# Exploring Traffic Congestion on Urban Expressways Considering Drivers’ Unreasonable Behavior at Merge/Diverge Sections in China

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## Abstract

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## 1. Introduction

- Short distance between on/off-ramps, resulting in numerous merging and weaving sections along the expressway mainline. According to the 2017 annual traffic analysis report of China’s major cities [1], the average distance between the on/off-ramps of expressways are 850, 850, and 890 m in Beijing, Xiamen, and Dalian, respectively.
- Drivers do not strictly follow the “mainline priority” in the merge/weave sections along the urban expressway. Vehicles from on-ramp often enter the expressway after mandatory lane changing, forcing vehicles on the mainline to decelerate intensely to avoid collision.
- Strong interaction between expressways and their adjacent road network. On-ramps and off-ramps are directly connected with the road network. Due to the short ramp length, traffic flow disturbance and congestion that occurs in the local road network may quickly spread to the expressway mainline, and vice versa.
- Large traffic volume on the expressway. Although the expressway mileage reached about 9.0% of the whole road network in Beijing, the ratio of traffic volume transported by expressway reached about 34.3%.

## 2. Literature Review

#### 2.1. Traffic Congestion Detection

#### 2.2. Expressway Traffic Flow Model and Simulation

## 3. Methodology

#### 3.1. Basic Idea

- Cell length parameters were introduced to CTM to accurately describe the complex and variable geometric shapes of the expressway.
- The merge section is divided into three cells: the upstream mainline cell, on-ramp cell, and downstream mainline cell. On domestic roads, there is no clear rule that drivers must obey the “mainline vehicle priority,” so forced merges and crossing multi-lane merges are general phenomena which have a great effect on the expressway mainline. Therefore, the merge ratio was introduced to improve the traditional CTM, in which the “forced merge” behavior can be considered in the merge area.
- The diverge section is divided into three cells: the upstream mainline cell, off-ramp cell, and downstream mainline cell. On Chinese expressways, congestion often occurred in the expressway diverge section site. Due to local streets, the remaining capacity is limited, and the off-ramp queue often extends the mainline rapidly to congest the expressway. In order to describe such traffic operation features, we introduced the capacity parameters for the off-ramp. Compared with the traditional CTM, the capacity of the off-ramp cell is no longer infinite; instead, when the off-ramp traffic volume is larger than the capacity of the local street, congestion will generate on the off-ramp, and spread to the mainline.

- There is, at most, one on-ramp or off-ramp in a single cell.
- There is a single cell including an on-ramp (off-ramp) in the start (end) position of the cell series.
- The basic road section is formed by a single cell without an on-ramp (off-ramp).
- There is the same number of traffic lanes in a single cell.

#### 3.2. Improved CTM

_{max}is the capacity of the road section, namely, the maximum traffic flow rate of the road section; k

_{jam}is the congestion density; v

_{f}is the free flow speed; ω is the shock wave speed when congestion occurs; and k

_{A}and k

_{B}are the corresponding minimum and maximum density when the traffic volume is maximum in the trapezoidal fundamental diagram.

_{i}is introduced in the basic CTM, as shown in Figure 2, L

_{c}is the standardized cell length of traditional CTM. The length of cells can be an inequality in the improved CTM, and must be greater than L

_{c}, that the vehicle travels at the free flow speed within unit time. Clearly, we can set L

_{c}according to the simulating time step length.

_{c}in the latter shade part in Figure 1. Similarly, the number of vehicles received by downstream cell i + 1 only includes the number of vehicles within L

_{c}in cell i. Therefore, the actual transmission number that flows into cell i at time t is related to l

_{i}and L

_{c}, as shown in Equation (2):

_{i}(t) is the quantity of vehicles in cell i at time t; y

_{i}(t) is the actual transmission quantity of cell i to cell i + 1; N

_{i}(t) is the max quantity of vehicles in cell i at time t; Q

_{i}(t) is the max actual transmission quantity cell i at time t; ω is the shock wave speed; v

_{f}is the free flow speed.

#### 3.2.1. Basic Road Segment Cell Model

#### 3.2.2. Merge Section Cell Model

_{U}(t), the receiving flow is A

_{U}(t), and the sending flow is S

_{U}(t); while traffic flow output of cell R is f

_{R}(t), the receiving flow is A

_{R}(t), and the sending flow is S

_{R}(t); and traffic flow of cell D is f

_{D}(t), the receiving flow is A

_{D}(t), and the sending flow is S

_{D}(t). According to the definition of cell receiving flow and sending flow, the merge area meets the following restrictions:

_{D}(t) < S

_{U}(t)+ S

_{R}(t), assume that merge ratio of ramp cell R is r

_{R}(t), denoting the ratio of ramp volume entered mainline to mainline volume downstream, then,

_{R}(t) is introduced omto CTM model. In this paper, the merge ratio r

_{R}(t) is set as a certain value, which can express the fact that ramp vehicles do not fully obey the “mainline priority” rule. Equations (3), (6), and (7) constitute the fundamental model of the merge area based on the improved CTM.

#### 3.2.3. Diverge Section Cell Model

_{G}(t), the receiving flow is A

_{G}(t), and the sending flow is S

_{G}(t). Therefore, the off-ramp cell and mainline cell in the diverge section should meet the following restrictions:

_{G}(t), to denote the ratio of off-ramp volume to the mainline volume, and off-ramp capacity as C

_{G}, then

_{G}, is mostly determined by its connecting local street or local intersection. When the traffic demand exceeds the off-ramp capacity, the vehicle in the off-ramp will get stuck in the off-ramp cell, and cause traffic congestion, and even spread to the mainline. Formulas (3) and (9) constitute the basic diverge section model, based on the improved CTM.

## 4. Simulation

#### 4.1. Road General Condition

#### 4.2. Parameter Calibration

## 5. Simulation Results

#### 5.1. Density/Delay Spatiotemporal Distribution

#### 5.2. Sensitivity Analysis & Discussion

#### 5.2.1. Effect of On-Ramp Traffic Volume on Mainline Traffic Congestion

_{R}as the ratio of the number of on-ramp vehicles to the number of vehicles on mainline of expressway. Four scenarios of different merge rate r

_{R}values were studied, in which r

_{R}= 0.2, 0.3, 0.4, and 0.5, in each.

_{R}, illustrated in Figure 10.

_{R}, in addition, the increasing rate of delay decreases gradually. Further analysis can reveal the concrete effect of on-ramp traffic volume. When the merge rate r

_{R}increases from 0.2 to 0.3, the delay in the merge area (Cell 5) and weaving area (Cell 10) increases by 35% and 34%, respectively. When the merge rate, r

_{R}, increases from 0.3 to 0.4, the delay in the merge area (Cell 5) and weaving area (Cell 10) increases by 26% and 25%. This phenomenon reveals that when merge rate r

_{R}increases, more vehicles will enter the merge/weave section, and interact with expressway mainline vehicles, and more disturbance will be generated in the traffic flow, due to the numerous unreasonable forced merging vehicles from on-ramp, and congestion will generate more frequently.

#### 5.2.2. Effect of Off-Ramp Capacity on Mainline Traffic Congestion

_{G}is mostly determined by local streets. To this end, we conducted simulation under different off-ramp capacity C

_{G}conditions. Six scenarios of different off-ramp capacity were studied, in which C

_{G}= 500, 600, 700, 800, 900, and 1000 veh/hr, in each. Traffic data were collected from 10:00 to 11:00, on 16 December 2017, and applied for simulation. Delay in four diverge cells (No. 6, 17, 24, 27) was collected from simulation, which are shown in the Figure 11.

_{G}increasing. For diverge Cell 6, when C

_{G}increases by 100 veh/hr, the delay of cell 6 decreases by about 10%. For Cell 17 and Cell 24, in the former part, the diverge cell delay decreases with C

_{G}increasing and, in the latter part, when C

_{G}reaches 700 veh/hr, the delay of the diverge cell is basically unchanged. Similarly, when C

_{G}reaches 600 veh/hr, delay of the diverge for Cell 27 remains unchanged. To sum up, the capacity of local street will determine capacity of off-ramp, which has a strong effect on operating state at expressway mainline. As a result, traffic congestion occurring in the local road network will quickly spread to the expressway mainline, and even cause congestion.

#### 5.3. Discussion

- Typical urban expressway or freeway traffic characteristics in China. Due to the common phenomena of sudden lane changing on urban road, merge rates were applied in the improved CTM in conformity with changing lane behaviors on an urban expressway or freeway.
- Exploring the design and layout methods for ramps on urban expressway or freeway. This paper provided theoretical basis for verifying the rationality of the ramp design and analyzing the traffic capacity.
- Making freeway or expressway traffic control and management methods. This paper proposed an appropriate simulative method to traffic control and management on the urban expressway or freeway.

## 6. Conclusions

- Most traffic congestion generates originally at merge, diverge, and weaving sections, then propagates to the next section upstream.
- Merge section congestion in an urban expressway is mostly caused by unreasonable driving behaviors, such as mandatory merging and lane-changing from on-ramp. Due to vehicles from on-ramp not obeying the “mainline priority” rule, on-ramp vehicles entering the merge section cell occupy a considerable ratio of the mainline capacity (sending flow), and the merge rate was used to represent the phenomena, and the delay of the merge and weaving sections increase between 25%–35% with the merge rate changed in the range of 0.2–0.4.

_{G}increasing per 100 veh/hr. Due to the unmatched capacity of off-ramp, the vehicle queue length often exceeds the off-ramp, and extends the mainline upstream. As a result, in the vehicle queue end, a dynamic bottleneck is generated at the diverge section, which reduces the capacity (receiving flow) of the diverge section cell.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Schematic configuration of CTM. (* Cited from Daganzo [20]).

Coefficient | |||||
---|---|---|---|---|---|

Not Standardized Coefficient | Standardized Coefficient | T | Sig. | ||

B | Standardized Error | Beta | |||

speed | 218.310 | 14.141 | 2.445 | 15.438 | 0.000 |

speed ^ 2 | −3.013 | 0.158 | −3.017 | −19.053 | 0.000 |

constant term | 1635.770 | 282.139 | 5.798 | 0.000 |

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

Simulation Time Length, T | hour | 24 |

Time Step interval, σ | second | 10 |

Mainline Capacity, Q_{max} | veh/hr | 5400 |

On-Ramp Capacity, Qr_{max} | veh/hr | 1200 |

Free Flow Speed, v_{f} | km/h | 75 |

Traffic Back Propagation Speed, ω | km/h | 25 |

Jam Density, k_{jam} | veh/(km × ln) | 122 |

On-Ramp Merge Ratio, r_{R} | __ | 0.3 |

Off-Ramp Diverge Ratio, r_{G} | __ | 0.1 |

Off-Ramp Capacity Local Street, C _{Gi} (i = 6, 10, 12, 17, 24, 27) | veh/hr | (1000, 1200, 1100, 800, 1200, 2000) |

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**MDPI and ACS Style**

Long, K.; Lin, Q.; Gu, J.; Wu, W.; Han, L.D.
Exploring Traffic Congestion on Urban Expressways Considering Drivers’ Unreasonable Behavior at Merge/Diverge Sections in China. *Sustainability* **2018**, *10*, 4359.
https://doi.org/10.3390/su10124359

**AMA Style**

Long K, Lin Q, Gu J, Wu W, Han LD.
Exploring Traffic Congestion on Urban Expressways Considering Drivers’ Unreasonable Behavior at Merge/Diverge Sections in China. *Sustainability*. 2018; 10(12):4359.
https://doi.org/10.3390/su10124359

**Chicago/Turabian Style**

Long, Kejun, Qin Lin, Jian Gu, Wei Wu, and Lee D. Han.
2018. "Exploring Traffic Congestion on Urban Expressways Considering Drivers’ Unreasonable Behavior at Merge/Diverge Sections in China" *Sustainability* 10, no. 12: 4359.
https://doi.org/10.3390/su10124359