# Analysis of Traffic Oversaturation Based on Multi-Objective Data

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Vissim Simulation Data

#### 2.2. Vehicle Formation

#### 2.3. Virtual Detector

#### 2.4. Quantitative Analysis of Oversaturation Degree

#### 2.4.1. TOSI—Temporal Oversaturation Severity Index

#### 2.4.2. SOSI—Spatial Oversaturated Severity Index

- (a).
- When queuing, the first vehicle of the queued needs to activate the detector, but the subsequent vehicle cannot activate the detector; that is, ${z}_{1,0}<{y}_{1}<{z}_{1,1}<{y}_{2}$, as shown in Figure 7;
- (b).
- When dissipating and the rear of the leading car leaving the detection area, the position of the head of the following car cannot make the detector active, that is: ${y}_{1}<{z}_{1,0}<{z}_{1,1}<{y}_{2}$, as shown in Figure 8;

- (a).
- If ${N}_{up}={N}_{down}\ne 0$ and $U{P}_{1}>DOW{N}_{1}$:$$SOSI=\frac{\mathrm{max}\{0,\text{}DOW{N}_{1}-(t-T)-{t}_{occ}\}+\mathrm{max}\{0,\text{}t-U{P}_{n}-{t}_{occ}\}+{{\displaystyle \sum}}_{n=2}^{j}\mathrm{max}\{0,DOW{N}_{n}-U{P}_{n-1}-{t}_{occ}\}}{{t}_{occ}}$$
- (b).
- If ${N}_{up}={N}_{down}\ne 0$ and $U{P}_{1}<DOW{N}_{1}$:$$SOSI=\frac{{{\displaystyle \sum}}_{n=1}^{j}\mathrm{max}\{0,DOW{N}_{n}-U{P}_{n}-{t}_{occ}\}}{{t}_{occ}}$$
- (c).
- If ${N}_{up}={N}_{down}+1$:$$SOSI=\frac{\mathrm{max}\left\{0,\text{}t-U{P}_{i}-{t}_{occ}\right\}+{{\displaystyle \sum}}_{n=2}^{j}\mathrm{max}\{0,DOW{N}_{n}-U{P}_{n}-{t}_{occ}\}}{{t}_{occ}}$$
- (d).
- If ${N}_{up}={N}_{down}-1$:$$SOSI=\frac{\mathrm{max}\left\{0,\text{}DOW{N}_{0}-\left(t-T\right)-{t}_{occ}\right\}+{{\displaystyle \sum}}_{n=2}^{j}\mathrm{max}\{0,DOW{N}_{n}-U{P}_{n-1}-{t}_{occ}\}}{{t}_{occ}}$$
- (e).
- If ${N}_{up}={N}_{down}=0$ and the detector is activated before the statistical period, but it never be inactivated during the statistical period;
- (f).
- If ${N}_{up}={N}_{down}=0$ and the detector is inactivated before the statistical period, but it never be activated during the statistical period.

- ${{N}^{\prime}}_{up}={{N}^{\prime}}_{down}=0$;
- ${{N}^{\prime}}_{up}=0\ne {{N}^{\prime}}_{down}$;
- ${{N}^{\prime}}_{up}\ne 0$, ${{N}^{\prime}}_{down}\ne 0$ and ${{UP}^{\prime}}_{i}<{{DOWN}^{\prime}}_{j}$.

- ${{N}^{\prime}}_{up}\ne 0$ and ${{N}^{\prime}}_{down}=0$;
- ${{N}^{\prime}}_{up}\ne 0$, ${{N}^{\prime}}_{down}\ne 0$ and ${{UP}^{\prime}}_{{i}^{\prime}}>{{DOWN}^{\prime}}_{{j}^{\prime}}$.

#### 2.5. Identification of Oversaturation Regime and Cause

#### 2.5.1. Identification of Oversaturation Regime

- The value of TOSI;
- $VE{H}_{{t}_{g,end},k}$, the number of vehicles in this movement at ${t}_{g,end}$;
- Whether the event $\mathcal{L}$ occur multiple times in consecutive cycles (this paper takes 2 or more occurrences in 4 cycles).

#### 2.5.2. Analysis of the Cause of Oversaturation

- (a).
- During the green time, the number of stop queues at ${t}_{i+1}$ is more than the number of stop queues at ${t}_{i}$;
- (b).
- During the green time, the length of a queue at ${t}_{i+1}$ is greater than the length of a queue at ${t}_{i}$;

- (a).
- The number of stop queues at ${t}_{i+1}$ is greater than the number of stop queues at ${t}_{i}$:$$count\left(Group{s}_{stop,{t}_{i}+1}\right)>count\left(Group{s}_{stop,{t}_{i}}\right)$$
- (b).
- If the number of stop queues at adjacent times is equal, the coordinate of the end of the queue at ${t}_{i+1}$ is greater than the coordinate of the end of the queue at ${t}_{i}$:$$\{\begin{array}{c}count\left(Group{s}_{stop,{t}_{i+1}}\right)=count\left(Group{s}_{stop,{t}_{i}}\right)\\ \mathrm{max}(Grou{p}_{m,{t}_{i+1}})>\mathrm{max}(Grou{p}_{m,{t}_{i}})\end{array}$$

## 3. Results

#### 3.1. Vehicle Formation and Virtual Detector

#### 3.2. Quantitative Analysis of Oversaturation

#### 3.3. Identification of Oversaturated Regimes

#### 3.4. Analysis of Cause of Oversaturation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Pulses of SOSI detectors in different scenes: (

**a**) When the green light starts and there is a stop queue in stop line, the first vehicle can pass the stop line without being affected by the spillback, and after the green time, the last vehicle cannot pass the stop line due to spillback; (

**b**) There is no stop queue before the green light starts and all vehicles can pass the stop line normally during the green time; (

**c**) There is no stop queue before the green light starts but the last vehicles cannot pass the stop line due to spillback; (

**d**) When the green light starts and there is a stop queue in stop line, all vehicles can pass the stop line normally during the green time; (

**e**) When the green light starts and there is a stop queue in stop line, the first vehicle cannot pass the stop line even the green light becomes red due to spillback; (

**f**) There is no stop queue before the green light starts and no vehicle passes the stop line during green time.

**Figure 15.**Corresponding vehicle formation of Figure 14.

**Figure 16.**Corresponding stop line virtual detector’s pulse of Figure 14.

**Figure 22.**Corresponding TOSI and SOSI of Figure 21.

**Figure 26.**Identification of abnormal queue in oversaturation (the trajectory space-time diagram corresponding to the traffic state).

Case Index | $\mathit{\mathcal{L}}$ | $\mathbf{Multiple}\text{}\mathit{\mathcal{L}}$ | $\mathbf{TOSI}{\varnothing}_{\mathit{T}\mathit{O}\mathit{S}\mathit{I}}$ | Regime of Oversaturation |
---|---|---|---|---|

1 | $\surd $ | $\surd $ | $\surd $ | Oversaturated operation |

2 | $\surd $ | $\surd $ | $\times $ | Recovery |

3 | $\surd $ | $\times $ | $\surd $ | Loading |

4 | $\surd $ | $\times $ | $\times $ | Recovery |

5 | $\times $ | $\surd $ | $\surd $ | Loading |

6 | $\times $ | $\surd $ | $\times $ | - |

7 | $\times $ | $\times $ | $\surd $ | Loading/Spillback |

8 | $\times $ | $\times $ | $\times $ | Undersaturation |

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**MDPI and ACS Style**

Huang, B.; Zhang, F.
Analysis of Traffic Oversaturation Based on Multi-Objective Data. *Sustainability* **2022**, *14*, 9043.
https://doi.org/10.3390/su14159043

**AMA Style**

Huang B, Zhang F.
Analysis of Traffic Oversaturation Based on Multi-Objective Data. *Sustainability*. 2022; 14(15):9043.
https://doi.org/10.3390/su14159043

**Chicago/Turabian Style**

Huang, Bingsheng, and Fusheng Zhang.
2022. "Analysis of Traffic Oversaturation Based on Multi-Objective Data" *Sustainability* 14, no. 15: 9043.
https://doi.org/10.3390/su14159043