Cascading Failures and Vulnerability Evolution in Bus–Metro Complex Bilayer Networks under Rainstorm Weather Conditions
Abstract
:1. Introduction
2. The Influence of Rainstorm on Bus–Metro CBN
2.1. The impact of rainstorm on roads and metro train tracks
2.2. The impact of rainstorm on vehicles
2.3. The impact of rainstorm on drivers and passengers
3. Models and Methods
3.1. Constructing the Bus–Metro CBN
3.1.1. Research Hypothesis
3.1.2. Symbolic Description of the Bus–Metro CBN
3.2. Cascading Failure Model of Bus–Metro CBN under Rainstorm Conditions
3.2.1. Passenger Flow Transfer Rules for Cascading Failures in Bus–Metro CBN
3.2.2. Cascading Failure Model based on CMLs
3.3. Vulnerability Analysis of Bus–Metro CBN under Rainstorm
4. Case Study
4.1. Research Area
4.2. Scenario Descriptions
4.3. Vulnerability Analysis of Bus–Metro CBN under Rainstorm Conditions
5. Conclusions and Recommendations
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Intensities of Rainfall | Influence on Bus–Metro CBN Operation |
---|---|
≥50 mm/24 h | Reduces the friction coefficient of road surfaces and increases the incidence of bus accidents. |
≥100 mm/24 h | Reduces the friction coefficient of road surfaces and increases the incidence of bus accidents; partial rail transit interruptions and delay. |
≥150 mm/24 h | Bus outage, delays, bus lines shrinkage; partial rail transit interruptions and delay, with orbiting system destroyed. |
Bus Stop | Bus Lines Operating at the Stop | Whether is a Transfer Stop |
---|---|---|
BAISHULIN | 258, 309, 706, 707 | No |
HONGHUJIE | 102, 103, 10, 12, 235, 28, 301, 506, 606, 702 | Yes |
… | … | … |
LUOMASHI | 706, 707 | No |
XIWUYUAN | 107, 703, 702 | No |
Bus line | No. of bus stops on the line | No. of transfer stops on the line |
4 | 8 | 3 |
20 | 4 | 1 |
… | … | … |
182 | 8 | 1 |
606 | 8 | 5 |
Metro station | Metro lines running through station | Whether is a transfer station |
ANYUANMEN | 2 | No |
BEIDAJIE | 1, 2 | Yes |
… | … | … |
ZHONGLOU | 2 | No |
WULUKOU | 1 | No |
Metro line | No. of metro stations on the line | No. of transfer stations on the line |
1 | 5 | 1 |
2 | 4 | 1 |
Network | Nodes | Edges | Average Degree | Average Path Length | Clustering Coefficient |
---|---|---|---|---|---|
Bus | 54 | 85 | 3.148 | 4.593 | 0.201 |
Metro | 8 | 7 | 1.750 | 2.286 | 0.000 |
Bus–Metro | 62 | 99 | 3.194 | 4.480 | 0.174 |
Scenario | s | α | ε1 | ε2 | Object of Research |
---|---|---|---|---|---|
1 | 1.00 | 0.3 | 0.2 | 0.2 | Impact of rainstorm on Bus–Metro CBN |
2 | 1.20 | 0.3 | 0.2 | 0.2 | |
3 | 1.40 | 0.3 | 0.2 | 0.2 | |
4 | 1.60 | 0.3 | 0.2 | 0.2 | |
5 | 1.80 | 0.3 | 0.2 | 0.2 | |
6 | 2.00 | 0.3 | 0.2 | 0.2 | |
7 | 1.00 | 0.0 | 0.2 | 0.2 | Impact of capacity tolerance on Bus–Metro CBN |
8 | 1.00 | 0.1 | 0.2 | 0.2 | |
9 | 1.00 | 0.2 | 0.2 | 0.2 | |
10 | 1.00 | 0.3 | 0.2 | 0.2 | |
11 | 1.00 | 0.4 | 0.2 | 0.2 | |
12 | 1.00 | 0.5 | 0.2 | 0.2 | |
13 | 1.00 | 0.3 | 0.2 | 0.2 | Influence of node coupling strength on Bus–Metro CBN |
14 | 1.00 | 0.3 | 0.4 | 0.2 | |
15 | 1.00 | 0.3 | 0.6 | 0.2 | |
16 | 1.00 | 0.3 | 0.8 | 0.2 | |
17 | 1.00 | 0.3 | 0.2 | 0.2 | Influence of edge coupling strength on Bus–Metro CBN |
18 | 1.00 | 0.3 | 0.2 | 0.4 | |
19 | 1.00 | 0.3 | 0.2 | 0.6 | |
20 | 1.00 | 0.3 | 0.2 | 0.8 |
Scenario | Variable | Value of Variable | Convergence Time (Step) | η(|N|) | η(R) | η(F) | V |
---|---|---|---|---|---|---|---|
1 | s | 1.00 | 14 | 0.355 | 0.615 | 0.318 | 0.429 |
2 | 1.20 | 8 | 0.145 | 0.314 | 0.217 | 0.227 | |
3 | 1.40 | 26 | 0.194 | 0.421 | 0.441 | 0.352 | |
4 | 1.60 | 15 | 0.532 | 0.740 | 0.583 | 0.618 | |
5 | 1.80 | 11 | 0.871 | 0.959 | 0.926 | 0.919 | |
6 | 2.00 | 10 | 0.871 | 0.962 | 0.923 | 0.919 | |
7 | α | 0.0 | 11 | 0.952 | 0.989 | 1.000 | 0.980 |
8 | 0.1 | 15 | 0.952 | 0.988 | 0.964 | 0.968 | |
9 | 0.2 | 15 | 0.790 | 0.898 | 0.799 | 0.829 | |
10 | 0.3 | 14 | 0.355 | 0.615 | 0.318 | 0.429 | |
11 | 0.4 | 43 | 0.161 | 0.293 | 0.136 | 0.197 | |
12 | 0.5 | 2 | 0.081 | 0.161 | 0.086 | 0.109 | |
7 | ε1 | 0.2 | 14 | 0.355 | 0.615 | 0.318 | 0.429 |
8 | 0.4 | 14 | 0.565 | 0.755 | 0.503 | 0.608 | |
9 | 0.6 | 14 | 0.565 | 0.766 | 0.542 | 0.624 | |
10 | 0.8 | 14 | 0.565 | 0.766 | 0.542 | 0.624 | |
11 | ε2 | 0.2 | 14 | 0.355 | 0.615 | 0.318 | 0.429 |
12 | 0.4 | 14 | 0.339 | 0.605 | 0.316 | 0.420 | |
13 | 0.6 | 14 | 0.403 | 0.656 | 0.327 | 0.462 | |
14 | 0.8 | 19 | 0.661 | 0.847 | 0.589 | 0.699 |
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Ma, F.; Liu, F.; Yuen, K.F.; Lai, P.; Sun, Q.; Li, X. Cascading Failures and Vulnerability Evolution in Bus–Metro Complex Bilayer Networks under Rainstorm Weather Conditions. Int. J. Environ. Res. Public Health 2019, 16, 329. https://doi.org/10.3390/ijerph16030329
Ma F, Liu F, Yuen KF, Lai P, Sun Q, Li X. Cascading Failures and Vulnerability Evolution in Bus–Metro Complex Bilayer Networks under Rainstorm Weather Conditions. International Journal of Environmental Research and Public Health. 2019; 16(3):329. https://doi.org/10.3390/ijerph16030329
Chicago/Turabian StyleMa, Fei, Fei Liu, Kum Fai Yuen, Polin Lai, Qipeng Sun, and Xiaodan Li. 2019. "Cascading Failures and Vulnerability Evolution in Bus–Metro Complex Bilayer Networks under Rainstorm Weather Conditions" International Journal of Environmental Research and Public Health 16, no. 3: 329. https://doi.org/10.3390/ijerph16030329