# 3.4: Trip Generation

- Page ID
- 47326

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)**Trip Generation** is the first step in the conventional four-step transportation forecasting process (followed by Destination Choice, Mode Choice, and Route Choice), widely used for forecasting travel demands. It predicts the number of trips originating in or destined for a particular traffic analysis zone.

Every trip has two ends, and we need to know where both of them are. The first part is determining how many trips originate in a zone and the second part is how many trips are destined for a zone. Because land use can be divided into two broad category (residential and non-residential) we have models that are household based and non-household based (e.g. a function of number of jobs or retail activity).

For the residential side of things, trip generation is thought of as a function of the social and economic attributes of households (households and housing units are very similar measures, but sometimes housing units have no households, and sometimes they contain multiple households, clearly housing units are easier to measure, and those are often used instead for models, it is important to be clear which assumption you are using).

At the level of the traffic analysis zone, the language is that of land uses "producing" or *attracting* trips, where by assumption trips are "produced" by households and "attracted" to non-households. Production and attractions differ from origins and destinations. Trips are produced by households even when they are returning home (that is, when the household is a destination). Again it is important to be clear what assumptions you are using.

## Activities

People engage in activities, these activities are the "purpose" of the trip. Major activities are home, work, shop, school, eating out, socializing, recreating, and serving passengers (picking up and dropping off). There are numerous other activities that people engage on a less than daily or even weekly basis, such as going to the doctor, banking, etc. Often less frequent categories are dropped and lumped into the catchall "Other".

Every trip has two ends, an origin and a destination. Trips are categorized by *purposes*, the activity undertaken at a destination location.

**Observed trip making from the Twin Cities (2000-2001) Travel Behavior Inventory by Gender**

Trip Purpose |
Males |
Females |
Total |

Work | 4008 | 3691 | 7691 |

Work related | 1325 | 698 | 2023 |

Attending school | 495 | 465 | 960 |

Other school activities | 108 | 134 | 242 |

Childcare, daycare, after school care | 111 | 115 | 226 |

Quickstop | 45 | 51 | 96 |

Shopping | 2972 | 4347 | 7319 |

Visit friends or relatives | 856 | 1086 | 1942 |

Personal business | 3174 | 3928 | 7102 |

Eat meal outside of home | 1465 | 1754 | 3219 |

Entertainment, recreation, fitness | 1394 | 1399 | 2793 |

Civic or religious | 307 | 462 | 769 |

Pick up or drop off passengers | 1612 | 2490 | 4102 |

With another person at their activities | 64 | 48 | 112 |

Some observations:

- Men and women behave differently on average, splitting responsibilities within households, and engaging in different activities,
- Most trips are not work trips, though work trips are important because of their peaked nature (and because they tend to be longer in both distance and travel time),
- The vast majority of trips are not people going to (or from) work.

People engage in activities in sequence, and may chain their trips. In the Figure below, the trip-maker is traveling from home to work to shop to eating out and then returning home.

## Specifying Models

How do we predict how many trips will be generated by a zone? The number of trips originating from or destined to a purpose in a zone are described by trip rates (a cross-classification by age or demographics is often used) or equations. First, we need to identify what we think the relevant variables are.

### Home-end

The total number of trips leaving or returning to homes in a zone may be described as a function of:

\[T_h = f(housing \text{ }units, household \text{ }size, age, income, accessibility, vehicle \text{ }ownership)\]

Home-End Trips are sometimes functions of:

- Housing Units
- Household Size
- Age
- Income
- Accessibility
- Vehicle Ownership
- Other Home-Based Elements

### Work-end

At the work-end of work trips, the number of trips generated might be a function as below:

\[T_w=f(jobs(area \text{ }of \text{ } space \text{ } by \text{ } type, occupancy \text{ } rate\]

Work-End Trips are sometimes functions of:

- Jobs
- Area of Workspace
- Occupancy Rate
- Other Job-Related Elements

### Shop-end

Similarly shopping trips depend on a number of factors:

\[T_s = f(number \text{ }of \text{ }retail \text{ }workers, type \text{ }of \text{ }retail, area, location, competition)\]

Shop-End Trips are sometimes functions of:

- Number of Retail Workers
- Type of Retail Available
- Area of Retail Available
- Location
- Competition
- Other Retail-Related Elements

## Input Data

A forecasting activity conducted by planners or economists, such as one based on the concept of economic base analysis, provides aggregate measures of population and activity growth. Land use forecasting distributes forecast changes in activities across traffic zones.

## Estimating Models

Which is more accurate: the data or the average? The problem with averages (or aggregates) is that every individual’s trip-making pattern is different.

### Home-end

To estimate trip generation at the home end, a cross-classification model can be used. This is basically constructing a table where the rows and columns have different attributes, and each cell in the table shows a predicted number of trips, this is generally derived directly from data.

In the example cross-classification model: The dependent variable is trips per person. The independent variables are dwelling type (single or multiple family), household size (1, 2, 3, 4, or 5+ persons per household), and person age.

The figure below shows a typical example of how trips vary by age in both single-family and multi-family residence types.

The figure below shows a moving average.

### Non-home-end

The trip generation rates for both “work” and “other” trip ends can be developed using Ordinary Least Squares (OLS) regression (a statistical technique for fitting curves to minimize the sum of squared errors (the difference between predicted and actual value) relating trips to employment by type and population characteristics.

The variables used in estimating trip rates for the work-end are Employment in Offices (\(E_{off}\)), Retail (\(E_{ret}\)), and Other (\(E_{oth}\))

A typical form of the equation can be expressed as:

\[T_{D,k}=a_1E_{off,k}+a_2E_{oth,k}+a_3E_{ret,k}\]

Where:

- \(T_{D,k}\) - Person trips attracted per worker in Zone k
- \(E_{off,i}\) - office employment in the ith zone
- \(E_{oth,i}\) - other employment in the ith zone
- \(E_{ret,i}\)- retail employment in the ith zone
- \(a_1,a_2,a_3\) - model coefficients

## Normalization

For each trip purpose (e.g. home to work trips), the number of trips originating at home must equal the number of trips destined for work. Two distinct models may give two results. There are several techniques for dealing with this problem. One can either assume one model is correct and adjust the other, or split the difference.

It is necessary to ensure that the total number of trip origins equals the total number of trip destinations, since each trip interchange by definition must have two trip ends.

The rates developed for the home end are assumed to be most accurate,

The basic equation for normalization:

\[T'_{D,j}=T_{D,j} \dfrac{ \displaystyle \sum{i=1}^I T_{O,i}}{\displaystyle \sum{j=1}^J T_{TD,j}}\]

## Sample Problems

Problem 1:

Planners have estimated the following models for the AM Peak Hour

\(T_{O,i}=1.5*H_i\)

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

Where:

\(T_{O,i}\) = Person Trips Originating in Zone \(i\)

\(T_{D,j}\) = 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.

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

**Solution to Trip Generation Problem Part A**Households Office Employees Other Employees Retail Employees Origins Destinations 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:

\[T'_{D,j}=T_{D,j} \dfrac{ \displaystyle \sum{i=1}^I T_{O,i}}{\displaystyle \sum{j=1}^J T_{TD,j}}=>T_{D,j} \dfrac{37500}{36750}=T_{D,j}*1.0204\]

**Solution to Trip Generation Problem Part B**Origins Destinations Adjustment Factor Normalized Destinations 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

Problem 2:

Modelers have estimated that the number of trips leaving Rivertown (\(T_O\)) is a function of the number of households (H) and the number of jobs (J), and the number of trips arriving in Marcytown (\(T_D\)) is also a function of the number of households and number of jobs.

\(T_O=1H+0.1J;R^2=0.9\)

\(T_D=0.1H+1J;R^2=0.5\)

Assuming all trips originate in Rivertown and are destined for Marcytown and:

Rivertown: 30000 H, 5000 J

Marcytown: 6000 H, 29000 J

Determine the number of trips originating in Rivertown and the number destined for Marcytown according to the model.

Which number of origins or destinations is more accurate? Why?

**Answer**-
Determine the number of trips originating in Rivertown and the number destined for Marcytown according to the model.

T_Rivertown =T_O ; T_O= 1(30000) + 0.1(5000) = 30500 trips

T_(MarcyTown)=T_D ; T_D= 0.1(6000) + 1(29000) = 29600 trips

Which number of origins or destinations is more accurate? Why?

Origins(T_{Rivertown}) because of the goodness of fit measure of the Statistical model (R^2=0.9).

Problem 3

Modelers have estimated that in the AM peak hour, the number of trip origins (T_O) is a function of the number of households (H) and the number of jobs (J), and the number of trip destinations (T_D) is also a function of the number of households and number of jobs.

\(T_O=1.0H+0.1J;R^2=0.9\)

\(T_D=0.1H+1J;R^2=0.5\)

Suburbia: 30000 H, 5000 J

Urbia: 6000 H, 29000 J

1) Determine the number of trips originating in and destined for Suburbia and for Urbia according to the model.

2) Does this result make sense? Normalize the result to improve its accuracy and sensibility?

3) If the interzonal travel cost (from Suburbia to Urbia or Urbia to Suburbia) is 10 minutes, and the intrazonal travel cost (trips within Suburbia or within Urbia) is 5 minutes, use a (doubly-constrained) gravity model wherein the impedance is\(f(t_{ij})=t_{ij}^{-2}\), calculate the impedance, balance the matrix to match trip generation, and determine the trip table (within 2 percent accuracy)

## Variables

- \(T_{O,i}\) - Person trips originating in Zone i
- \(T_{D,j}\) - Person Trips destined for Zone j
- \(T_{O,i'}\) - Normalized Person trips originating in Zone i
- \(T_{D,j'}\) - Normalized Person Trips destined for Zone j
- \(T_h\) - Person trips generated at home end (typically morning origins, afternoon destinations)
- \(T_w\) - Person trips generated at work end (typically afternoon origins, morning destinations)
- \(T_s\) - Person trips generated at shop end
- \(H_i\) - Number of Households in Zone i
- \(E_{off,k}\) - office employment in Zone k
- \(E_{ret,k}\) - retail employment in Zone k
- \(E_{oth,k}\) - other employment in Zone k
- \(B_n\) - model coefficients

## Abbreviations

- H2W - Home to work
- W2H - Work to home
- W2O - Work to other
- O2W - Other to work
- H2O - Home to other
- O2H - Other to home
- O2O - Other to other
- HBO - Home based other (includes H2O, O2H)
- HBW - Home based work (H2W, W2H)
- NHB - Non-home based (O2W, W2O, O2O)

## External Exercises

Use the ADAM software at the STREET website and try Assignment #1 to learn how changes in analysis zone characteristics generate additional trips on the network.

## Additional Problems

Homework

- Keep a travel diary for the next week. Analyze your personal travel diary. Summarize the number of trips by mode, by purpose, by time of day, etc. To do so, for each trip record the following information
- the start and end time (to the nearest minute)
- start and end location of each trip,
- primary mode you took (drive alone, car driver with passenger, car passenger, bus, LRT, walk, bike, motorcycle, taxi, Zipcar, other). (use the codes provided)
- purpose (to work, return home, work related business, shopping, family/personal business, school, church, medical/dental, vacation, visit friends or relatives, other social recreational, other) (use the codes provided)
- if you traveled with anyone else, and if so whether they lived in your household or not.

**Bonus: Email your professor at the end of everyday with a detailed log of your travel diary.** **(+5 points on the first exam)**

Additional Problems

- Are number of destinations always less than origins?
- Pose 5 hypotheses about factors that affect work, non-work trips? How do these factors affect accuracy, and thus normalization?
- What is the acceptable level of error?
- Describe one variable used in trip generation and how it affects the model.
- What is the basic equation for normalization?
- Which of these models (home-end, work-end) are assumed to be more accurate? Why is it important to normalize trip generation models
- What are the different trip purposes/types trip generation?
- Why is it difficult to know who is traveling when?
- What share of trips during peak afternoon peak periods are work to home (>50%, <50%?), why?
- What does ORIO abbreviate?
- What types of employees (ORIO) are more likely to travel from work to home in the evening peak
- What does the trip rate tell us about various parts of the population?
- What does the “T-statistic” value tell us about the trip rate estimation?
- Why might afternoon work to home trips be more or less than morning home to work trips? Why might the percent of trips be different?
- Define frequency.
- Why do individuals > 65 years of age make fewer work to home trips?
- Solve the following problem. You have the following trip generation model:

\[Trips=B_1Off+B_2Ind+B_3Ret\]

And you are given the following coefficients derived from a regression model.

B_1 = 0.61 B_2 = 0.15 B_3 = 0.123

If there are 600 office employees, 300 industrial employees, and 200 retail employees, how many trips are going from work to home?