# An Agent-Based Model of Heterogeneous Driver Behaviour and Its Impact on Energy Consumption and Costs in Urban Space

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## Abstract

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## 1. Introduction

_{2}that is harmful for the environment. During a well-to-wheel (WTW) analysis of ICEV and EV efficiency, Ref. [4] found that EVs, when using renewable energy, can reach an efficiency level of 40 to 70% depending on the location and environmental factors. In contrast, gasoline- and diesel-powered ICEVs had an WTW energy efficiency of 11–27% and 25–37%, respectively. Almost all vehicle manufacturing companies have started building and testing EV/PHEVs for the commercial market [5,6]. Governments are facilitating benefits to persuade people to replace ICEVs with EVs through economic incentives or legislation. However, not all countries have renewable technology to power these vehicles; some countries, such as China, still depend on coal to power the majority of their electric grid infrastructure [7,8]. In Australia, only 24% of electricity is generated from renewable sources [9]. In their review of EVs and their impact on the climate, Ref. [10] found that vehicles using electricity from sources with lower global warming potentials (GWP) [11] are better than ICEVs. In contrast, Ref. [12] found it was counterproductive to promote EV uptake in countries where electricity is produced from fossil fuels. The statistics mentioned above reaffirm the need to explore the impact these technologies have on future cities.

## 2. Background

## 3. Model Description

#### 3.1. Purpose

#### 3.2. Variables

- The vehicle mass parameter, drawn from a random uniform distribution between 1000 and 3000 kg (inclusive), allows the model to simulate a wider variety of vehicle types, from sedans to SUVs and hatchback. The rationale behind this distribution was to try intersect the EV and ICEV vehicle types, which larger vehicles such as vans or trucks are not part of; the model distributes vehicles arbitrarily across the environment with varying weights (source [39]).
- The top speed measure is between 30 and 45 mph (48, 72 km/h) and is only applied to vehicles that do not adhere to speed limits. This measure is applied only if Speed Adherence is ≥1 (source [40]).
- The gap acceptance parameter can be between 1 to 10 for each vehicle. The variable assigns a distance between two vehicles in meters. This ensures a wider variety of visual impairment is captured as some people with healthier eyes keep a fair distance from vehicles in front usually adhering to the 2-s rule compared to people with worse vision. Furthermore, the distance had to be relative to the average road distance in the model.

- The number of vehicles generated in the model, N. This can be between 1 and 500. However, this can be adjusted depending on the compute power accessible. The hardware accessible at the time of writing this article could only efficiently simulate up to 500 vehicles in 3D space while yielding valid results (refer to the Conclusions section for more on this limitation).
- The speed adherence variable can be between $0\le x\le N$. This quantifies the proportion of vehicles that will not adhere to the speed limits applied to the road they are driving on.
- The urban road network consists of 1295 roads which vehicles drive on and 354 intersections which consist of traffic rules (Algorithm 1, Ref. [28]). The road network has been designed to depict a small urban town.

#### 3.3. Model Overview

#### 3.4. Agent

#### 3.5. Environment

- (A) A two-way local road with a speed limit of 20 mph (32 km/h);
- (B) A two-way corner road with a speed limit of 10 mph (16 km/h);
- (C) A two-way fixed road with a speed limit of 30 mph (48 km/h);
- (D) An eight-way intersection. Right-of-way is for traffic on horizontal lanes, and the speed limit is 10 mph (16 km/h);
- (E) A two-way t-junction. Right-of-way is for horizontal lanes, and the speed limit is 10 mph (16 km/h).

## 4. Results

- That it produces outputs at a time resolution of 15 min; our model, on the other hand, has a time resolution of 1 s. This way, we can capture finer detail such as the impact of traffic lights on acceleration/deceleration and momentary traffic congestion;
- That it only captures trips that are split into commuters and non-commuters. Thus, the modelled scenarios revolve around two profiles of drivers. Our model manipulates the entire system from the street network to traffic rules and vehicles; thus, no single driver profile is modelled, but a heterogeneous set of behaviours are captured.

#### 4.1. Electric Energy Consumption Calculation

- For Equation (A3), F is calculated by using the following parameter variables: $\theta =0$ as the surface area is flat, ${C}_{D}=0.33$, $A=3.078\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ (where height = 1.71 m, width = 1.80 m), m = 1925 kg (Table 3), $a=\frac{\mathsf{\Delta}v}{\mathsf{\Delta}t}$, where $\mathsf{\Delta}v$ is the velocity change over time period $\mathsf{\Delta}t$, and lastly, v = velocityMagnitude (Table 2).

#### 4.2. Experiments

#### 4.2.1. Fuel Consumption of Internal Combustion Engine Vehicle Fleet

- For Equation (A3), F is calculated by using the following parameter variables: $\theta =0$ as the surface area is flat, ${C}_{D}=0.341$, $A=2.851\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ (where height = 1.469 m, width = 1.941 m), m = 1635 kg (Table 5), $a=\frac{\mathsf{\Delta}v}{\mathsf{\Delta}t}$ where $\mathsf{\Delta}v$ is the velocity change over time period $\mathsf{\Delta}t$, and lastly, v = velocityMagnitude (Table 2).

#### 4.2.2. Monetary Costs of Fuel and Electric Consumption

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Energy Calculation

- F is the force provided by the engine driving the vehicle forward (N);
- m is the mass of the vehicle (kg);
- g is the gravitational acceleration (m/s
^{2}); - $\theta $ is the angle of the surface on which the vehicle is driving on;
- $\rho $ is the density of air (1.225 kg/m
^{3}); - ${C}_{D}$ is the drag coefficient;
- A is the reference area of the vehicle (m
^{2}) (width × height); - v is the velocity (m/s), and;
- ${C}_{rr}$ is the coefficient of rolling resistance.

## Appendix B

#### Tables

Variable | Output Type |
---|---|

VelocityChange | Float |

Acceleration | Float |

Deceleration | Float |

Braking Energy (kWh) ^{1} | Float |

Drag_Force | Float |

Acceleration_Force | Float |

Total_Force | Float |

Drag_Work | Float |

Acceleration_Work | Float |

Total_Work | Float |

Energy_Input (kWh) | Float |

Energy_Input_Sum (kWh) | Float |

^{1}An amount of energy is generated every time a vehicle brakes (decelerates), also known as regenerative braking. This is accounted for in the notebook using the braking energy formula from the following source: [77].

MC | PHEV | ICEV |
---|---|---|

1 | 0.60 | 0.92 |

2 | 0.43 | 0.56 |

3 | 0.22 | 0.34 |

4 | 1.93 | 4.42 |

5 | 1.50 | 2.25 |

6 | 0.67 | 1.22 |

7 | 2.79 | 5.66 |

8 | 1.72 | 3.71 |

9 | 1.12 | 1.98 |

## Appendix C

#### Appendix C.1. Figures

**Figure A2.**Thetotal sum of electric costs (GBP) for each PHEV, model conditions 4 to 6. Where (

**D**): 50 vehicles, 50 non-adherence, (

**E**): 50 vehicles, 25 non-adherence and (

**F**): 50 vehicles, 0 non-adherence.

**Figure A3.**The total sum of electric costs (GBP) for each PHEV, model conditions 7 to 9. Where (

**G**): 100 vehicles, 100 non-adherence, (

**H**): 100 vehicles, 50 non-adherence and (

**I**): 100 vehicles, 0 non-adherence.

**Figure A4.**The total sum of petrol costs (GBP) for each ICEV, model conditions 4 to 6. Where (

**D**): 50 vehicles, 50 non-adherence, (

**E**): 50 vehicles, 25 non-adherence and (

**F**): 50 vehicles, 0 non-adherence.

**Figure A5.**The total sum of petrol costs (GBP) for each ICEV, model conditions 7 to 9. Where (

**G**): 100 vehicles, 100 non-adherence, (

**H**): 100 vehicles, 50 non-adherence and (

**I**): 100 vehicles, 0 non-adherence.

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**Figure 1.**Workflow diagram depicting processes the UTS undergoes during run-time including the Energy Calculation Extension.

**Figure 2.**Urban Street Network roads and intersections (source: [28]).

**Figure 3.**Model output comparison: electric energy consumption (kWh) against distance travelled (km), with 15 vehicles over a 1 h drive cycle (5 vehicles break speed limits).

**Figure 5.**Distribution of the cumulative energy consumption (kWh) for each experiment condition: (

**a**) 10 vehicles, 10 non-adherence; (

**b**) 10 vehicles, 5 non-adherence; (

**c**) 10 vehicles, 0 non-adherence; (

**d**) 50 vehicles, 50 non-adherence; (

**e**) 50 vehicles, 25 non-adherence; (

**f**) 50 vehicles, 0 non-adherence; (

**g**) 100 vehicles, 100 non-adherence; (

**h**) 100 vehicles, 50 non-adherence; (

**i**) 100 vehicles, 0 non-adherence.

**Figure 8.**The total sum of petrol/electric costs (GBP) for each experiment condition across all vehicles.

**Figure 9.**The total sum of electric costs (GBP) for each PHEV, model conditions 1 to 3. Where (

**A**): 10 vehicles, 10 non-adherence, (

**B**): 10 vehicles, 5 non-adherence and (

**C**): 10 vehicles, 0 non-adherence.

**Figure 10.**The total sum of petrol costs (GBP) for each ICEV, model conditions 1 to 3. Where (

**A**): 10 vehicles, 10 non-adherence, (

**B**): 10 vehicles, 5 non-adherence and (

**C**): 10 vehicles, 0 non-adherence.

**Table 1.**Model entities and parameter values (source: [28]).

Entity | Parameter | Values |
---|---|---|

Vehicle | Mass | [1000, 3000] (kg) |

Top speed | [30, 45] (mph), [48, 72] (km/h) | |

Gap acceptance | [1, 10] (m) | |

Environment | N. of vehicles | [1, 500] |

Speed adherence | [0, N] | |

Roads | 1295 | |

Intersections | 354 |

Variable | Output Type |
---|---|

AgentID | Integer |

xAxisPos | Float |

zAxisPos | Float |

collisions | Integer |

topSpeed (mph) | Float |

currentSpeed (mph) | Float |

distanceOfTravel (meters) | Float |

gapAcceptance (raycastLength) | Integer |

tractionControl | Bool |

velocityMagnitude | Float |

vehicleMass | Integer |

downforce | Float |

date-time | DateTime |

Parameter | Value |
---|---|

Height (m) | 1.71 |

Width (m) | 1.80 |

k | 65% (source [56]) ^{1} |

m (kg) | 1925 |

${C}_{D}$ | 0.33 |

^{1}The official engine efficiency statistic is not provided by the vehicle manufacturer; therefore, an average engine efficiency for PHEVs was acquired from the cited academic source.

Variable | Low Adherence | Medium Adherence | High Adherence |
---|---|---|---|

Low Density | Condition 1, 10 vehicles, 10 non-adherence | Condition 2, 10 vehicles, 5 non-adherence | Condition 3, 10 vehicles, 0 non-adherence |

Mid Density | Condition 4, 50 vehicles, 50 non-adherence | Condition 5, 50 vehicles, 25 non-adherence | Condition 6, 50 vehicles, 0 non-adherence |

High Density | Condition 7, 100 vehicles, 100 non-adherence | Condition 8, 100 vehicles, 50 non-adherence | Condition 9, 100 vehicles, 0 non-adherence |

**Table 5.**Vehicle parameters (source [61]) (ICEV).

Parameter | Value |
---|---|

Height (m) | 1.469 |

Width (m) | 1.941 |

k | 0.33% ([62]) ^{1} |

m (kg) | 1635 |

${C}_{D}$ | 0.341 |

^{1}The official engine efficiency statistic is not provided by the vehicle manufacturer; therefore, an average engine efficiency for ICEVs was acquired from the cited source.

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**MDPI and ACS Style**

Olmez, S.; Thompson, J.; Marfleet, E.; Suchak, K.; Heppenstall, A.; Manley, E.; Whipp, A.; Vidanaarachchi, R. An Agent-Based Model of Heterogeneous Driver Behaviour and Its Impact on Energy Consumption and Costs in Urban Space. *Energies* **2022**, *15*, 4031.
https://doi.org/10.3390/en15114031

**AMA Style**

Olmez S, Thompson J, Marfleet E, Suchak K, Heppenstall A, Manley E, Whipp A, Vidanaarachchi R. An Agent-Based Model of Heterogeneous Driver Behaviour and Its Impact on Energy Consumption and Costs in Urban Space. *Energies*. 2022; 15(11):4031.
https://doi.org/10.3390/en15114031

**Chicago/Turabian Style**

Olmez, Sedar, Jason Thompson, Ellie Marfleet, Keiran Suchak, Alison Heppenstall, Ed Manley, Annabel Whipp, and Rajith Vidanaarachchi. 2022. "An Agent-Based Model of Heterogeneous Driver Behaviour and Its Impact on Energy Consumption and Costs in Urban Space" *Energies* 15, no. 11: 4031.
https://doi.org/10.3390/en15114031