# The Effect of Speed Humps on Instantaneous Traffic Emissions

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## Abstract

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## 1. Introduction

## 2. Related Work

#### 2.1. Traffic-Calming and Emissions

#### 2.2. Cellular Automata and Traffic Flow

#### 2.3. Emission Models

## 3. Traffic Flow and Instantaneous Emission Models

#### 3.1. The Modified NaSch Model

- Acceleration If ${v}_{t}<{V}_{\mathrm{max}}$ then increase the speed of the vehicle$${v}_{t+1}\leftarrow min({v}_{t}+1,{V}_{\mathrm{max}})$$
- Deceleration If the speed hump is close enough then reduce the speed; if the vehicle is on the speed hump then reduce its velocity to its minimum. Otherwise the new velocity is given by the original deceleration rule of the NaSch model. For all cases also consider the distance to the front vehicle.$${v}_{t+1}=\left(\right)open="\{"\; close>\begin{array}{c}min({D}_{d},{d}_{n})\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{D}_{d}{v}_{t+1}\hfill \\ min(1,{d}_{n})\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{D}_{d}=0\hfill \\ min({v}_{t+1},{d}_{n})\phantom{\rule{4.pt}{0ex}}\mathrm{otherwise}\phantom{\rule{4.pt}{0ex}}\hfill \end{array}$$
- Randomization Decrease the velocity of the vehicle with brake probability P$${v}_{t+1}\leftarrow max({v}_{t+1}-1,0)$$
- Vehicle movement Update the position of the vehicle$${x}_{t+1}\leftarrow {x}_{t}+{v}_{t+1}$$

#### 3.2. Instantaneous Traffic Emission Model

## 4. Results and Discussion

#### 4.1. The Impact of Speed Humps on Average Velocity and Traffic Flow

#### 4.2. The Impact of Speed Humps on Instant Emissions

#### 4.2.1. The Impact of Speed Humps on CO${}_{2}$ Emissions

- a few speed humps at roads with low density of vehicles generate more CO${}_{2}$ than roads with high densities ($\rho =0.8$),
- a large number of speed humps at roads with low densities generates more CO${}_{2}$ than roads with low to middle densities ($\rho =0.3$).

#### 4.2.2. The Impact of Speed Humps on NO${}_{x}$ Emissions

#### 4.2.3. The Impact of Speed Humps on VOC Emissions

- for a moderate number of speed humps, a road with a low number of vehicles generates more VOC emissions than a highly occupied road ($\rho =0.8$),
- for a larger number of speed humps, a road with a high number of vehicles generates more VOC emissions than a low to middle density roads ($\rho =[0.1,0.3]$),
- for a large number of speed humps, a road with a low number of vehicles ($\rho =0.1$) produces a similar quantity of VOC emissions than a road with a moderate number of vehicles ($\rho =0.3$).

#### 4.2.4. The Impact of Speed Humps on PM Emissions

## 5. Conclusions

- There are at least three phases for traffic flow and pollutants emissions as a function of density, these phases are in the range: $0<\rho \le 0.12$ for the first phase, $0.12<\rho \le 0.48$ for the second phase, and $0.48<\rho \le 1$ for the third phase.
- For low density of vehicles, the rise on CO${}_{2}$, NO${}_{x}$ and PM emissions as we increase the number of speed humps on a lane provides evidence of the influence of speed humps on traffic emissions. We also found that slight variations on the position and distance between speed humps influence the generation of pollutants at low densities.
- For high density of vehicles, the impact of speed humps on average velocity and traffic flow may be ignored because most of the vehicles are not moving due to traffic jams.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**A sketch of the model, where the road is represented by an array of $L=1500$ equivalent to a lane of 11.25 km. Here, ${d}_{n}$ is the spatial-headway and ${D}_{d}$ is the number of empty cells between a vehicle and the closest speed hump ahead.

**Figure 3.**Average velocity as a function of density. The velocity indicates the average number of cells to move forward per simulation step, and the density $\rho =N/L$.

**Figure 4.**Flow J as a function of density. The flow is given as the average number of vehicles passing through a cell per simulation step, and the density $\rho =N/L$.

**Figure 5.**Flow and velocity as a function of speed humps. The flow is given as the average number of vehicles passing through a cell per simulation step, and the velocity indicates the average number of cells to move forward per simulation step.

Density $\mathit{\rho}$ | 3 sh | 61 sh | 66 sh | 71 sh |
---|---|---|---|---|

0.1 | 0.590 | 1.227 | 1.261 | 1.216 |

**Table 2.**Emission functions values; a is the acceleration of a vehicle; selected and reproduced from [51].

Pollutant | Vehicle Type | ${\mathit{E}}_{0}$ | ${\mathit{f}}_{1}$ | ${\mathit{f}}_{2}$ | ${\mathit{f}}_{3}$ | ${\mathit{f}}_{4}$ | ${\mathit{f}}_{5}$ | ${\mathit{f}}_{6}$ |
---|---|---|---|---|---|---|---|---|

CO${}_{2}$ | Petrol car | 0 | 5.53 $\times {10}^{-1}$ | 1.61 $\times {10}^{-1}$ | −2.89 $\times {10}^{-3}$ | 2.66 $\times {10}^{-1}$ | 5.11 $\times {10}^{-1}$ | 1.83 $\times {10}^{-1}$ |

NO${}_{x}$ | Petrol car ($a\ge -0.5$ m/s${}^{2}$) | 0 | 6.19 $\times {10}^{-4}$ | 8.00 $\times {10}^{-5}$ | −4.03 $\times {10}^{-6}$ | −4.13 $\times {10}^{-4}$ | 3.80 $\times {10}^{-4}$ | 1.77 $\times {10}^{-4}$ |

NO${}_{x}$ | Petrol car ($a<-0.5$ m/s${}^{2}$) | 0 | 2.17 $\times {10}^{-4}$ | 0 | 0 | 0 | 0 | 0 |

VOC | Petrol car ($a\ge -0.5$ m/s${}^{2}$) | 0 | 4.47 $\times {10}^{-3}$ | 7.32 $\times {10}^{-7}$ | −2.87 $\times {10}^{-8}$ | −3.41 $\times {10}^{-6}$ | 4.94 $\times {10}^{-6}$ | 1.66 $\times {10}^{-6}$ |

VOC | Petrol car ($a<-0.5$ m/s${}^{2}$) | 0 | 2.63 $\times {10}^{-3}$ | 0 | 0 | 0 | 0 | 0 |

PM | Petrol car | 0 | 0 | 1.57 $\times {10}^{-5}$ | −9.21 $\times {10}^{-7}$ | 0 | 3.75 $\times {10}^{-5}$ | 1.89 $\times {10}^{-5}$ |

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**MDPI and ACS Style**

Pérez-Sansalvador, J.C.; Lakouari, N.; Garcia-Diaz, J.; Hernández, S.E.P.
The Effect of Speed Humps on Instantaneous Traffic Emissions. *Appl. Sci.* **2020**, *10*, 1592.
https://doi.org/10.3390/app10051592

**AMA Style**

Pérez-Sansalvador JC, Lakouari N, Garcia-Diaz J, Hernández SEP.
The Effect of Speed Humps on Instantaneous Traffic Emissions. *Applied Sciences*. 2020; 10(5):1592.
https://doi.org/10.3390/app10051592

**Chicago/Turabian Style**

Pérez-Sansalvador, Julio César, Noureddine Lakouari, Jesus Garcia-Diaz, and Saúl E. Pomares Hernández.
2020. "The Effect of Speed Humps on Instantaneous Traffic Emissions" *Applied Sciences* 10, no. 5: 1592.
https://doi.org/10.3390/app10051592