Queue length estimation model for mixed traffic flow of intelligent connected vehicles and human-driven vehicles
Ningbo CAO1(),Jiahui CHEN2,Liying ZHAO3,*()
1. College of Transportation Engineering, Chang’an University, Xi’an 710061, China 2. School of Automation, Northwestern Polytechnical University, Xi’an 710129, China 3. School of Economics and Management, Xi’an University of Technology, Xi’an 710048, China
A dynamic queue length estimation model based on probability statistics and Bayesian theorem was proposed, to solve the problem of queue length estimation at intersections with mixed traffic of intelligent connected vehicles (ICVs) and human-driven vehicles (HDVs). Firstly, taking into account factors such as the position, speed, and penetration rate of ICVs in the queue, models for estimating the queue lengths of observable and unobservable queues, as well as the penetration rate, were constructed. Real-time estimation of queue lengths and penetration rate was achieved through iteration. Then, the distribution characteristics of ICVs in the queue under different penetration rate conditions were simulated using random seeds. The estimation accuracy of the model under different traffic conditions was analyzed. Comparison analysis with existing models showed that, under low penetration rate conditions of ICVs (10%) during off-peak hours, the average absolute percentage error (MAPE) of the proposed model was 29.35%, while the existing model had an MAPE of 59.68%; during peak hours, the MAPE of this model was 26.50%, compared to 34.66% for the existing model. Under high penetration rate conditions of ICVs (90%) during off-peak hours, the MAPE of this model was 6.90%, while the existing model had an MAPE of 17.85%; during peak hours, the MAPE of this model was 1.45%, compared to 1.05% for the existing model, with similar errors. The proposed queue estimation model for mixed traffic of ICVs and human-driven vehicles has better estimation accuracy under both low and high penetration rate conditions.
Ningbo CAO,Jiahui CHEN,Liying ZHAO. Queue length estimation model for mixed traffic flow of intelligent connected vehicles and human-driven vehicles. Journal of ZheJiang University (Engineering Science), 2024, 58(9): 1935-1944.
Fig.1Observation diagram of vehicle queuing process
Fig.2Construction and validation flowchart of queue length estimation model
Fig.3Schematic diagram of simplified queuing status
条件
${P_{\text{e}}} $
G=0
G=1
G=2
G=3
G=4
G=5
$\lambda = 3,p = 10 $%
0.16
0.23
0.17
0.12
0.09
0.06
$\lambda = 3,p = 20 $%
0.31
0.34
0.17
0.09
0.05
0.02
$\lambda = 3,p = 30 $%
0.44
0.37
0.13
0.04
0.01
0.01
$\lambda = 3,p = 40 $%
0.56
0.35
0.07
0.02
0.00
0.00
$\lambda = 3,p = 50 $%
0.66
0.30
0.04
0.00
0.00
0.00
$\lambda = 4,p = 10 $%
0.20
0.28
0.18
0.12
0.08
0.05
$\lambda = 4,p = 20 $%
0.37
0.37
0.15
0.06
0.03
0.01
$\lambda = 4,p = 30 $%
0.51
0.37
0.09
0.02
0.01
0.00
$\lambda = 4,p = 40 $%
0.63
0.32
0.04
0.01
0.00
0.00
$\lambda = 4,p = 50 $%
0.73
0.25
0.02
0.00
0.00
0.00
Tab.1Probability of queue errors
Fig.4Schematic diagram of intersection data selection
Fig.5Queue length estimation process
开始时间
$C$/s
${N^{\text{C}}}$
${T_{\text{g}}}$/s
${\text{Lane1}}$
${\text{Lane2}}$
${\text{Lane3}}$
14:30
167
46
46
5.76
5.71
5.70
18:20
167
43
46
9.49
10.19
10.47
Tab.2Queue length survey data
${N^{{\text{All}}}}$
${N^{{\text{ICV}}}}$
${N^{{\text{HDV}}}}$
$p$/%
$\widehat p$/%
777
156
621
20.07
19.03
Tab.3Results of penetration rate estimation
Fig.6MAPE during off-peak and peak hours based on proposed model
时段
seed
${Q_{{\text{a}}}} $
$\bar {{Q_{{\text{a}}}}} $
${Q_{{\text{p}}}} $
$ \bar{{ Q_{{\text{p}}}}} $
MAE
A-MAE
MAPE /%
A-MAPE /%
14:30— 16:30 (非高峰)
8
5.63
5.63
4.53
4.46
1.10
1.17
19.61
20.86
10
5.63
4.31
1.32
23.38
12
5.63
4.53
1.10
19.58
18:20— 20:20 (高峰)
8
10.03
10.03
8.84
8.59
1.19
11.83
14.33
10
10.03
8.58
1.45
1.44
14.46
12
10.03
8.36
1.67
16.68
Tab.4Estimated queue lengths based on proposed model
Fig.7MAPE during off-peak and peak hours based on proposed model ($p = 20\text{%} $)
$p $/%
${Q_{\text{a}}} $
${Q_{\text{p}}} $
MAE
MAPE/%
$\widehat p $/%
10
5.63
3.98
1.65
29.35
9.90
20
5.63
4.08
1.54
27.47
18.28
30
5.63
4.21
1.41
25.09
29.60
50
5.63
4.92
0.70
12.48
54.24
80
5.63
5.07
0.55
9.89
78.63
90
5.63
5.24
0.38
6.90
92.02
Tab.5Estimated queue lengths during off-peak hours based on proposed model under different penetration rates
$p $/%
${Q_{\text{a}}} $
${Q_{\text{p}}} $
MAE
MAPE/%
$\widehat p $/%
10
10.03
7.37
2.66
26.50
10.12
20
10.03
7.86
2.17
21.65
21.36
30
10.03
8.14
1.89
18.85
28.64
50
10.03
9.31
0.72
7.16
50.95
80
10.03
9.73
0.30
3.03
79.59
90
10.03
9.88
0.15
1.45
90.51
Tab.6Estimated queue lengths during peak hours based on proposed model under different penetration rates
Fig.8MAPE during off-peak and peak hours based on Bayesian theorem ($p = 20\text{%} $)
$p $/%
${Q_{\text{a}}} $
${Q_{\text{p}}} $
MAE
MAPE/%
$\widehat p $/%
10
5.63
8.99
3.36
59.68
9.90
20
5.63
7.71
2.08
36.91
18.28
30
5.63
4.06
1.67
29.72
29.60
50
5.63
6.87
1.24
22.06
54.24
80
5.63
6.68
1.05
18.65
78.63
90
5.63
6.63
1.00
17.85
92.02
Tab.7Estimated queue lengths during off-peak hours based on Bayesian theorem under different penetration rates
$p $/%
${Q_{\text{a}}} $
${Q_{\text{p}}} $
MAE
MAPE/%
$\widehat p $/%
10
10.03
6.55
3.48
34.66
10.12
20
10.03
7.11
2.92
29.11
21.36
30
10.03
12.45
2.42
24.08
28.64
50
10.03
9.39
0.64
6.42
50.95
80
10.03
9.80
0.23
2.33
79.59
90
10.03
9.92
0.11
1.05
90.51
Tab.8Estimated queue lengths during peak hours based on Bayesian theorem under different penetration rates
Fig.9MAPE of proposed model and Bayesian theorem model with different variables
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