# Autonomous Vehicles for Enhancing Expressway Capacity: A Dynamic Perspective

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## Abstract

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## 1. Introduction

- A theoretical analysis model framework for MTF capacity was established. In contrast to previous research, which only considered simplified MTF, this study considered the heterogeneity of HDVs, AVs, and CAVs, especially considering that CAVs could not communicate with the vehicles in front and degenerated into AVs.
- From the perspective of saturated headways, we demonstrated that, as AV and CAV technologies progress, the existing road infrastructure would still have an extremely large RC. Furthermore, we investigated RC formulation comprising deterministic and random expressions, which theoretically proved the scale effects of AV and CAV penetration rates on road operation efficiency.
- A simulation framework was developed to calculate the capacity of a single lane under a variable MPR. Based on numerical analysis, the theoretical model was verified, and a ROW reallocation method was analyzed for capacity enhancement.

## 2. Problem Description

#### 2.1. Fundamental Assumptions

- (1)
**Expressway segment without an on/off ramp****:**We considered the capacity of the freeway segment without considering ramps and off-ramps.- (2)
**Traffic flow composition:**Although there are two types of autonomous driving technologies, that is, AVs and CAVs, the micro behaviors of vehicles (including car following, lane changing, and CAV platooning) of different brands and technical levels (L1–L5) [38] are bound to be different. We simplified MTFs into three categories: HDVs, AVs, and CAVs. When a CAV follows an HDV or an AV, and there is no real-time interaction with the vehicle in front based on the internet-connected communication function, the CAVs degrade to AVs [14,24]. Section 2.2 provides details on those specific analyses.- (3)
**Steady flow:**For modeling traffic flow at the freeway segment, in this study, we assumed a fixed headway as an estimate of the mean headway for a given car-following scenario. This simplified the model analysis and solution process. To derive the macroscopic theoretical capacity formulation, the detailed effects of lane changes and dynamic CAV platooning processes at the microscopic level were not considered.

#### 2.2. Vehicle-Following Analysis

**Scenario (1): HDV following others.**This mode is referred to as H-O. Here, an HDV follows an HDV, an AV, or a CAV with a headway of ${h}_{HV}$. Considering that the following HDV does not communicate, information cannot be shared between vehicles. Therefore, when the longitudinal driving behavior (acceleration and deceleration) of the front car changes, the following car should identify it and take acceleration and deceleration measures (corresponding to human behavior). According to previous research [39,40,41], the average headway between HDVs is approximately 1.8–2.5 s.

**Scenario (2): AV following others.**This mode is referred to as A-O. Here, an AV follows an HDV, an AV, or a CAV with a headway of ${h}_{AV}$. Considering that the following car does not communicate, information cannot be shared between vehicles (similar to H-O). However, the following car can identify when the longitudinal driving behavior (acceleration and deceleration) of the front car changes using advanced sensing equipment and take corresponding acceleration and deceleration measures using autonomous technology. According to previous research [33,42,43], the average headway between AVs following other vehicles is approximately 0.9–2.0 s.

**Scenario (3): CAV following HDV/AV.**This mode is referred to as C-HA. Here, a CAV follows an HDV or AV, and there is no real-time interaction with the vehicle in front based on the internet-connected communication function. The CAV degenerates into an AV. Therefore, the CAV follows with a headway of ${h}_{AV}$.

**Scenario (4): CAV following CAV.**This mode is referred to as C-C. Here, the CAV follows with a headway of ${h}_{CAV}$. When a CAV follows a CAV, communication between them is possible, and the following vehicles share information through real-time communication. The car in front can share its subsequent longitudinal driving behavior (acceleration and deceleration) with the car behind it in advance, which allows synchronous changes in the driving behavior between the two cars. It can be considered that the two vehicles form a team when acceleration and deceleration changes are conducted simultaneously (a platoon). According to previous research [37,44,45], the average headway between CAVs following CAVs is approximately 0.5–1.1 s.

#### 2.3. CAV Platooning

#### 2.4. Capacity Assessment

#### 2.4.1. Reserved Capacity

#### 2.4.2. Monotonicity and Convexity of Capacity

## 3. Methodology

#### 3.1. Monte Carlo Simulation Framework

#### 3.2. Right-of-Way Allocation

## 4. Numerical Analyses

#### 4.1. Market Penetration Rate

#### 4.2. Platooning Rate

#### 4.3. Right-of-Way Management

## 5. Conclusions and Future Studies

#### 5.1. Conclusions

- (1)
- Owing to the improvement in the MPRs of AVs and CAVs in MTF, the capacity of the expressway system can be improved significantly. In an ideal scenario, where all CAVs operate at a 0.5 s headway, the maximum single-lane capacity of the expressway segment can reach 7200 pcu/h. However, the existing facilities still have a considerable RC under autonomous and connected vehicle scenarios.
- (2)
- In the future, traffic flow is expected to comprise HDVs, AVs, and CAVs simultaneously, and the capacity of mixture flow is expected to be quite complex (which can be affected by the MPRs of AVs and CAVs in MTF, saturation headway in multiple vehicle-following scenarios, and platooning rates of CAVs). Additionally, the capacity is convex to the MPRs of AVs and CAVs, which indicates that the growth in capacity is not linear (AVs and CAVs have a “scale effect” on capacity growth). In other words, the population of AVs and CAVs does not necessarily lead to a rapid increase in capacity when the MPR is >40%; therefore, the long-term operating efficiency of existing urban transportation facilities can be improved significantly.
- (3)
- In autonomous and connected vehicle environments, the ROW reallocation (the setting of dedicated lanes for CAVs) should be based on the MPR of CAVs, considering that it can improve the capacity of expressway segments. However, traffic flow should be sufficient enough to fulfill the dedicated lane to saturated (7200 pcu/h), rather than unsaturated levels.

#### 5.2. Future Studies

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**RC distribution under different PRs: ${P}_{HDV}:{P}_{AV}$:${P}_{CAV}$ = (

**a**) 90%:5%:5%, (

**b**) 60%:20%:20%, (

**c**) 30%:35%:35%, (

**d**) 30%:10%:60%, and (

**e**) 30%:60%:10%.

Variable | Description |
---|---|

HDV(s) | Human-driven vehicle(s) |

AV(s) | Autonomous vehicle(s) |

CAV(s) | Connective-and-autonomous vehicle(s) |

RC | Reserved capacity |

${P}_{HDV}$ | Penetration rate of HDVs in MTF |

${P}_{AV}$ | Penetration rate of AVs in MTF |

${P}_{CAV}$ | Penetration rate of CAVs in MTF |

${P}_{{h}_{HDV}}$ | Probability headway of ${h}_{HDV}$ occurring |

${P}_{{h}_{AV}}$ | Probability headway of ${h}_{AV}$ occurring |

${P}_{{h}_{CAV}}$ | Probability headway of ${h}_{CAV}$ occurring |

$\overline{h}$ | Average critical headway per cycle |

${C}_{HDV}$ | Capacity with only HDVs |

${C}_{MTF}$ | Capacity of MTF |

${C}_{RES}$ | Reserved capacity |

Lane Number | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 |
---|---|---|---|---|---|---|---|---|---|

$\begin{array}{c}\hfill MPR\hfill \\ \hfill ({P}_{HDV}:{P}_{AV}:{P}_{CAV})\hfill \end{array}$ | No | No | No | Yes | No | No | Yes | Yes | No |

(50:50:0) | 2880 | 2880 | 2880 | 0 | 2880 | 2880 | 0 | 0 | 2880 |

(45:45:10) | 2949.5 | 2949.5 | 2949.5 | 640 | 2880 | 2880 | 320 | 320 | 2880 |

(40:40:20) | 3049 | 3049 | 3049 | 1440 | 2880 | 2880 | 720 | 720 | 2880 |

(35:35:30) | 3183.2 | 3183.2 | 3183.2 | 2469 | 2880 | 2880 | 1234 | 1234 | 2880 |

(30:30:40) | 3361 | 3361 | 3361 | 3840 | 2880 | 2880 | 1920 | 1920 | 2880 |

(25:25:50) | 3596.4 | 3596.4 | 3596.4 | 5768 | 2880 | 2880 | 2880 | 2880 | 2880 |

(20:20:60) | 3908.6 | 3908.6 | 3908.6 | 7200 | 3000 | 3000 | 4320 | 4320 | 2880 |

(15:15:70) | 4332.3 | 4332.3 | 4332.3 | 7200 | 3333 | 3333 | 6720 | 6720 | 2880 |

(10:10:80) | 4926.6 | 4926.6 | 4926.6 | 7200 | 4000 | 4000 | 7200 | 7200 | 3920 |

(5:5:90) | 5802 | 5802 | 5802 | 7200 | 5080 | 5080 | 7200 | 7200 | 5800 |

(0:0:100) | 7200 | 7200 | 7200 | 7200 | 7200 | 7200 | 7200 | 7200 | 7200 |

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**MDPI and ACS Style**

Liu, C.-J.; Wang, F.-K.; Wang, Z.-Z.; Wang, T.; Jiang, Z.-H.
Autonomous Vehicles for Enhancing Expressway Capacity: A Dynamic Perspective. *Sustainability* **2022**, *14*, 5193.
https://doi.org/10.3390/su14095193

**AMA Style**

Liu C-J, Wang F-K, Wang Z-Z, Wang T, Jiang Z-H.
Autonomous Vehicles for Enhancing Expressway Capacity: A Dynamic Perspective. *Sustainability*. 2022; 14(9):5193.
https://doi.org/10.3390/su14095193

**Chicago/Turabian Style**

Liu, Cong-Jian, Fang-Kai Wang, Zhuang-Zhuang Wang, Tao Wang, and Ze-Hao Jiang.
2022. "Autonomous Vehicles for Enhancing Expressway Capacity: A Dynamic Perspective" *Sustainability* 14, no. 9: 5193.
https://doi.org/10.3390/su14095193