# Coordinated Control Method for Passive Bus Priority Arterials Considering Multi-Conversion Standard and Bus Stopping Time

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## Abstract

**:**

## 1. Introduction

## 2. Single Conversion Standard Delay Calculation Method

#### 2.1. Parameter Definition

#### 2.2. Single Conversion Standard

- (1)
- Taking the car as the conversion standard, convert the bus into a car to determine the input parameters of the total delay calculation, and calculate the total delay of all vehicles. The input parameters for the total delay calculation take the following values.

- (2)
- Based on the ratio of the number of cars to the converted number of buses, the delays of both vehicles are calculated simultaneously, and thus the average vehicle delay is determined.

#### 2.3. Analysis of Vehicle Characteristics Differences

#### 2.3.1. Acceleration

#### 2.3.2. Speed

#### 2.3.3. Bus Stops

## 3. Multi-Conversion Standard Delay Calculation Method

#### 3.1. By-Vehicle Type

- (1)
- Calculate the average car delay

- (2)
- Calculate the average bus delay

#### 3.2. By-Bus-Line Type

- (1)
- Taking the bus as the conversion standard, cars are converted into buses to calculate the vehicle arrival rate ${q}^{m}$.

- (2)
- Calculate the arrival and maximum departure rates of vehicles on each bus line based on the ratio of the number of vehicles entered on each bus line to the total number of converted buses.

- (3)
- Taking the number of vehicles ${N}_{bi}{}^{m}$, the speed ${v}_{bi}{}^{m}$, the arrival rate ${q}_{bi}{}^{m}$, and the maximum departure rate ${s}_{bi}{}^{m}$ as input parameters, the total delay ${D}_{bi}{}^{m}$ of each bus line is calculated, and then the average delay of each bus line ${d}_{bi}{}^{m}$ is obtained.

## 4. Coordinated Control Example and Simulation

#### 4.1. Coordinated Control Example

#### 4.1.1. Example Data Generation

- (1)
- Intersection Attribute Parameters

- (2)
- Traffic flow related parameters

- ${t}_{bi}$—stop time of bus line $i$;
- $v$—the speed of the bus;
- ${t}_{ad}$—acceleration and deceleration loss time;

- ${\alpha}_{a}$—the starting acceleration;
- ${\alpha}_{b}$—the braking deceleration.

- (3)
- Signal timing parameters

#### 4.1.2. Data Distribution of the Examples

- (1)
- Number of cars

- (2)
- Number of buses

- (3)
- The ratio of the number of buses to the number of cars

#### 4.1.3. Delay Calculation

#### 4.2. Simulation

#### 4.2.1. Construction of the Simulation Model

#### 4.2.2. Calibration of Simulation Parameters

- (1)
- The average delay and stopping time of vehicles were used as evaluation indicators, and the actual intersection data were counted.
- (2)
- A reasonable range of values and step sizes for the six parameters were determined, and the actual data from the statistics were input into the simulation model. The parameter values were changed for multiple simulations, and the average delay and stopping time for each inlet lane were extracted.
- (3)
- The simulated average vehicle delays and stopping times were compared with the statistical actual values to calculate the error for each simulation and determine the most suitable parameter combination. The errors before and after the parameter calibration were 25.5% and 20%, respectively, which were reduced by 5.5% and were more consistent with the actual operating conditions of the vehicle. The calibration results are shown in Table 2.

#### 4.2.3. Simulation Results

## 5. Delay Calculation Error Analysis

#### 5.1. Calculation Errors of Single Conversion Standard and By-Vehicle Type

- (1)
- Average delay of cars

- (2)
- Average delay of buses

#### 5.2. Calculation Errors of By-Vehicle Type and By-Bus-Line Type

## 6. Optimization Model for Coordinated Control of Bus Priority Arterial Road

#### 6.1. Stopping Time

#### 6.2. Impact of Stopping Time on Bus Delay

#### 6.3. Objective Function

- ${p}_{c}$ is the passenger capacity of the car;
- ${p}_{bi}{}^{down}$ is the passenger capacity of bus line $i$ in the downward direction;
- ${p}_{bi}{}^{up}$ is the passenger capacity of bus route $i$ in the upward direction.

#### 6.4. Model Construction

#### 6.5. Model Solving

## 7. Results and Analysis

#### 7.1. Validity Analysis

- (1)
- Average bus delay

- (2)
- Per capita delay

- (3)
- Average car delay

- (4)
- Average vehicle delay

#### 7.2. Sensitivity Analysis

#### 7.2.1. The Proportion of Buses

#### 7.2.2. Bus Passenger Capacity

#### 7.2.3. Bus Stopping Time

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Parameters | Definition |
---|---|

$l$ | Adjacent intersection spacing (m) |

$C$ | Intersection common signal period (s) |

${\lambda}^{m}$ | Downstream intersection arterial direction (coordinated control phase) green-signal ratio |

${O}^{m}$ | Relative phase difference of the downstream intersection to the upstream intersection (s) |

${N}_{c}{}^{m}$ | Number of cars in the direction of the downstream intersection arterials (vehicles) |

${N}_{b}{}^{m}$ | Number of buses in the direction of downstream intersection arterials (vehicles) |

${N}_{bi}{}^{m}$ | Number of vehicles of each bus line in the direction of the downstream intersection artery (vehicles) |

${v}_{c}{}^{m}$ | Speed of the car (m/s) |

${v}_{bi}{}^{m}$ | Speed of each bus line vehicle (m/s) |

${v}_{b}{}^{m}$ | Speed of all buses (m/s) |

$s$ | Saturated flow rate in the direction of the intersection arterial (pcu/hour) |

${q}^{m}$ | Vehicle arrival rate at downstream intersections (pcu/hour) |

${E}_{b}$ | Conversion factor for public transport vehicles |

Average Parking Spacing | Additional Parts of the Safety Distance | Multiplier Part of the Safety Distance | Minimum Headroom | Overtake the Maximum Deceleration of the Car | Maximum Deceleration of Overtaken Vehicles | |
---|---|---|---|---|---|---|

Default Value | 2 | 2 | 3 | 0.5 | −4 | −3 |

Calibration results | 2.2 | 2 | 3 | 0.5 | −4 | −3.5 |

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## Share and Cite

**MDPI and ACS Style**

Zou, L.; Li, Z.; Zhu, L.; Yu, Z.
Coordinated Control Method for Passive Bus Priority Arterials Considering Multi-Conversion Standard and Bus Stopping Time. *Appl. Sci.* **2023**, *13*, 3634.
https://doi.org/10.3390/app13063634

**AMA Style**

Zou L, Li Z, Zhu L, Yu Z.
Coordinated Control Method for Passive Bus Priority Arterials Considering Multi-Conversion Standard and Bus Stopping Time. *Applied Sciences*. 2023; 13(6):3634.
https://doi.org/10.3390/app13063634

**Chicago/Turabian Style**

Zou, Liang, Zhifan Li, Lingxiang Zhu, and Zhitian Yu.
2023. "Coordinated Control Method for Passive Bus Priority Arterials Considering Multi-Conversion Standard and Bus Stopping Time" *Applied Sciences* 13, no. 6: 3634.
https://doi.org/10.3390/app13063634