# The Double Lanes Cell Transmission Model of Mixed Traffic Flow in Urban Intelligent Network

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## Abstract

**:**

## 1. Introduction

## 2. Research Methodology

#### 2.1. The Analysis of Driving Characteristics

#### 2.1.1. Car-Following Model

- HV car-following model based on IDM

- AV car-following model based on ACC

- CAV car-following model based on CACC

#### 2.1.2. Vehicle Proportion Allocation

- AV is only degenerated by CAV following HV.
- When CAV forms a fleet, only the first vehicle of the fleet degenerates to AV.
- The mesoscopic model IDM does not consider the response time of vehicles in the same lane of the same road section.

#### 2.1.3. Analytical Expression of Traffic Flow

#### 2.2. Lane-Changing Judgment Mechanism

#### 2.2.1. Random Utility Theory

#### 2.2.2. Lane-Changing Revenue Model

**Figure 2.**The lane-changing scene of (

**a**) mesoscopic traffic flow model, and (

**b**) abstraction of double-lane traffic flow transfer.

#### 2.3. Double Lanes CTM

#### 2.3.1. Cell Connection

- Normal cell

- Convergent cell

- Divergent cell

#### 2.3.2. Dynamic Cell Transfer

## 3. Simulation Experiment Results

#### 3.1. Mixed-Traffic Flow Fundamental Diagram Considering Fleet

#### 3.2. Utility Function Calibration

#### 3.3. Dynamic Transmission Effect of Mixed-Traffic Flow

## 4. Conclusions and Discussion

- (1)
- With the increase of CAV penetrance rate $p$ and fleet size ${n}_{c}$, the capacity of mixed-traffic flow can be effectively improved, as well as the critical density and maximum flow.
- (2)
- When CAV penetration rate and fleet size are within a certain range, the capacity can be improved more clearly. When $p=0.4$, the maximum flow growth rate stays at a high level, and when fleet size ${n}_{c}$ is 6–8, the maximum flow growth rate is more than 2.5%.
- (3)
- Through analysis of simulation, it is verified that double lanes CTM established is in line with actual traffic flow change trend, proving effectiveness and feasibility of the model.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CAV | Connected and autonomous vehicle |

AV | Autonomous vehicle |

HV | Human driving vehicle |

CACC | Cooperative adaptive cruise control |

ACC | Adaptive cruise control |

OV | Optimal velocity |

GF | Generalized force |

FVD | Full velocity difference |

MVD | Multiple velocity difference |

CA | Cellular automata |

MITSIM | Microscopic traffic simulator |

CTM | Cell transmission model |

FIFO | First-in, first-out |

V2V | Vehicle to vehicle |

IDM | Intelligent Driver Model |

Symbol | Meaning |

${\dot{v}}_{IDM}(t)$ | Acceleration at moment $t$ of HV |

$v(t)$ | Speed at moment $t$ |

$\Delta v(t)$ | Difference between vehicle and the front at moment $t$ |

$h(t)$ | Distance headway between vehicle and the front at moment $t$ |

$\tilde{v}$ | Speed of free traffic flow |

$\tilde{s}$ | Minimum safety distance |

$a$ | Expected maximum acceleration |

$b$ | Expected deceleration |

$T$ | Expected safe time headway |

$\sigma $ | Acceleration index |

$l$ | Length of the vehicle |

${\dot{v}}_{ACC}(t)$ | Acceleration at moment $t$ of AV |

$\Delta t$ | Control step |

${v}_{CACC}(t+\Delta t)$ | $\mathrm{Speed}\text{}\mathrm{at}\text{}\mathrm{moment}\text{}t+\Delta t$ of CAV |

$e(t)$ | Error between actual and expected spacing at moment $t$ |

$\dot{e}(t)$ | $\mathrm{Differential}\text{}\mathrm{term}\text{}\mathrm{of}\text{}e(t)$ with respect to $t$ |

$k$ | Control coefficient |

$p$ | Penetration rate of intelligent vehicles |

${n}_{c}$ | Fleet size of CAV |

${P}_{CAV}$ | Probability of CAV fleet |

${P}_{AV}$ | Probability of AV |

${P}_{HV}$ | Probability of HV |

$U$ | Utility |

$A$ | The set of all candidate options for travelers |

$V$ | Fixed utility |

$\alpha $ | Unobservable random term |

${X}_{n}$ | Characteristic variable |

${\beta}_{n}$ | $\mathrm{Coefficient}\text{}\mathrm{of}\text{}{X}_{n}$ |

${P}_{11}$ | $\mathrm{Probability}\text{}\mathrm{of}\text{}\mathrm{going}\text{}\mathrm{straight}\text{}\mathrm{from}\text{}\mathrm{current}\text{}\mathrm{lane}\text{}{L}_{1}$ |

${P}_{12}$ | $\mathrm{Probability}\text{}\mathrm{of}\text{}\mathrm{changing}\text{}\mathrm{lanes}\text{}\mathrm{from}\text{}\mathrm{current}\text{}\mathrm{lane}\text{}{L}_{1}$$\text{}\mathrm{to}\text{}\mathrm{lane}\text{}{L}_{2}$ |

${P}_{21}$ | $\mathrm{Probability}\text{}\mathrm{of}\text{}\mathrm{changing}\text{}\mathrm{lanes}\text{}\mathrm{from}\text{}\mathrm{current}\text{}\mathrm{lane}\text{}{L}_{2}$$\text{}\mathrm{to}\text{}\mathrm{lane}\text{}{L}_{1}$ |

${P}_{22}$ | $\mathrm{Probability}\text{}\mathrm{of}\text{}\mathrm{going}\text{}\mathrm{straight}\text{}\mathrm{from}\text{}\mathrm{existing}\text{}\mathrm{lane}\text{}{L}_{2}$ |

$n(t)$ | The number of vehicles in cell on current step $t$ |

$S(t)$ | Supply of cell on current step $t$ |

$R(t)$ | Demand of cell on current step $t$ |

$f(t)$ | Actual traffic flow from one cell to another on time step $t$ |

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**Figure 7.**Fundamental diagram of different CAV fleet size and penetrance rate with (

**a**) $p=0.2$; (

**b**) $p=0.4$; (

**c**) $p=0.6$; (

**d**) $p=0.8$.

**Figure 9.**There are all HVs on the road under (

**a**) the free flow state; (

**b**) the state of ${L}_{1}$; (

**c**) the state of ${L}_{2}$ respectively showing the congestion expresses on different lands. When CAV penetration rate is 0.4 under (

**d**) the free flow state; (

**e**) the congestion state of ${L}_{1}$; (

**f**) the congestion state of ${L}_{2}$. Similarly, when CAV penetration rate is 0.8 under (

**g**) the free flow state; (

**h**) the congestion state of ${L}_{1}$; (

**i**) the congestion state of ${L}_{2}$.

Parameter | Unit | CAV Penetration Rate | ||
---|---|---|---|---|

$\mathit{p}=0$ | $\mathit{p}=0.4$ | $\mathit{p}=0.8$ | ||

${Q}_{i}$ | veh/h | 2050 | 2572 | 3085 |

${v}_{f}$ | km/h | 75.95 | 79.63 | 82.65 |

$w$ | km/h | 19.08 | 23.27 | 27.83 |

${k}_{crit}$ | veh/km | 26.99 | 32.30 | 37.25 |

${k}_{jam}$ | veh/km | 134.41 | 142.82 | 148.11 |

B | S.E. | Wals | df | Sig. | |
---|---|---|---|---|---|

$\overline{{k}_{1}}$ | 3.895 | 0.563 | 47.880 | 1 | 0.000 |

$\overline{{v}_{1}}$ | −4.287 | 0.544 | 62.062 | 1 | 0.000 |

$\Delta {k}_{12}$ | −2.643 | 0.721 | 13.448 | 1 | 0.000 |

$\Delta {v}_{12}$ | 3.279 | 0.919 | 12.729 | 1 | 0.000 |

Constant | 0.849 | 0.556 | 2.329 | 1 | 0.000 |

B | S.E. | Wals | df | Sig. | |
---|---|---|---|---|---|

$\overline{{k}_{2}}$ | 1.034 | 0.474 | 4.753 | 1 | 0.029 |

$\overline{{v}_{2}}$ | −1.570 | 0.758 | 4.293 | 1 | 0.038 |

$\Delta {k}_{21}$ | −2.752 | 0.686 | 16.102 | 1 | 0.000 |

$\Delta {v}_{21}$ | 3.436 | 0.924 | 13.842 | 1 | 0.000 |

Constant | −1.039 | 0.759 | 1.877 | 1 | 0.000 |

CL Has Been Predicted | Percentage Correction | |||
---|---|---|---|---|

0 | 1 | |||

CL has been predicted | 0 | 203 | 85 | 70.5 |

1 | 91 | 197 | 68.4 | |

Percentage in total | 69.4 |

CL Has Been Predicted | Percentage Correction | |||
---|---|---|---|---|

0 | 1 | |||

CL has been predicted | 0 | 165 | 123 | 57.3 |

1 | 107 | 181 | 62.8 | |

Percentage in total | 60.1 |

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## Share and Cite

**MDPI and ACS Style**

Tian, W.; Ma, J.; Qiu, L.; Wang, X.; Lin, Z.; Luo, C.; Li, Y.; Fang, Y. The Double Lanes Cell Transmission Model of Mixed Traffic Flow in Urban Intelligent Network. *Energies* **2023**, *16*, 3108.
https://doi.org/10.3390/en16073108

**AMA Style**

Tian W, Ma J, Qiu L, Wang X, Lin Z, Luo C, Li Y, Fang Y. The Double Lanes Cell Transmission Model of Mixed Traffic Flow in Urban Intelligent Network. *Energies*. 2023; 16(7):3108.
https://doi.org/10.3390/en16073108

**Chicago/Turabian Style**

Tian, Wenjing, Jien Ma, Lin Qiu, Xiang Wang, Zhenzhi Lin, Chao Luo, Yao Li, and Youtong Fang. 2023. "The Double Lanes Cell Transmission Model of Mixed Traffic Flow in Urban Intelligent Network" *Energies* 16, no. 7: 3108.
https://doi.org/10.3390/en16073108