Optimization Models of Actuated Control Considering Vehicle Queuing for Sustainable Operation
Abstract
:1. Introduction
2. Literature Review
3. Vehicle Queuing Model Based on Improved Traffic Wave Model
3.1. Improved Traffic Wave Model
3.2. Vehicle Queuing and Dispersion Process
3.2.1. Vehicle Queuing Process
3.2.2. Vehicle Dispersion Process
3.3. Vehicle-Queuing Model
4. Optimization Models of Basic Parameters
4.1. Minimal Green Time Optimization Model
4.2. Maximal Green Time Optimization Model
5. Solving Algorithm for the Optimization Model
5.1. Variable Coding
5.2. Fitness Function
5.3. Genetic Manipulation
6. Verification
6.1. Verification of Minimal Green Time Calculation Model
6.2. Verification of Maximal Green Time Calculation Model
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Phase Schemes | Schematic Diagrams |
---|---|
F1 | |
F2 | |
F3 | |
F4 | |
Phase Schemes | Objective Function and Constraints | |
---|---|---|
F1 | Delay | |
Capacity | ||
Constraints | ||
F2 | Delay | |
Capacity | ||
Constraints | ||
F3 | Delay | |
Capacity | ||
Constraints | ||
F4 | Delay | |
Capacity | ||
Constraints |
Index | Simulation Time (s) | HCM Model (s) | Relative Error | Optimization Model (s) | Relative Error |
---|---|---|---|---|---|
1 | 22.40 | 22.80 | 1.79% | 21.60 | 3.57% |
2 | 20.80 | 22.80 | 9.62% | 21.60 | 3.85% |
3 | 23.80 | 25.40 | 6.72% | 25.20 | 5.88% |
4 | 19.79 | 22.80 | 15.21% | 21.60 | 9.15% |
5 | 20.00 | 22.80 | 14.00% | 21.60 | 8.00% |
6 | 26.34 | 29.40 | 11.62% | 28.60 | 8.58% |
7 | 21.20 | 23.00 | 8.49% | 22.00 | 3.77% |
8 | 22.65 | 24.60 | 8.61% | 23.40 | 3.31% |
9 | 21.30 | 22.80 | 7.04% | 21.60 | 1.41% |
10 | 21.56 | 22.80 | 5.75% | 21.60 | 0.19% |
11 | 21.30 | 22.80 | 7.04% | 21.60 | 1.41% |
12 | 22.62 | 24.60 | 8.75% | 23.40 | 3.45% |
13 | 21.70 | 22.80 | 5.07% | 21.60 | 0.46% |
14 | 24.38 | 22.80 | 6.48% | 21.60 | 11.40% |
15 | 21.79 | 22.80 | 4.64% | 21.60 | 0.87% |
16 | 21.90 | 23.40 | 6.85% | 23.80 | 8.68% |
17 | 20.52 | 22.80 | 11.11% | 21.60 | 5.26% |
18 | 22.40 | 24.60 | 9.82% | 23.40 | 4.46% |
19 | 18.36 | 21.00 | 14.38% | 19.80 | 7.84% |
20 | 19.51 | 21.00 | 7.64% | 19.80 | 1.49% |
21 | 21.00 | 22.80 | 8.57% | 21.60 | 2.86% |
22 | 26.10 | 28.30 | 8.43% | 27.60 | 5.75% |
23 | 20.33 | 21.00 | 3.30% | 19.80 | 2.61% |
24 | 16.90 | 19.20 | 13.61% | 18.00 | 6.51% |
25 | 24.13 | 27.20 | 12.72% | 26.40 | 9.41% |
26 | 24.89 | 27.20 | 9.28% | 26.40 | 6.07% |
27 | 21.12 | 22.80 | 7.95% | 21.60 | 2.27% |
28 | 18.57 | 20.60 | 10.93% | 19.80 | 6.62% |
29 | 20.80 | 21.00 | 0.96% | 19.80 | 4.81% |
30 | 26.58 | 28.20 | 6.09% | 28.00 | 5.34% |
Queue Length (m) | Simulation Time (s) | HCM Model | Optimization Model | ||
---|---|---|---|---|---|
Time (s) | Relative Error | Time (s) | Relative Error | ||
25 | 9.92 | 11.56 | 18.13% | 10.06 | 3.90% |
35 | 12.01 | 13.20 | 10.41% | 12.13 | 3.39% |
45 | 18.41 | 19.73 | 7.29% | 19.13 | 3.83% |
55 | 21.82 | 23.54 | 8.42% | 22.53 | 4.84% |
65 | 24.54 | 26.17 | 7.94% | 25.22 | 4.91% |
Average relative error | 10.44% | 4.18% |
Traffic Flow Direction | Traffic Volume (pcu/h) | Saturated Flow (pcu/h) | Ratio | |
---|---|---|---|---|
SB | TH | 912 | 2750 | 0.33 |
LT | 356 | 1550 | 0.23 | |
NB | TH | 832 | 2750 | 0.30 |
LT | 144 | 1550 | 0.09 | |
WB | TH | 288 | 2450 | 0.08 |
LT | 428 | 2150 | 0.20 | |
EB | TH | 248 | 2750 | 0.09 |
LT | 216 | 1550 | 0.14 |
Phase Schemes | Index | WB LT (s) | B TH (s) | NB LT (s) | SB TH (s) | EB LT (s) | WB TH (s) | SB LT (s) | NB TH (s) |
---|---|---|---|---|---|---|---|---|---|
F1 | ① | 32 | 15 | 37 | 54 | 32 | 15 | 37 | 54 |
② | 18 | 22 | 20 | 53 | 17 | 23 | 20 | 53 | |
F2 | ① | 24 | 10 | 39 | 39 | 24 | 10 | 39 | 39 |
② | 25 | 15 | 36 | 36 | 14 | 26 | 36 | 36 | |
F3 | ① | 16 | 16 | 18 | 24 | 16 | 16 | 18 | 24 |
② | 13 | 13 | 12 | 36 | 13 | 13 | 22 | 26 | |
F4 | ① | 12 | 12 | 20 | 20 | 12 | 12 | 20 | 20 |
② | 10 | 10 | 22 | 22 | 10 | 10 | 22 | 22 |
Phase Schemes | Index | Average Vehicle Delay (s) | Traffic Capacity (pcu/h) | Optimization Ratio |
---|---|---|---|---|
F1 | ① | 59.62 | 4279 | / |
② | 42.69 | 4472 | 12.79% | |
F2 | ① | 24.75 | 3185 | / |
② | 24.15 | 3742 | 10.75% | |
F3 | ① | 26.07 | 3328 | / |
② | 22.57 | 3741 | 11.45% | |
F4 | ① | 7.84 | 7733 | / |
② | 7.57 | 7668 | 2.10% | |
Average optimization ratio | 9.27% |
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Wang, X.; Wu, X.; Liu, J. Optimization Models of Actuated Control Considering Vehicle Queuing for Sustainable Operation. Sustainability 2022, 14, 8998. https://doi.org/10.3390/su14158998
Wang X, Wu X, Liu J. Optimization Models of Actuated Control Considering Vehicle Queuing for Sustainable Operation. Sustainability. 2022; 14(15):8998. https://doi.org/10.3390/su14158998
Chicago/Turabian StyleWang, Xinyue, Xianyu Wu, and Jiarui Liu. 2022. "Optimization Models of Actuated Control Considering Vehicle Queuing for Sustainable Operation" Sustainability 14, no. 15: 8998. https://doi.org/10.3390/su14158998