# Using Probability Distributions for Projecting Changes in Travel Behavior

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emission and traffic jams. A case of rebound effects regarding fuel efficiency improvements and the following increase in car traffic demand is shown and discussed in [2]. Because human behavior is not strictly logical or economical in every way these models have to deal with many uncertainties and cope with the errors statistically. Therefore, understanding why people leave their homes, how this behavior has changed over the years and how to forecast it is crucial for the quality of travel demand modeling to show pathways to a sustainable transport system with respect to the mobility needs. The Mobilität in Deutschland (MiD, Mobility in Germany) survey tracks mobility patterns of the German population since 2002 [3]. With its second [4] and third instalment [5] one can see a change in travel behavior over time. A summary of the development of these surveys can be seen in the MiD time series report [6].

## 2. Materials and Methods

#### 2.1. Data

- age;
- working, educational or retiree status;
- sex; and
- car-ownership.

- The weekday;
- Region class (metropolitan, rural area etc.), i.e., where the person lives.

- The activity; and
- The start and end time of the trips to distinguish between full time and part time work.

- A set of trips, we write for the trips ${t}_{1},{t}_{2},\cdots ,{t}_{{n}_{d}}\in d,{n}_{d}\in \mathbb{N}$;
- An activity of a trip t is denoted by a or $a\left(t\right)$ with$$a\in A\{\mathrm{Any}\phantom{\rule{4.pt}{0ex}}\mathrm{Activity},\phantom{\rule{0.166667em}{0ex}}\mathrm{Education}/\mathrm{School},\phantom{\rule{0.166667em}{0ex}}\mathrm{Free}\phantom{\rule{4.pt}{0ex}}\mathrm{Time},\phantom{\rule{0.166667em}{0ex}}\mathrm{Personal}\phantom{\rule{4.pt}{0ex}}\mathrm{Activity},\phantom{\rule{0.166667em}{0ex}}\mathrm{Shopping},\phantom{\rule{0.166667em}{0ex}}\mathrm{Work}\};$$
- ${g}_{d}\left(d\right)$ denotes the diary group of diary d; and
- ${g}_{p}\left(d\right)$ denotes the person group to which the reporting person of diary d belongs.

#### 2.2. Synthetic Population and Weighting

- Changes in the population, i.e., increase in younger or older people, changes in employment etc.; and
- Changes in individual travel behavior like working less, having more free time or e-commerce replacing some amount of shopping trips.

- Diaries of all regions from Monday to Sunday; and
- Diaries from regions with more than 0.5 M inhabitants during core weekdays (Tuesday to Thursday) only.

#### 2.3. Diary Classes and Probability Distributions

- (1) which comes after (2), (3), (4), (5); and
- (6) which comes after (7), (8), (9), (10)

## 3. Results

#### 3.1. MiD Data Results

#### 3.2. Diary Class Distribution Results

- The development of free time and any activity is never met;
- –
- These two activities have the lowest priority according to our diary group order;

- The development of education is only achieved for all regions and all days (it rises twice from 2002 to 2017) but not for bigger cities in the core workdays (again rises twice). The probability prediction states an increase at first and a smaller decrease from 2008 to 2017;
- –
- A (half) mis-prediction despite being the highest priority group for children, pupils, students, and trainees;
- –
- The share of educational trips in diaries not in diary class (11), (12), (13), (24) are 1.28% (2002), 1.15% (2008) and 1.17% (2017) for all regions and days. Because of these diaries which can fall into any diary group the number of estimated educational trips seems always lower than the reported number from the MiD;
- –
- For bigger cities, Tuesday–Thursday we have 1.68%, 1.56% and 2.26%. This also leads to an increased error (again using all diaries but with probabilities from the filtered set), especially for the 2017 set;

- The trends of work, personal matters and shopping are reached in both cases.

#### 3.3. Union of Diaries

## 4. Discussion

_{2}and noise emission, especially considering trips by cars. The projection of these changes in travel behavior together with a demographic change need to be considered for developing evaluation strategies and political measures towards a sustainable mobility. A similar reasoning and its connection between the mobility behavior and the environment is explained in the DLR project report of Transport and the Environment (VEU) [21].

#### Problems Needing Further Investigation

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MiD | Mobilität in Deutschland (Mobility in Germany) survey |

d | Diary |

${D}_{x}$ | Diaries of all regions and all weekdays of year x |

${\overline{D}}_{x}$ | Diaries of regions with more than 0.5 M inhabitants from Tuesday |

to Thursday of year x | |

${g}_{d}$ | Diary group |

${g}_{p}$ | Person group |

${G}_{d}$ | Set of all diary groups |

${G}_{p}$ | Set of all person groups |

$pro{b}_{y}$ | Probability distribution with respect to diaries ${D}_{y}$ |

${\overline{prob}}_{y}$ | Probability distribution with respect to diaries ${\overline{D}}_{y}$ |

$\left|X\right|$ | Number of elements in set X. |

## References

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**Figure 1.**Number of trips per day ([6], compare p. 60 Figure 35).

**Figure 3.**Diary group distribution. (

**a**) Dx, all Regions from Monday to Sunday. (

**b**) Dx, cities with ≥0.5 M inhabitants from Tuesday to Thursday.

**Figure 4.**Activity share in the MiD over time. (

**a**) All regions, Monday–Sunday. (

**b**) Cities with more than 0.5 M people, Tuesday–Thursday.

**Figure 5.**Difference in percentage points. The differences are taken against the MiD values of the same year as the probability distributions. (

**a**) All regions, Monday to Sunday (

**b**) Cities ≥0.5 M, Tuesday to Thursday.

**Figure 6.**Difference in percentage points. Probability distributions of each survey combined with the whole set of diaries ${D}_{all}$ of the three reports (2002, 2008, 2017). The differences are taken against the MiD values of the same year as the probability distributions. (

**a**) All regions, Monday to Sunday. (

**b**) Cities ≥0.5 M, Tuesday to Thursday.

MiD | Diaries | Trips |
---|---|---|

2002 | 43,876 | 160,011 |

2008 | 49,591 | 179,486 |

2017 | 239,503 | 835,805 |

Person | 1 | 1 | 1 | 2 | ⋯ |

Trip | 1 | 2 | 3 | 1 | ⋯ |

Activity | free time | work | free time | shopping | ⋯ |

Age | 26 | 26 | 26 | 41 | ⋯ |

Status | student | student | student | not working | ⋯ |

Sex | f | f | f | m | ⋯ |

Cars | 0 | 0 | 0 | 1 | ⋯ |

Weekday | Wed | Wed | Wed | Sat | ⋯ |

Start Time | 7:30 | 9:00 | 18:00 | 10:00 | ⋯ |

End Time | 7:45 | 9:30 | 18:30 | 10:10 | ⋯ |

Region | ≥0.5 M inh. | ≥0.5 M inh. | ≥0.5 M inh. | <5000 inh. | ⋯ |

Diary Group | 5 | 5 | 5 | 20 | ⋯ |

Person Group | Student | Student | Student | Not working, ≥25, <45, m, w/Car | ⋯ |

Diary Group Number | Diary Group |
---|---|

(1) | Full time work trip |

(2) | Full time work with escort trip, |

(3) | Full time work with personal matter trip, |

(4) | Full time work with shopping trip |

(5) | Full time work with free time trip |

(6) | Part time work trip |

(7) | Part time work with escort trip |

(8) | Part time work with personal matter trip |

(9) | Part time work with shopping trip |

(10) | Part time work with free time trip |

(11) | Educational trip for students |

(12) | Educational trip for pupils |

(13) | Kindergarten/Educational trip for children <6 |

(14) | With Escort trip |

(15) | Personal matter trip for full/part-time worker |

(16) | Personal matter trip, students, pupils, children |

(17) | Personal matter trip, non-working, retirees |

(18) | Shopping trip for full/part-time worker |

(19) | Shopping trip, students, pupils, children |

(20) | Shopping trip, non-working, retirees |

(21) | Free time trip for full/part-time worker |

(22) | Free time trip, students, pupils, children |

(23) | Free time trip, non-working, retirees |

(24) | Educational trip for Trainees |

(90) | Other diaries |

All Regions, Mon–Sun | ≥0.5 M, Tue–Thu | |||||
---|---|---|---|---|---|---|

2002 | 2008 | 2017 | 2002 | 2008 | 2017 | |

Any Activity | 7.58 | 9.06 | 7.85 | 7.91 | 9.97 | 8.50 |

Education/School | 5.42 | 6.05 | 6.43 | 6.92 | 8.08 | 8.20 |

Free Time | 34.68 | 34.83 | 35.25 | 27.16 | 27.10 | 28.59 |

Personal Activity | 12.87 | 13.00 | 15.07 | 13.63 | 13.45 | 14.97 |

Shopping | 22.50 | 20.60 | 18.00 | 23.27 | 20.90 | 16.93 |

Work | 16.96 | 16.47 | 17.40 | 21.11 | 20.50 | 22.81 |

**Table 5.**Overview of activity percentages for each combination of diary and probability distribution. Columns where the years of diaries correspond to the probability distribution are highlighted. ${D}_{x},pro{b}_{y}$ and ${\overline{D}}_{x},{\overline{prob}}_{y}$ are the respective filters 1 and 2.

Diaries ${\mathit{D}}_{\mathit{x}}$ | 2002 | 2008 | 2017 | ||||||
---|---|---|---|---|---|---|---|---|---|

Distribution $pro{b}_{y}$ | 2002 | 2008 | 2017 | 2002 | 2008 | 2017 | 2002 | 2008 | 2017 |

ine Any Activity | 7.51 | 8.37 | 9.46 | 7.96 | 8.86 | 9.96 | 6.46 | 7.28 | 7.58 |

Education/School | 5.25 | 5.60 | 5.85 | 5.10 | 5.46 | 5.71 | 5.22 | 5.58 | 5.77 |

Free Time | 35.19 | 35.94 | 33.54 | 34.77 | 35.47 | 33.04 | 36.17 | 37.00 | 35.35 |

Personal Activity | 12.93 | 12.97 | 14.50 | 12.83 | 12.88 | 14.41 | 13.60 | 13.68 | 15.31 |

Shopping | 22.12 | 20.89 | 19.87 | 22.29 | 21.05 | 20.03 | 20.64 | 19.38 | 18.30 |

Work | 17.00 | 16.23 | 16.78 | 17.05 | 16.30 | 16.84 | 17.91 | 17.08 | 17.70 |

ine Diaries ${\overline{D}}_{x}$ | 2002 | 2008 | 2017 | ||||||

Distribution ${\overline{prob}}_{y}$ | 2002 | 2008 | 2017 | 2002 | 2008 | 2017 | 2002 | 2008 | 2017 |

ine Any Activity | 7.44 | 8.72 | 9.43 | 7.87 | 9.23 | 9.94 | 6.43 | 7.96 | 7.86 |

Education/School | 6.22 | 6.95 | 6.74 | 6.07 | 6.79 | 6.60 | 6.29 | 7.07 | 6.76 |

Free Time | 28.67 | 30.00 | 28.08 | 28.48 | 29.68 | 27.76 | 29.47 | 30.56 | 29.46 |

Personal Activity | 13.55 | 13.23 | 14.50 | 13.41 | 13.10 | 14.33 | 14.18 | 13.91 | 15.22 |

Shopping | 22.28 | 21.02 | 19.03 | 22.30 | 21.02 | 19.08 | 20.64 | 19.36 | 17.31 |

Work | 21.83 | 20.08 | 22.22 | 21.86 | 20.17 | 22.28 | 22.99 | 21.14 | 23.39 |

**Table 6.**Activity shares using the diaries ${D}_{all}$ of 2002, 2008 and 2017 together with the probability distributions of a single year.

Filter | All Regions, Mon–Sun | ≥0.5 M, Tue–Thu | ||||
---|---|---|---|---|---|---|

Distribution ${\mathit{prob}}_{\mathit{y}}$ | 2002 | 2008 | 2017 | 2002 | 2008 | 2017 |

Any Activity | 6.76 | 7.59 | 8.03 | 6.70 | 8.19 | 8.24 |

Education/School | 5.18 | 5.54 | 5.74 | 6.22 | 6.99 | 6.70 |

Freetime | 35.93 | 36.74 | 34.95 | 29.33 | 30.45 | 29.20 |

Personal Activity | 13.42 | 13.48 | 15.09 | 14.00 | 13.72 | 15.02 |

Shopping | 21.06 | 19.81 | 18.74 | 21.08 | 19.81 | 17.78 |

Work | 17.66 | 16.85 | 17.45 | 22.67 | 20.85 | 23.07 |

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**MDPI and ACS Style**

Radke, A.; Heinrichs, M.
Using Probability Distributions for Projecting Changes in Travel Behavior. *Sustainability* **2021**, *13*, 10101.
https://doi.org/10.3390/su131810101

**AMA Style**

Radke A, Heinrichs M.
Using Probability Distributions for Projecting Changes in Travel Behavior. *Sustainability*. 2021; 13(18):10101.
https://doi.org/10.3390/su131810101

**Chicago/Turabian Style**

Radke, Andreas, and Matthias Heinrichs.
2021. "Using Probability Distributions for Projecting Changes in Travel Behavior" *Sustainability* 13, no. 18: 10101.
https://doi.org/10.3390/su131810101