Cell transmission model considering queuing characteristics of channelized zone at intersections

HUANG Wei; HU Yang

doi:10.19818/j.cnki.1671-1637.2023.02.015

Volume 23 Issue 2

Apr. 2023

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Article Contents

Abstract

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0. introduction

1. The Relationship Model between Linear Index of Ultra high Transition Section and Skiing Speed

2. Calculation of water skiing speed for small passenger cars in ultra-high transition section

3. The Influence of Linear Index of Ultra high Transition Section on the Skiing Speed of Small Passenger Cars

4. conclusion

References

Article Navigation > Journal of Traffic and Transportation Engineering > 2023 > 23(2): 212-224

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HUANG Wei, HU Yang. Cell transmission model considering queuing characteristics of channelized zone at intersections[J]. Journal of Traffic and Transportation Engineering, 2023, 23(2): 212-224. doi: 10.19818/j.cnki.1671-1637.2023.02.015

Citation:

HUANG Wei, HU Yang. Cell transmission model considering queuing characteristics of channelized zone at intersections[J]. Journal of Traffic and Transportation Engineering, 2023, 23(2): 212-224. doi: 10.19818/j.cnki.1671-1637.2023.02.015

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Cell transmission model considering queuing characteristics of channelized zone at intersections

doi: 10.19818/j.cnki.1671-1637.2023.02.015

HUANG Wei,
HU Yang

School of Intelligent Systems Engineering, Sun Yat-sen University, Guangzhou 510006, Guangdong, China

Funds:

National Natural Science Foundation of China 52102401

Guangdong Basic and Applied Basic Research Foundation 2019A1515111083

More Information

Author Bio:
HUANG Wei(1986-), female, associate professor, PhD, huangwei5@mail.sysu.edu.cn
Received Date: 2022-10-05
Available Online: 2023-05-09
Publish Date: 2023-04-25

Abstract

Abstract

In order to describe the evolution law of traffic flows at urban intersections more accurately, the signalized intersection with entrance widening areas and shared lanes was taken as the research object, and the cell transmission model (CTM) was improved by considering four practical factors: queue discharge process, divergence process, optional lane changing, and shared lanes. According to the geometric characteristics of the intersection, a method to divide cells at road sections was proposed based on lane groups. On this basis, the cell sending capacity function was adjusted to reflect and model the queue discharge process. The blocking factors were introduced in the divergence process modeling to describe the interaction of spatial queuing among different lane groups. The optional lane changing behavior in the transition zone was modeled with the goal of balancing the spatial queuing of adjacent lane groups, and the conflict effect of traffic flows with different directions was considered in the modeling of shared lanes. On the basis of an actual intersection, the maximum queue length of the lane group cycle was selected as the evaluation index to verify the effectiveness of the improved CTM. Test results show that the improved CTM can simultaneously estimate the queue lengths of different lane groups. With the increase in the proportion of through traffic flows, the estimation error of the improved CTM decreases. The mean absolute error (MAE), root mean square error (RMSE), and weighted mean absolute percentage error (WMAPE) of the maximum queue length at road sections are less than 16.43, 21.36 m, and 13.51%, respectively, under different traffic scenarios. Compared with the benchmark method, the improved CTM can reduce the MAE by 15.31%-90.03% for the maximum queue length at road sections under different scenarios, and the estimation accuracy under high-traffic scenarios improves more obviously. Thus, it can be seen that the improved CTM can more accurately describe the operational characteristics of traffic flow at intersections and improve the estimation accuracy of queue length, which can be used as an important basis for the traffic management and control.
- traffic management,
- queue length estimation,
- cell transmission model,
- signalized intersection,
- optional lane changing,
- shared lane

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0. introduction

It can be seen that existing research focuses on analyzing the influence of factors such as tire texture, road surface structure, vehicle load, and water film thickness on the speed of vehicle hydroplaning, and lacks research on the influence of highway geometry on hydroplaning speed, especially in special sections such as ultra-high transition sections where road water accumulation is significantly affected by geometry; In addition, due to the lack of comprehensive consideration of multivariate combinations such as rainfall and road geometry, the existing research on the critical speed of vehicle hydroplaning cannot scientifically guide the speed management of vehicles in flooded sections of highways under rainy weather.

1. The Relationship Model between Linear Index of Ultra high Transition Section and Skiing Speed

1.1 The relationship between water skiing speed and water film thickness

The principle behind the phenomenon of car tire skidding is as follows:Figure 1As shown, when the vehicle quickly enters the water accumulation area, the relative relationship between the water accumulation and the tires can be divided into three areas: in Zone I, there is a large dynamic water pressure between the water accumulation on the road surface and the tires, and the tires will be subjected to upward lifting force, resulting in the separation of the tire surface from the road surface; In Zone II, there is a thin water film separating the tread from the road surface, and only a portion of the tire is lifted; In Zone III, the tire tread is in full contact with the road surface without any water film. As the vehicle speed gradually increases, the length of zones I and II will continue to increase, and the range of zone III will gradually decrease to disappear. Eventually, the tire will completely separate from the road surface, resulting in tire skidding.

Figure 1. Hydroplaning status of tire

DownLoad: Full-Size Img PowerPoint

$F=0.285 h^{0.313} v^{2.01}$

(1)

$N=F=0.285 h^{0.313} v^{2.01}$

(2)

In the formula:NLoad on vehicle tires.

This article takes small passenger cars as the research model, considering the most common tire types and axle loads in small passenger cars as input variables for calculation. The typical tire type is determined to be 225/50R16 92V, and the axle load is 6.17 kN^[26]Obtain the vehicle's water skiing speedvCompared to the thickness of the water filmhThe relationship between them is

$v=128.65 h^{-0.156}$

(3)

1.2 超高过渡段水膜厚度计算方法

$h=0.068 L^{0.32} q^{0.41} d^{1.17} I^{-0.31}$

(4)

Figure 2. Paths of water flows

DownLoad: Full-Size Img PowerPoint

$T=\left[\frac{2 b}{g \sin (s)}\right]^{0.5}$

(5)

In the formula:TFor drainage time;bThe width of the road surface;gAcceleration due to gravity;sThe cross slope gradient of the road.

$\left\{\begin{array}{l} t=\frac{T}{M} \\ x_m=\frac{1}{2} g t^2 \sin \left(s_m\right) \\ y_m=\frac{1}{2} g t^2 \sin \left(i_m\right) \end{array}\right.$

(6)

In the formula:s_mFor the thmThe cross slope gradient of the road within the section;i_mFor the thmThe longitudinal slope gradient of the road within the section.

$p=\frac{b\left(S_2-S_1\right)}{D}$

(7)

By combining equations (5) to (7), the length of the water flow path can be obtainedLdo

$L=\sum\limits_{m=1}^M\left\{\left(s_0-\frac{p \sum\limits_{m=1}^{M-1} y_m}{b}\right) t^2+\frac{1}{2} g t^2 \sin \left(s_0-\frac{p \sum\limits_{m=1}^{M-1} y_m}{b}\right)+\right. \\ \left.\left[m g t^2 \sin \left(i_m\right)+\frac{1}{2} t^2 \sin \left(i_m\right)\right]^2\right\}$

(8)

$L=b^{0.31} i_m^{0, 61} p^{-0.89}$

(9)

Table 1. Fitting result

影响因素	标准误差	拟合优度
b	0.047	0.96
i_m	0.025
p	0.024

| Show Table

DownLoad: CSV

To verify the accuracy of equation (9), fluid simulation experiments were conducted for comparative verification. Based on the Fluent platform, establish a three-dimensional road model that is the same as the subsequent calculation of critical water skiing speed, and conduct 9 sets of simulation experiments on the length of water flow paths. One set of simulation results is as follows:Figure 3As shown.

Figure 3. Simulation result of flow path length

DownLoad: Full-Size Img PowerPoint

Figure 4. Comparison of theoretical calculation and simulation data

DownLoad: Full-Size Img PowerPoint

1.3 超高过渡段几何线形与滑水速度关系模型

$v=176.594 q^{-0.064} p^{0.044} i_m^{-0.03}\left(i_m^2+0.0004\right)^{0.024}$

(10)

2. Calculation of water skiing speed for small passenger cars in ultra-high transition section

From the force state of the tires during the water skiing process, it can be seen that the higher the vehicle's driving speed, the greater the water flow lifting force generated, and the more prominent the water skiing phenomenon. Therefore, the current maximum design speed of 120 km · h for Chinese highways is selected^-1To design speed control conditions. According to the relevant provisions of the "Highway Route Design Specification" (JTG D20-2017), the range of longitudinal slope gradient under this design speed is 0.3%~3.0%, and the range of superelevation gradient is 1/330~1/200. Wu Jianjun and others^[31]Research has found that short-term heavy rainfall has a greater impact on traffic safety. A rainfall of 50 mm or more within 3 hours is referred to as heavy rainfall, with rainfall intensity ranging from 20 to 80 mm · h^-1The range of factors affecting the speed of water skiing in the ultra-high transition section of this article is as follows:Table 2As shown.

Table 2. Ranges of influence factors

影响因素	纵坡坡度/%	超高渐变率	降雨强度/(mm·h^-1)
取值范围	0.3~3.0	1/330~1/200	20~80

| Show Table

DownLoad: CSV

Orthogonal experiments were conducted with longitudinal slope gradient, superelevation gradient rate, and rainfall intensity as variables to calculate the water skiing speed of small passenger cars in the superelevation transition section under multivariate combinations. The calculation results of water skiing speed when taking the extreme values of three influencing factors are as follows:Table 3As shown in the figure, it can be seen that for a two-way four lane expressway, the maximum water sliding speed of vehicles occurs at a longitudinal slope gradient of 0.3%, a superelevation gradient rate of 1/200, and a rainfall intensity of 20 mm · h^-1Under the combination, it is 115.5 km · h^-1The minimum value occurs when the longitudinal slope gradient is 3.0%, the superelevation gradient rate is 1/330, and the rainfall intensity is 80 mm · h^-1Under the combination, it is 99.3 km · h^-1.

Table 3. Hydroplaning speeds under extreme combinations of influencing factors

降雨强度/(mm·h^-1)	纵坡坡度/%	超高渐变率	滑水速度/(km·h^-1)
20	0.3	1/330	110.0
	0.3	1/200	115.5
	3.0	1/330	108.5
	3.0	1/200	112.9
80	0.3	1/330	101.6
	0.3	1/200	104.3
	3.0	1/330	99.3
	3.0	1/200	102.0

| Show Table

DownLoad: CSV

3. The Influence of Linear Index of Ultra high Transition Section on the Skiing Speed of Small Passenger Cars

3.1 超高渐变率的影响

Figure 5. Influence of superelevation gradient rate on hydroplaning speed

DownLoad: Full-Size Img PowerPoint

3.2 纵坡坡度的影响

Select rainfall intensities of 20, 40, 60, and 80 mm · h respectively^-1Calculate the water skiing speed of small passenger cars under different longitudinal slope gradients, and the results are as follows:Figure 6As shown, it can be seen that under the same rainfall intensity, the water skiing speed of small passenger cars decreases with the increase of longitudinal slope gradient; At different rainfall intensities, the minimum water skiing speed occurs when the longitudinal slope gradient is 3.0%, which prolongs the length of the water flow path, increases the thickness of the collected water film, and reduces the water skiing speed; Under different combinations of rainfall intensity and ultra-high gradient rate, when the longitudinal slope gradient increases from 0.3% to 3.0%, the water skiing speed of small passenger cars decreases by about 2.68%.

Figure 6. Influence of longitudinal slope on hydroplaning speed

DownLoad: Full-Size Img PowerPoint

3.3 纵坡坡度与超高渐变率的影响程度比较

To compare the impact of longitudinal slope gradient and super-high gradient on the water skiing speed of small passenger cars, calculate the difference between the maximum and minimum water skiing speeds of small passenger cars under different longitudinal slope gradient conditions, and obtain the range of water skiing speed caused by longitudinal slope gradient. Similarly, obtain the range of water skiing speed caused by super-high gradient gradientFigure 7As shown. causeFigure 7It can be seen that under different rainfall intensities, the range of water skiing speed caused by longitudinal slope gradient and superelevation gradient is relatively close, but the influence of longitudinal slope gradient is always greater than that of superelevation gradient; As the intensity of rainfall increases, the impact of both on water skiing speed decreases and tends to flatten out.

Figure 7. Extreme values of hydroplaning speed

DownLoad: Full-Size Img PowerPoint

3.4 Consider limiting the speed of small passenger cars on a two-way four lane highway for water skiing

Table 4. Recommended limit speeds of car at superelevation transition section km·h^-1

降雨强度/(mm·h^-1)	纵坡坡度/%	超高渐变率
降雨强度/(mm·h^-1)	纵坡坡度/%	1/330	1/300	1/250	1/225	1/200
20	0.3	110	110	110	115	115
	1.0	110	110	110	110	110
	2.0	105	105	110	110	110
	3.0	105	105	105	110	110
40	0.3	105	105	105	105	105
	1.0	100	100	105	105	105
	2.0	100	100	100	100	105
	3.0	100	100	100	100	100
60	0.3	100	100	100	100	100
	1.0	100	100	100	100	100
	2.0	100	100	100	100	100
	3.0	95	100	100	100	100
80	0.3	100	100	100	100	100
	1.0	100	100	100	100	100
	2.0	95	100	100	100	100
	3.0	95	95	100	100	100

| Show Table

DownLoad: CSV

4. conclusion

(2) Analyzed the influence of longitudinal slope gradient and superelevation gradient on the water skiing speed of small passenger cars in the superelevation transition section. When the rainfall intensity is constant, the water skiing speed increases with the increase of the super-high gradient rate. The increase in longitudinal slope gradient leads to an increase in the length of the water flow path, which in turn reduces the speed of water skiing. The influence of longitudinal slope gradient on water skiing speed is greater than that of superelevation gradient rate, but as the rainfall intensity increases, the influence of longitudinal slope gradient and superelevation gradient rate on water skiing speed tends to be gentle.

(4) The study considered the influence of longitudinal slope gradient and geometric shape factors of superelevation gradient on water skiing speed. Further research is needed to consider the water skiing speed in the superelevation transition section of drainage facilities and heavy-duty vehicles.

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Cell transmission model considering queuing characteristics of channelized zone at intersections

doi: 10.19818/j.cnki.1671-1637.2023.02.015