leq 6$
- $6 < Income \leq 9$
- $9 < Income \leq 12$
- $12 < Income \leq 15$
- $> 15$
  For each combination, we list all the household numbers that fall in that combination:

Schermata 2025-04-01 alle 12.54.24.png

For example, we can see that for a HH with income between 9 and 12 thousand pesos and 1 car, we have an HH 7 and HH 18 that combined produce 15 trips (read from first table: 7 produces 7 trips and 18 produces 8 trips).

We then calculate the average number of trips produced in each category. For example, for income between 9 and 12 thousands and 1 car, we have $\frac{7 + 8}{2} = \frac{15}{2} = 7.5$ trips:

Schermata 2025-04-01 alle 13.01.19.png

Linear Regression Analysis

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