Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks
Abstract
:1. Introduction
- (i)
- First, we abstract the interdependent networks into various CPS models and attack at a fixed ratio to obtain the influence of different methods on enhancing the robustness of interdependent networks.
- (ii)
- Second, the high betweenness centrality and high eigenvector centrality swapping inter-links strategies have a better performance than other methods in enhancing G and in all CPS models, respectively.
2. Literature Review
3. The Model
3.1. Interdependent Networks Model
3.2. Cascading Failures Model
- This node must belong to the giant component of its network;
- The node must have at least one inter-link from other networks.
- All nodes are removed, and the interdependent networks are completely collapsing;
- The rest of the nodes both obey conditions I and II. These nodes will not continue to fail nor propagate failures. In this case, the interdependent networks achieve a steady state.
4. The Method
4.1. Strategy 1: Low Degree (LD)
4.2. Strategy 2: High Degree (HD)
4.3. Strategy 3: Low Betweenness (LB)
4.4. Strategy 4: High Betweenness (HB)
4.5. Strategy 5: Low Eigenvector Centrality (LEC)
4.6. Strategy 6: High Eigenvector Centrality (HEC)
5. Simulation Results and Analysis
- All swapping strategies perform better than NONE in improving G and . The values of G are clearly bigger in swapping strategies than NONE when increases. For example, the values of G in NONE are lower than the other strategies when in Figure 5a. When , the value of G in NONE is lower than other strategies in Figure 6b. This situation can be observed in all four subfigures in Figure 5, Figure 6 and Figure 7.
- In Figure 5, Figure 6 and Figure 7, all curves can be divided into three categories. The first is NONE, which shows the worst performance in improving system reliability. The second is swapping inter-links by low centrality values, which are LD, LB, and LEC strategies. Although they show better performance than NONE in enhancing G and , they are not the best choices to achieve more robust systems. The last category is swapping inter-links with high centrality values. High centrality swapping strategies increase the values of G and . We should adopt a high centrality value swapping strategy for improving system reliability. This finding is the same conclusion as in [39,44].
- The sharp drop of G gets relief under all swapping strategies. This phenomenon is best reflected in Figure 5d, Figure 6d and Figure 7d. When gets close to , the G value of NONE is sharply decreased. The stark contrast is the G value under the HB strategy in the SF–SF system, which is smoother. This finding means that swapping inter-links in a CPS combined by SF networks is more sensitive in enhancing reliability than combining by ER networks. This conclusion is also found in the ‘one-to-one correspondence’ model [44].
- From all subfigures, we plot in Figure 5, Figure 6 and Figure 7. We conclude that the HB swapping strategy can be the first choice in improving G and HEC is the first choice in improving values. HB strategy shows the best performance in improving the value of G, and the HEC strategy is better in enhancing values. The values of in Figure 5a–d figures under the HEC strategy are 0.66, 0.69, 0.73 and 0.84, in Figure 6a–d are 0.68, 0.69, 0.75 and 0.85, and in Figure 7a–d are 0.68, 0.7, 0.78 and 0.82. This conclusion is more significant in the SF–SF CPS model. In Figure 5d, the value of under HEC is close to 0.8. The value of with HEC is more than 0.8 in Figure 6d. This finding is different from [39,44]. We reveal that network construction plays a vital role in system reliability.
6. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
References
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Approaches | Pros | Cons |
---|---|---|
Protecting critical network nodes | This method has strong pertinence | Finding the critical nodes is an NP-hard problem |
Making nodes autonomous | It can make the failure node recover its function and reduce manpower | Expensive; Hard to choosing important nodes |
Refiguring the topology of network | It can achieve the purpose of enhancing network reliability | It is not suitable for the existing network |
Adding intra-links in systems | Simple; More choices | Increase cost |
Adjusting dependency link allocation | The amount that needs to be exchanged is relatively small | The inter-link’s distance between nodes is longer than intra-link |
Symbol | Meaning |
---|---|
The fraction of attacked nodes at the first stage | |
, | The fraction of nodes in the giant component of network A, B in stage i |
, | The number of nodes remaining in network A, B in stage i |
The fraction of remaining in network nodes | |
The fraction of normal operation nodes in network | |
, | The generating functions of network A, B |
x, y | The final stage nodes’ number of network A, B |
Symbol | Values |
---|---|
15,000 | |
5000 | |
4 | |
3 | |
simulation times of each | 20 |
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Peng, H.; Liu, C.; Zhao, D.; Hu, Z.; Han, J. Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks. Sensors 2020, 20, 6123. https://doi.org/10.3390/s20216123
Peng H, Liu C, Zhao D, Hu Z, Han J. Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks. Sensors. 2020; 20(21):6123. https://doi.org/10.3390/s20216123
Chicago/Turabian StylePeng, Hao, Can Liu, Dandan Zhao, Zhaolong Hu, and Jianmin Han. 2020. "Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks" Sensors 20, no. 21: 6123. https://doi.org/10.3390/s20216123
APA StylePeng, H., Liu, C., Zhao, D., Hu, Z., & Han, J. (2020). Security Evaluation under Different Exchange Strategies Based on Heterogeneous CPS Model in Interdependent Sensor Networks. Sensors, 20(21), 6123. https://doi.org/10.3390/s20216123