# Isolated and Single Pedestrians and Pedestrian Groups on Sidewalks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data, Methodology, and Variables

#### 2.1. Area of Study

#### 2.2. Data Collection and Reduction

#### 2.3. Methodology and Variables

_{0}+ β

_{1}X

_{1}+ β

_{2}X

_{2}+ … + β

_{n}X

_{n}+ ε

- Y is the dependent variable;
- X
_{1}, …, X_{n}are independent variables; - β
_{0}is the constant parameter (intercept); - β
_{1}, …, β_{n}are model parameters (regression coefficients); - ε is the error component in the model.

^{2}(coefficient of determination) and the RMSPE (root mean square percent error).

_{v}

^{2}and RMSPE

_{v}.

^{2}and RMSPE of this global model are calculated; also in this case, observed and predicted speeds have good agreement if, graphically, data lie roughly on a 45 degree line.

- Y
_{1}= mean walking speed for each age class [m/s]; - Y
_{2}= mean walking speed for each age class according pedestrians gender [m/s].

_{n}are:

- X
_{1}= age classes for each sidewalk. The classes are: 1—from 0 to 18 years old; 2—from 19 to 40 years old; 3—from 41 to 65 years old; 4—from 66 to 75 years old; 5—over 75 years old. - X
_{2}= the facing type: 0—blind; 1—accesses; 2—shop windows. - X
_{3}= pedestrian gender: 0—female; 1—male.

## 3. Models for Isolated Pedestrians

_{1}) is expressed as a function of age classes (X

_{1}) and facing type (X

_{2}); in the second one the mean walking speed (Y

_{2}) is expressed as a function of age classes (X

_{1}), facing type (X

_{2}), and gender (X

_{3}).

#### 3.1. Model No. 1: Mean Walking Speed, Age Classes, and Facing Type

_{1}= 1.7769 − 0.1237X

_{1}− 0.0752X

_{2}

^{2}= 0.79; RMSPE = 0.0607. Validation phase: R

_{v}

^{2}= 0.81; RMSPE

_{v}= 0.0652.

_{1}= 1.7522 − 0.1169X

_{1}− 0.0674X

_{2}

^{2}= 0.77; RMSPE = 0.0624.

#### 3.2. Model No. 2: Mean Walking Speed, Age Classes, Facing Type, and Gender

_{2}= 1.7188 − 0.1264X

_{1}− 0.0693X

_{2}+ 0.1089X

_{3}

^{2}= 0.74; RMSPE = 0.0683. Validation phase: R

_{v}

^{2}= 0.76; RMSPE

_{v}= 0.0647.

_{2}= 1.6999 − 0.1214X

_{1}− 0.0605X

_{2}+ 0.1099X

_{3}

^{2}= 0.73; RMSPE = 0.0684.

## 4. Models for Single Pedestrians

_{1}) is expressed as a function of the square of the age classes (X

_{1}) and facing type (X

_{2}); in the second one the mean walking speed (Y

_{2}) is expressed as a function of the square of the age classes (X

_{1}), facing type (X

_{2}), and gender (X

_{3}).

#### 4.1. Model No. 1: Mean Walking Speed, Age Classes, and Facing Type

_{1}= 1.5564 − 0.0167X

_{1}

^{2}− 0.0909X

_{2}

^{2}= 0.76; RMSPE = 0.0696. Validation phase: R

_{v}

^{2}= 0.93; RMSPE

_{v}= 0.0354.

_{1}= 1.5531 − 0.0165X

_{1}

^{2}− 0.0878X

_{2}

^{2}= 0.78; RMSPE = 0.0669.

#### 4.2. Model No. 2: Mean Walking Speed, Age Classes, Facing Type, and Gender

_{2}= 1.5101 − 0.0187X

_{1}

^{2}− 0.0755X

_{2}+ 0.0803X

_{3}

^{2}= 0.76; RMSPE = 0.0698. Validation phase: R

_{v}

^{2}= 0.88; RMSPE

_{v}= 0.0414.

_{2}=1.5354 − 0.0191X

_{1}

^{2}− 0.0830X

_{2}+ 0.0783X

_{3}

^{2}= 0.82; RMSPE = 0.0596.

## 5. Models for Groups

_{1}) is expressed as a function of age classes (X

_{1}) and the facing type (X

_{2}).

#### Model No. 1: Mean Walking Speed, Age Classes, and Facing Type

_{1}= 1.4124 − 0.0186X

_{1}

^{2}− 0.0969X

_{2}

^{2}= 0.93; RMSPE = 0.0375. Validation phase: R

_{v}

^{2}= 0.98; RMSPE

_{v}= 0.0586.

_{1}= 1.4042 − 0.0179X

_{1}

^{2}− 0.0980X

_{2}

^{2}= 0.92; RMSPE = 0.0400.

## 6. Comparison between Models

- Whatever the facing type, the three curves keep themselves in the same order, speeds tend to decrease from the isolated pedestrian to the single one and to the groups. This is certainly related to interferences that a user receives from others who, somehow, tend to influence their behavior. Using terminology borrowed from the road, “driving freedom tends to decrease” due to the presence of a pedestrian flow.
- The facing type affects the speed in the sense that the more “interesting” the side is, the slower a pedestrian moves, whatever the movement motive, demonstrating that the attractiveness of the urban context influences the user behavior.
- Differences between the isolated pedestrian and the single pedestrian tend to grow with the variation in the facing. In fact, if in the blind facing they are practically coincident (average difference about 2.15%), in the case of accesses facing there is an average difference of 4% and 6.10% for shop windows facing. They also maintain the same trend: when they grow older they tend to get closer. Even in this case the consideration about the interactions between pedestrians is valid. The single user is affected by those near him and tends to move more slowly. This affirmation is very strong in young people and adults, while it loses meaning for the elderly, demonstrating that when the age-related psycho-physical conditions worsen, speeds not only decrease but are probably related to factors independent of the presence of other road users, such as the general health condition.
- Differences between single pedestrians and groups are, however, clearly marked and the two curves seem to be parallel. The data analysis shows instead that they tend slightly to diverge as the age classes increase. The average differences vary from 11.70% of the first case to 15% of the last, thus being negligible. The strong influence that the presence of a pedestrian flow exerts on user behavior is clear here, while age tends to lose importance.
- Differences between isolated pedestrians and groups, given what was said earlier are, therefore, greater.

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Comparison between observed and estimated datasets: construction phase (

**a**); and validation phase (

**b**).

**Figure 3.**Comparison between the observed and estimated datasets: construction phase (

**a**); and validation phase (

**b**).

**Figure 5.**Comparison between the observed and estimated datasets: construction phase (

**a**); and validation phase (

**b**).

**Figure 7.**Comparison between observed and estimated dataset: construction phase (

**a**); and validation phase (

**b**).

**Figure 9.**Comparison between observed and estimated dataset: construction phase (

**a**); validation phase (

**b**).

**Figure 11.**Models A, B and C. Comparison between users type behavior: (

**a**) facing type: blind; (

**b**) facing type: accesses; and(

**c**) facing type: shop windows.

Sidewalks | Width [m] | Average Walking Speed [m/s] | Standard Deviation σ | Pedestrian Volume | Men [%] | Women [%] | Groups [%] |
---|---|---|---|---|---|---|---|

Viale Trieste | 2.15 | 1.20 | 0.28 | 715 | 58.0 | 42.0 | 24.6 |

Via Roma | 3.45 | 1.37 | 0.27 | 970 | 57.5 | 42.5 | 33.2 |

Via B.Rossi | 1.45 | 1.30 | 0.32 | 194 | 53.6 | 46.4 | 22.5 |

Via Sonnino | 1.35 | 1.17 | 0.28 | 204 | 49.0 | 51 | 35.2 |

Via G. Deledda | 2.05 | 1.35 | 0.31 | 508 | 47.0 | 53.0 | 46.5 |

Via Paoli sez.1 | 2.85 | 1.21 | 0.32 | 795 | 39.8 | 60.1 | 28.1 |

Via Paoli sez.2 | 3.95 | 1.17 | 0.40 | 939 | 38.0 | 62.0 | 30.7 |

Via Leopardi | 2.50 | 1.25 | 0.30 | 280 | 46.0 | 54.0 | 39.8 |

Via M.Santo | 1.30 | 1.30 | 0.33 | 267 | 46.0 | 54.0 | 26.1 |

Regression Statistics | ||||||

Multiple R | 0.879398 | |||||

R Square | 0.773341 | |||||

Adjusted R Square | 0.75771 | |||||

Standard Error | 0.076153 | |||||

Observation | 32 | |||||

Analysis of Variance | ||||||

Variable | df | SQ | MQ | F | Significance F | |

Regression | 2 | 0.573811 | 0.286905 | 49.47285 | <0.0001 | |

Residual | 29 | 0.168178 | 0.005799 | |||

Total | 31 | 0.741989 | ||||

Coeff. | Standard Error | t Stat | p-Value | Lower 95% | Upper 95% | |

Intercept | 1.752226 | 0.048316 | 36.26633 | <0.0001 | 1.65341 | 1.851043 |

(X_{1}) Age Class | −0.11686 | 0.012902 | −9.05795 | <0.0001 | −0.14325 | −0.09048 |

(X_{2}) Facing Type | −0.0674 | 0.015325 | −4.398 | 0.000135 | −0.09874 | −0.03606 |

Regression Statistics | ||||||

Multiple R | 0.851898 | |||||

R^{2} | 0.72573 | |||||

Adjusted R^{2} | 0.710205 | |||||

Standard Error | 0.085461 | |||||

Observation | 57 | |||||

Analysis of Variance | ||||||

Variable | df | SQ | MQ | F | Significance F | |

Regression | 3 | 1.02425 | 0.341417 | 46.74671 | <0.0001 | |

Residual | 53 | 0.387088 | 0.007304 | |||

Total | 56 | 1.411338 | ||||

Coeff. | Standard Error | t Stat | p-Value | Lower 95% | Upper 95% | |

Intercept | 1.699911 | 0.042397 | 40.09515 | <0.0001 | 1.614874 | 1.784949 |

(X_{1}) Age Class | −0.1214 | 0.011338 | −10.7071 | <0.0001 | −0.14414 | −0.09866 |

(X_{2}) Facing Type | −0.06048 | 0.012872 | −4.69836 | <0.0001 | −0.0863 | −0.03466 |

(X_{3}) Gender | 0.109945 | 0.022826 | 4.816716 | <0.0001 | 0.064162 | 0.155728 |

Regression Statistics | ||||||

Multiple R | 0.881142 | |||||

R^{2} | 0.776411 | |||||

Adjusted R^{2} | 0.761986 | |||||

Standard Error | 0.08138 | |||||

Observation | 34 | |||||

Analysis of Variance | ||||||

Variable | df | SQ | MQ | F | Significance F | |

Regression | 2 | 0.712914 | 0.356457 | 53.82367 | <0.0001 | |

Residual | 31 | 0.205303 | 0.006623 | |||

Total | 33 | 0.918217 | ||||

Coeff. | Standard Error | t Stat | p-Value | Lower 95% | Upper 95% | |

Intercept | 1.553102 | 0.032839 | 47.29409 | <0.0001 | 1.486126 | 1.620078 |

(X_{1}^{2}) Square of Age Class | −0.01651 | 0.001839 | −8.97392 | <0.0001 | −0.02026 | −0.01275 |

(X_{2}) Facing Type | −0.0878 | 0.015752 | −5.57404 | <0.0001 | −0.11993 | −0.05568 |

Regression Statistics | ||||||

Multiple R | 0.905187 | |||||

R^{2} | 0.819363 | |||||

Adjusted R^{2} | 0.808942 | |||||

Standard Error | 0.074541 | |||||

Observation | 56 | |||||

Analysis of Variance | ||||||

Variable | df | SQ | MQ | F | Significance F | |

Regression | 3 | 1.310593 | 0.436864 | 78.62342 | <0.0001 | |

Residual | 52 | 0.288934 | 0.005556 | |||

Total | 55 | 1.599526 | ||||

Coeff. | Standard Error | t Stat | p-Value | Lower 95% | Upper 95% | |

Intercept | 1.535384 | 0.025014 | 61.38175 | <0.0001 | 1.48519 | 1.585578 |

(X_{1}^{2}) Square of Age Class | −0.01912 | 0.001419 | −13.4676 | <0.0001 | −0.02197 | −0.01627 |

(X_{2}) Facing Type | −0.08303 | 0.011298 | −7.34962 | <0.0001 | −0.1057 | −0.06036 |

(X_{3}) Gender | 0.078262 | 0.0202 | 3.874327 | 0.000301 | 0.037727 | 0.118796 |

Regression Statistics | ||||||

Multiple R | 0.959439 | |||||

R Square | 0.920523 | |||||

Adjusted R Square | 0.91441 | |||||

Standard Error | 0.043519 | |||||

Observation | 29 | |||||

Analysis of Variance | ||||||

df | SQ | MQ | F | Significance F | ||

2 | 0.57034 | 0.28517 | 150.5698 | <0.0001 | ||

26 | 0.049242 | 0.001894 | ||||

28 | 0.619582 | |||||

Coeff. | Standard Error | t Stat | p-Value | Lower 95% | Upper 95% | |

Intercept | 1.40423 | 0.019192 | 73.16787 | <0.0001 | 1.364781 | 1.44368 |

(X_{1}^{2}) Square of Age Class | −0.01788 | 0.00123 | −14.5316 | <0.0001 | −0.02041 | −0.01535 |

(X_{2}) Facing Type | −0.09804 | 0.008958 | −10.9452 | <0.0001 | −0.11646 | −0.07963 |

A | Y _{1} = 1.7522 − 0.1169X_{1} − 0.0674X_{2} | (3) | Isolated Pedestrians |

B | Y_{1} = 1.5531 − 0.0165X_{1}^{2} − 0.0878 X_{2} | (7) | Single pedestrians |

C | Y_{1} = 1.4042 − 0.0179X_{1}^{2} − 0.0980X_{2} | (11) | Groups |

D | Y_{2} = 1.6999 − 0.1214X_{1} − 0.0605X_{2} + 0.1099X_{3} | (5) | Isolated pedestrians |

E | Y_{2} = 1.5354 − 0.0191X_{1}^{2} − 0.0830X_{2} + 0.0783X_{3} | (9) | Single pedestrians |

where: | |||

Y_{1} | Mean walking speed | X_{2} | Facing type |

X_{1} | Age classes | X_{3} | Gender |

© 2017 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**

Pinna, F.; Murrau, R.
Isolated and Single Pedestrians and Pedestrian Groups on Sidewalks. *Infrastructures* **2017**, *2*, 21.
https://doi.org/10.3390/infrastructures2040021

**AMA Style**

Pinna F, Murrau R.
Isolated and Single Pedestrians and Pedestrian Groups on Sidewalks. *Infrastructures*. 2017; 2(4):21.
https://doi.org/10.3390/infrastructures2040021

**Chicago/Turabian Style**

Pinna, Francesco, and Roberto Murrau.
2017. "Isolated and Single Pedestrians and Pedestrian Groups on Sidewalks" *Infrastructures* 2, no. 4: 21.
https://doi.org/10.3390/infrastructures2040021