Optimization Model of Regional Traffic Signs for Inducement at Road Works
Abstract
:1. Introduction
2. Data Collection
2.1. Node Characteristics
2.2. Traffic Volume
2.3. Section Saturation
3. Model Construction and Solution
3.1. Existing Models
3.2. Model Building
3.3. Model Solving
4. Model Application
4.1. Calculate Node Importance
4.2. Determination of Index Weight
4.3. Calculation of Parameters of Objective Function at Alternative Points
4.4. Sensitivity Analysis of the Solution Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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ID | Decision Point or Not (1—Yes, 0—No) x1 | The Number of Decision Points Excluding the Construction Section x2 | The Number of Nodes That Intersect with the Construction Road x3 |
---|---|---|---|
1 | 1 | 3 | 1 |
2 | 1 | 2 | 0 |
3 | 0 | 0 | 0 |
4 | 1 | 1 | 0 |
5 | 1 | 3 | 1 |
8 | 1 | 3 | 1 |
9 | 1 | 3 | 1 |
11 | 1 | 3 | 1 |
12 | 1 | 3 | 0 |
13 | 1 | 2 | 0 |
14 | 1 | 1 | 0 |
15 | 1 | 2 | 0 |
16 | 1 | 3 | 1 |
17 | 0 | 0 | 0 |
18 | 1 | 1 | 0 |
19 | 1 | 2 | 1 |
20 | 1 | 3 | 1 |
21 | 1 | 2 | 1 |
22 | 1 | 3 | 1 |
26 | 1 | 3 | 1 |
27 | 1 | 2 | 0 |
28 | 1 | 3 | 1 |
29 | 0 | 0 | 0 |
ID | Decision Point or Not (1—Yes, 0—No) x1 | The Number of Decision Points Excluding the Construction Section x2 | The Number of Nodes That Intersect with the Construction Road x3 |
---|---|---|---|
1 | 1 | 3 | 0 |
2 | 1 | 2 | 1 |
3 | 0 | 0 | 1 |
4 | 1 | 1 | 1 |
5 | 1 | 3 | 0 |
8 | 1 | 3 | 0 |
9 | 1 | 3 | 0 |
11 | 1 | 3 | 0 |
12 | 1 | 3 | 1 |
13 | 1 | 2 | 1 |
14 | 1 | 1 | 1 |
15 | 1 | 2 | 1 |
16 | 1 | 3 | 0 |
17 | 0 | 0 | 1 |
18 | 1 | 1 | 1 |
19 | 1 | 2 | 0 |
20 | 1 | 3 | 0 |
21 | 1 | 2 | 0 |
22 | 1 | 3 | 0 |
26 | 1 | 3 | 0 |
27 | 1 | 2 | 1 |
28 | 1 | 3 | 0 |
29 | 0 | 0 | 1 |
ID | Decision Point or Not (1—Yes, 0—No) x1 | The Number of Decision Points Excluding the Construction Section x2 | The Number of Nodes that Intersect with the Construction Road x3 |
---|---|---|---|
1 | 0.39 | 0.86 | 0.96 |
2 | 0.39 | −0.08 | −1.04 |
3 | −2.58 | −1.97 | −1.04 |
4 | 0.39 | −1.03 | −1.04 |
5 | 0.39 | 0.86 | 0.96 |
8 | 0.39 | 0.86 | 0.96 |
9 | 0.39 | 0.86 | 0.96 |
11 | 0.39 | 0.86 | 0.96 |
12 | 0.39 | 0.86 | −1.04 |
13 | 0.39 | −0.08 | −1.04 |
14 | 0.39 | −1.03 | −1.04 |
15 | 0.39 | −0.08 | −1.04 |
16 | 0.39 | 0.86 | 0.96 |
17 | −2.58 | −1.97 | −1.04 |
18 | 0.39 | −1.03 | −1.04 |
19 | 0.39 | −0.08 | 0.96 |
20 | 0.39 | 0.86 | 0.96 |
21 | 0.39 | −0.08 | 0.96 |
22 | 0.39 | 0.86 | 0.96 |
26 | 0.39 | 0.86 | 0.96 |
27 | 0.39 | −0.08 | −1.04 |
28 | 0.39 | 0.86 | 0.96 |
29 | −2.58 | −1.97 | −1.04 |
ID | x1 | x2 | x3 | cj |
---|---|---|---|---|
0.380 | 0.081 | 0.539 | ||
1 | 1 | 3 | 0 | 0.536 |
2 | 1 | 2 | 1 | 0.930 |
3 | 0 | 0 | 1 | 0.464 |
4 | 1 | 1 | 1 | 0.861 |
5 | 1 | 3 | 0 | 0.536 |
8 | 1 | 3 | 0 | 0.536 |
9 | 1 | 3 | 0 | 0.536 |
11 | 1 | 3 | 0 | 0.536 |
12 | 1 | 3 | 1 | 1.000 |
13 | 1 | 2 | 1 | 0.930 |
14 | 1 | 1 | 1 | 0.861 |
15 | 1 | 2 | 1 | 0.930 |
16 | 1 | 3 | 0 | 0.536 |
17 | 0 | 0 | 1 | 0.464 |
18 | 1 | 1 | 1 | 0.861 |
19 | 1 | 2 | 0 | 0.466 |
20 | 1 | 3 | 0 | 0.536 |
21 | 1 | 2 | 0 | 0.466 |
22 | 1 | 3 | 0 | 0.536 |
26 | 1 | 3 | 0 | 0.536 |
27 | 1 | 2 | 1 | 0.930 |
28 | 1 | 3 | 0 | 0.536 |
29 | 0 | 0 | 1 | 0.464 |
Traffic Volume | Node Importance | Standard Deviation of Road Saturation | |
---|---|---|---|
Traffic volume | 1 | 1/1.75 | 3 |
Node importance | 1.75 | 1 | 5 |
Standard deviation of road saturation | 1/3 | 1/5 | 1 |
NO | Nodes Location | Weights | Z | ||
---|---|---|---|---|---|
Traffic Volume | Node Importance | Standard Deviation of Road Saturation | |||
32.7% | 56.2% | 11.1% | |||
1 | north–1 | 0.293 | 0.536 | 0.394 | 0.441 |
2 | east–1 | 0.324 | 0.536 | 0.347 | 0.446 |
3 | 1–28 | 0.416 | 0.536 | 0.277 | 0.468 |
4 | 28–1 | 0.416 | 0.536 | 0.421 | 0.484 |
5 | north–2 | 0.403 | 0.930 | 0.379 | 0.697 |
6 | 1–2 | 1.000 | 0.930 | 0.419 | 0.896 |
7 | 2–3 | 0.556 | 0.464 | 0.000 | 0.443 |
8 | 3–2 | 0.541 | 0.930 | 0.412 | 0.745 |
9 | 2–27 | 0.616 | 0.930 | 0.673 | 0.799 |
10 | 27–2 | 0.483 | 0.930 | 0.068 | 0.688 |
11 | 3–4 | 0.633 | 0.861 | 0.554 | 0.752 |
12 | 4–3 | 0.619 | 0.464 | 0.000 | 0.463 |
13 | 5–4 | 0.629 | 0.861 | 0.610 | 0.757 |
14 | 4–18 | 0.052 | 0.861 | 0.294 | 0.533 |
15 | 18–4 | 0.025 | 0.861 | 0.056 | 0.498 |
16 | north–5 | 0.416 | 0.536 | 0.239 | 0.464 |
17 | 6–5 | 0.641 | 0.536 | 0.218 | 0.535 |
18 | 5–16 | 0.570 | 0.536 | 0.149 | 0.504 |
19 | 7–8 | 0.068 | 0.536 | 0.403 | 0.368 |
20 | north–8 | 0.206 | 0.536 | 0.401 | 0.413 |
21 | 8–9 | 0.054 | 0.536 | 0.383 | 0.361 |
22 | 9–8 | 0.168 | 0.536 | 0.211 | 0.380 |
23 | 8–13 | 0.260 | 0.930 | 0.065 | 0.615 |
24 | 10–9 | 0.179 | 0.536 | 0.265 | 0.389 |
25 | north–9 | 0.077 | 0.536 | 0.376 | 0.368 |
26 | 9–12 | 0.186 | 1.000 | 0.440 | 0.672 |
27 | 10–11 | 0.343 | 0.536 | 0.372 | 0.455 |
28 | west–11 | 0.198 | 0.536 | 0.936 | 0.470 |
29 | south–11 | 0.087 | 0.536 | 0.830 | 0.422 |
30 | 11–12 | 0.149 | 1.000 | 0.254 | 0.639 |
31 | 12–13 | 0.382 | 0.930 | 0.060 | 0.654 |
32 | 22–12 | 0.303 | 1.000 | 0.432 | 0.709 |
33 | 21–13 | 0.386 | 0.930 | 0.015 | 0.651 |
34 | 13–14 | 0.355 | 0.861 | 0.786 | 0.687 |
35 | 14–13 | 0.311 | 0.930 | 0.057 | 0.631 |
36 | 14–15 | 0.410 | 0.930 | 0.566 | 0.720 |
37 | 15–14 | 0.363 | 0.861 | 0.987 | 0.712 |
38 | 20–14 | 0.314 | 0.861 | 0.201 | 0.609 |
39 | 15–17 | 0.142 | 0.464 | 0.000 | 0.307 |
40 | 17–15 | 0.131 | 0.930 | 0.549 | 0.626 |
41 | 15–16 | 0.493 | 0.536 | 0.959 | 0.569 |
42 | 16–15 | 0.501 | 0.930 | 0.589 | 0.752 |
43 | 19–15 | 0.605 | 0.930 | 0.519 | 0.778 |
44 | 16–18 | 0.056 | 0.861 | 0.064 | 0.509 |
45 | 18–16 | 0.093 | 0.536 | 0.068 | 0.339 |
46 | 17–18 | 0.042 | 0.861 | 0.229 | 0.523 |
47 | 18–17 | 0.030 | 0.464 | 0.000 | 0.271 |
48 | 19–20 | 0.190 | 0.536 | 0.923 | 0.466 |
49 | 20–19 | 0.135 | 0.466 | 0.244 | 0.333 |
50 | 25–19 | 0.500 | 0.466 | 0.388 | 0.468 |
51 | 20–21 | 0.190 | 0.466 | 0.424 | 0.371 |
52 | 21–20 | 0.138 | 0.536 | 1.000 | 0.457 |
53 | 24–20 | 0.203 | 0.536 | 0.855 | 0.463 |
54 | 23–21 | 0.158 | 0.466 | 0.100 | 0.325 |
55 | west–22 | 0.357 | 0.536 | 0.606 | 0.485 |
56 | south–22 | 0.257 | 0.536 | 0.595 | 0.451 |
57 | west–26 | 0.592 | 0.536 | 0.204 | 0.517 |
58 | south–26 | 0.530 | 0.536 | 0.282 | 0.506 |
59 | 25–26 | 0.620 | 0.536 | 0.280 | 0.535 |
60 | 26–27 | 0.653 | 0.930 | 0.209 | 0.759 |
61 | east–28 | 0.200 | 0.536 | 0.194 | 0.388 |
62 | north–28 | 0.293 | 0.536 | 0.338 | 0.435 |
63 | 28–27 | 0.709 | 0.930 | 0.308 | 0.789 |
64 | east–29 | 0.351 | 0.464 | 0.000 | 0.376 |
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Wang, L.; Zhang, H.; Shi, L.; He, Q.; Xu, H. Optimization Model of Regional Traffic Signs for Inducement at Road Works. Sustainability 2021, 13, 6996. https://doi.org/10.3390/su13136996
Wang L, Zhang H, Shi L, He Q, Xu H. Optimization Model of Regional Traffic Signs for Inducement at Road Works. Sustainability. 2021; 13(13):6996. https://doi.org/10.3390/su13136996
Chicago/Turabian StyleWang, Lianzhen, Han Zhang, Lingyun Shi, Qingling He, and Huizhi Xu. 2021. "Optimization Model of Regional Traffic Signs for Inducement at Road Works" Sustainability 13, no. 13: 6996. https://doi.org/10.3390/su13136996