# Model for Estimating Urban Mobility Based on the Records of User Activities in Public Mobile Networks

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## Abstract

**:**

## 1. Introduction

## 2. Overview of the Previous Research

## 3. Research Methodology

#### 3.1. The Methodology Overview

- B is an indicator of the duration of the journey for each individual trip;
- $t{\left(i\right)}_{orig}$ is a time denotement in which the user activity was recorded at the base station and identified as the trip origin;
- $t{\left(i\right)}_{dest}$ is a time denotement in which the user activity was recorded at the base station and identified as the trip destination;
- $\Delta t\left(i,j\right)$ is the travel time between two base stations.

- $D1\left(i,j\right)$ is the speed of movement for each individual journey within a timeframe;
- $C\left(i,j\right)$ is the Euclidean distance between base station pairs;
- $B\left(i,j\right)$ is the duration of the journey, for each individual trip within a timeframe.

- $A\left(i,j\right)$ is the total number of the recorded (registered) trips between the individual base station pairs (trip matrix);
- $Trip\_ID\left(i,j\right)$ is a trip between two base stations in an appropriate timeframe, all assumptions being met.

- $\overline{{B}_{i,j}}$ is the median value of all travel times between each pair of base stations over a timeframe;
- $B\left(i,j\right)$ is the value of the trip duration for each individual trip in a timeframe;
- $n$ is the number of trips registered between each base station pair in a timeframe.

- $norm{A}_{\left(i,j\right)}$ is the normalized value of the number of trips for the corresponding base station pair for all timeframes within one day;
- $norm\overline{{B}_{i,j}}$ is the normalized value of the median trip duration value for the corresponding base station pair for all timeframes within one day;
- $norm{C}_{\left(i,j\right)}$ is the normalized value of the distance indicator for the corresponding base station pair.

- $IM$ is the urban mobility index for the timeframe;
- $pI{M}_{i,j}$ is the partial urban mobility index for the corresponding base station pair within the appropriate timeframe;
- $n$ is the total number of origin and destination pairs for which the mobility assessment was performed.

- ${\alpha}_{i,j}$ is the total mobility share coefficient for each origin and destination pair (base station pair);
- ${A}_{\left(i,j\right)}$ is the value of the trip number indicator in a specific timeframe;
- ${C}_{\left(i,j\right)}$ is the value of the distance indicator for a corresponding base station pair.

#### 3.2. The Relationship between the Mobility Indicators and the Urban Mobility Index Assessment

^{3}), a total number of 27 questions is set.

## 4. Model of the Urban Mobility Index

## 5. The Application of the Urban Mobility Index Estimation Process

#### 5.1. Process Implementation in a Programming Environment

#### 5.2. The Application of the Procedure over a Real-World Dataset

^{2}(30 × 30 km). It is estimated that approximately 1.2 million people live in the area, while approximately 25 million live in the urban agglomeration together with the suburban settlements [73]. The entire urban agglomeration (together with suburban settlements) covers approximately 20,000 m

^{2}. The dataset used for the analysis consists of 38,218,717 telecommunication activity records for one characteristic day, for 24 h. It contains data on the telecommunications activities of approximately 450,000 users, representing 37.5% of the population in the area. On average, the record contains 85 telecommunication activities per user on a typical day. According to the number of the base stations, the coverage area is divided into 480 urban areas. The average surface area covered by one base station is 2.69 km

^{2}. The shortest distance between the base station pairs is 0.007 km (the distance between the base station 475 and 476), with a total of 12 base station pairs less than 100 meters apart, and 1345 base station pairs within a kilometer distance. The longest distance is 42.9 km (the distance between base stations 36 and 476). The average distance between all base station pairs in the network is 1.81 km. Next, is the migration identification process. A total of 2,133,369 migrations were identified in the analyzed dataset. By applying the filter, all ineligible migrations were eliminated, leaving those longer than 1 km, lasting between 10 and 60 min, and with an average speed less than 100 km/h. As a result of the filtering, almost 95% of the identified migrations were removed, i.e., from 91% to 97% per timeframe, leaving 110,902 migrations. The following is the calculation of the only remaining indicator (medium travel time), normalization of the values of all indicators and the calculation of the partial urban mobility indices for each base station pair. The values of the partial urban mobility index for one timeframe is shown in Figure 14. Using the calculated values of the partial urban mobility indices, the calculation of the urban mobility index for each timeframe is carried out. The values of the urban mobility index by timeframes for the basic dataset and for the validation dataset are shown in Table 6. The validation of the model uses a dataset consisting of 20% of the total dataset and shows that deviations are possible in the range from 3% to 11%, relative to the value obtained through using the basic dataset. The deviation within seven timeframes does not exceed the value of 7%, and in only one frame has a value greater than 11%. The average deviation for all timeframes is 6%, showing the model reliability of 94%.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The relationship between the indicators and parameters in the process of the urban mobility index calculation.

**Figure 3.**The graphical representation of the rules in the initial fuzzy logic model (1st column = number of trips, 2nd column = trip duration, 3rd column = distance, and 4th column urban mobility estimation).

**Figure 4.**The graphical representation of the model after the completion of the model learning process (1st column = number of trips, 2nd column = trip duration, 3rd column = distance, and 4th column urban mobility estimation).

**Figure 5.**A learning error dependent on the number of epochs for the fuzzy inference system number 27.

**Figure 11.**The model result: The relationship between the trip duration indicators and the number of trips with respect to the mobility estimate (taken from the MATLAB v 9.0, 2016 programming tool).

**Figure 12.**The model result: The relationship between the trip duration indicators and the distance indicators with respect to the mobility estimate (taken from the MATLAB v 9.0, 2016 programming tool).

**Figure 13.**The model result: The relationship between the trip distance indicators and the number of trips with respect to the mobility estimate (taken from the MATLAB v 9.0, 2016 programming tool).

**Figure 15.**The comparison of the urban mobility index from the basic dataset with the validation data.

**Figure 17.**The visualisation of an overall urban mobility table (480 × 480) for a sum of values within the frame O1-O8.

Trip Duration Indicator | Trip Duration |
---|---|

Short trip duration | up to 33% of the longest lasting trip |

Medium trip duration | from 34% to 66% of the longest lasting trip |

Long trip duration | from 67% to 100% of the longest lasting trip |

Traveled Distance Indicator | Trip Distance |
---|---|

Short distance | up to 33% of the longest trip |

Medium distance | from 34% to 66% of the longest trip |

Long distance | from 67% to 100% of the longest trip |

Number of Trips | Trip Duration Indicator | Travel Distance Indicator |
---|---|---|

Low number of trips | Short trip duration | Short distance |

Medium number of trips | Medium trip duration | Medium distance |

High number of trips | Long trip duration | Long distance |

Mobility Rating | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

No. | MIN | MAX | AVG | STDEV | 1 | 2 | 3 | 4 | 5 | 6 | |

Scenario | 1 | 3 | 6 | 4.44 | 1.44 | 0% | 0% | 44% | 11% | 0% | 44% |

2 | 3 | 6 | 4.22 | 1.24 | 0% | 0% | 44% | 11% | 22% | 22% | |

3 | 2 | 6 | 4.44 | 1.18 | 0% | 11% | 0% | 44% | 22% | 22% | |

4 | 2 | 5 | 3.22 | 1.15 | 0% | 44% | 0% | 44% | 11% | 0% | |

5 | 2 | 5 | 3.11 | 1.01 | 0% | 33% | 33% | 22% | 11% | 0% | |

6 | 2 | 6 | 3.44 | 1.18 | 0% | 11% | 67% | 0% | 11% | 11% | |

7 | 1 | 3 | 1.33 | 0.68 | 78% | 11% | 11% | 0% | 0% | 0% | |

8 | 1 | 4 | 2.00 | 0.96 | 33% | 44% | 11% | 11% | 0% | 0% | |

9 | 1 | 4 | 2.33 | 0.96 | 22% | 33% | 33% | 11% | 0% | 0% | |

10 | 3 | 6 | 4.33 | 0.83 | 0% | 0% | 11% | 56% | 22% | 11% | |

11 | 2 | 6 | 4.33 | 1.07 | 0% | 11% | 0% | 44% | 33% | 11% | |

12 | 1 | 6 | 4.67 | 1.43 | 11% | 0% | 0% | 11% | 56% | 22% | |

13 | 2 | 4 | 3.00 | 0.68 | 0% | 22% | 56% | 22% | 0% | 0% | |

14 | 3 | 4 | 3.11 | 0.32 | 0% | 0% | 89% | 11% | 0% | 0% | |

15 | 2 | 4 | 3.33 | 0.83 | 0% | 22% | 22% | 56% | 0% | 0% | |

16 | 1 | 6 | 2.78 | 1.57 | 11% | 56% | 11% | 0% | 11% | 11% | |

17 | 1 | 5 | 3.00 | 1.35 | 11% | 33% | 22% | 11% | 22% | 0% | |

18 | 1 | 5 | 3.00 | 1.07 | 11% | 11% | 56% | 11% | 11% | 0% | |

19 | 4 | 6 | 4.78 | 0.80 | 0% | 0% | 0% | 44% | 33% | 22% | |

20 | 4 | 6 | 4.89 | 0.75 | 0% | 0% | 0% | 33% | 44% | 22% | |

21 | 5 | 6 | 5.78 | 0.42 | 0% | 0% | 0% | 0% | 22% | 78% | |

22 | 2 | 4 | 3.33 | 0.68 | 0% | 11% | 44% | 44% | 0% | 0% | |

23 | 2 | 5 | 3.67 | 0.96 | 0% | 11% | 33% | 33% | 22% | 0% | |

24 | 2 | 6 | 4.22 | 1.15 | 0% | 11% | 11% | 33% | 33% | 11% | |

25 | 1 | 5 | 2.56 | 1.36 | 33% | 11% | 33% | 11% | 11% | 0% | |

26 | 1 | 4 | 2.67 | 1.07 | 11% | 44% | 11% | 33% | 0% | 0% | |

27 | 1 | 5 | 3.22 | 1.24 | 11% | 11% | 44% | 11% | 22% | 0% |

**Table 5.**The comparison of the intervals of the input membership functions, before and after the model learning.

Input Variable | Fuzzy Set | Function Interval in the Initial Fuzzy Logic System | Membership Function Interval after the Learning Process in the Chosen Fuzzy Logic System |
---|---|---|---|

Number of trips | Small number of trips | [− 0.35 − 0.15 0.15 0.35] | [− 0.35 − 0.15 0.1512 0.361] |

Medium number of trips | [0.15 0.35 0.65 0.85] | [0.1501 0.3512 0.6497 0.85] | |

Large amount of trips | [0.65 0.85 1.15 1.35] | [0.6473 0.8497 1.15 1.35] | |

Trip duration | Short trip duration | [− 0.35 − 0.15 0.15 0.35] | [− 0.35 − 0.15 0.1514 0.3628] |

Medium trip duration | [0.15 0.35 0.65 0.85] | [0.1501 0.3514 0.6504 0.85] | |

Long trip duration | [0.65 0.85 1.15 1.35] | [0.6544 0.8504 1.15 1.35] | |

Distance | Short distance | [− 0.35 − 0.15 0.15 0.35] | [− 0.35 − 0.15 0.1507 0.3568] |

Medium distance | [0.15 0.35 0.65 0.85] | [0.1501 0.3507 0.6505 0.85] | |

Long distance | [0.65 0.85 1.15 1.35] | [0.6558 0.8505 1.15 1.35] |

**Table 6.**The values of the urban mobility index by timeframes for the basic dataset and for the dataset used for validation.

O1 | O2 | O3 | O4 | O5 | O6 | O7 | O8 | |
---|---|---|---|---|---|---|---|---|

IM | 51.14% | 54.50% | 69.02% | 64.03% | 66.65% | 7.,57% | 56.14% | 52.65% |

IM (validation) | 54.57% | 57.83% | 70.92% | 68.20% | 70.13% | 69.14% | 58.71% | 56.59% |

Difference | 6% | 6% | 3% | 6% | 5% | −11% | 4% | 7% |

Timeframe | O1 | O2 | O3 | O4 | O5 | O6 | O7 | O8 |
---|---|---|---|---|---|---|---|---|

Amount of mobility | 76.365 | 114.043 | 223.260 | 152.107 | 192.886 | 151.974 | 347.662 | 301.795 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vidović, K.; Šoštarić, M.; Mandžuka, S.; Kos, G.
Model for Estimating Urban Mobility Based on the Records of User Activities in Public Mobile Networks. *Sustainability* **2020**, *12*, 838.
https://doi.org/10.3390/su12030838

**AMA Style**

Vidović K, Šoštarić M, Mandžuka S, Kos G.
Model for Estimating Urban Mobility Based on the Records of User Activities in Public Mobile Networks. *Sustainability*. 2020; 12(3):838.
https://doi.org/10.3390/su12030838

**Chicago/Turabian Style**

Vidović, Krešimir, Marko Šoštarić, Sadko Mandžuka, and Goran Kos.
2020. "Model for Estimating Urban Mobility Based on the Records of User Activities in Public Mobile Networks" *Sustainability* 12, no. 3: 838.
https://doi.org/10.3390/su12030838